From c9875dccd281e6fe7d9b28a38f6c385141df0950 Mon Sep 17 00:00:00 2001 From: thu-nmrc Date: Sun, 25 Oct 2026 07:12:56 +0800 Subject: [PATCH 1/6] Construct a phase-correct joint native odd-E8 cross-cube primitive --- .../EMBEDDING-PROOF.md | 175 + .../odd-e8-polarized-native/EMBEDDING.json | 10295 ++++++++++++++++ .../INDEPENDENT-REVIEW.json | 87 + research/odd-e8-polarized-native/MODULE.json | 91 + .../odd-e8-polarized-native/POLARIZATION.md | 54 + .../POLARIZED-CHANNELS.json.gz | Bin 0 -> 9748 bytes .../POLARIZED-CROSS-CUBE.json | 2085 ++++ .../odd-e8-polarized-native/PROGRAM.json.gz | Bin 0 -> 740380 bytes research/odd-e8-polarized-native/PROOF.md | 214 + research/odd-e8-polarized-native/README.md | 133 + research/odd-e8-polarized-native/RESULT.json | 5388 ++++++++ research/odd-e8-polarized-native/REVIEW.md | 200 + research/odd-e8-polarized-native/SOURCES.json | 47 + research/odd-e8-polarized-native/TASK.json | 78 + .../odd-e8-polarized-native/VALIDATION.json | 36 + research/odd-e8-polarized-native/VERIFY.json | 108 + .../odd-e8-polarized-native/anchor_audit.py | 75 + research/odd-e8-polarized-native/check.py | 166 + research/odd-e8-polarized-native/embed.py | 228 + .../odd-e8-polarized-native/frame_tools.py | 56 + .../independent_review.py | 300 + .../inputs/NORMALIZERS.json | 126 + .../inputs/POLARIZED-CHANNELS.json.gz | Bin 0 -> 9748 bytes .../inputs/clifford_exact.py | 149 + research/odd-e8-polarized-native/module.py | 169 + .../polarized_cross_cube.py | 234 + 26 files changed, 20494 insertions(+) create mode 100644 research/odd-e8-polarized-native/EMBEDDING-PROOF.md create mode 100644 research/odd-e8-polarized-native/EMBEDDING.json create mode 100644 research/odd-e8-polarized-native/INDEPENDENT-REVIEW.json create mode 100644 research/odd-e8-polarized-native/MODULE.json create mode 100644 research/odd-e8-polarized-native/POLARIZATION.md create mode 100644 research/odd-e8-polarized-native/POLARIZED-CHANNELS.json.gz create mode 100644 research/odd-e8-polarized-native/POLARIZED-CROSS-CUBE.json create mode 100644 research/odd-e8-polarized-native/PROGRAM.json.gz create mode 100644 research/odd-e8-polarized-native/PROOF.md create mode 100644 research/odd-e8-polarized-native/README.md create mode 100644 research/odd-e8-polarized-native/RESULT.json create mode 100644 research/odd-e8-polarized-native/REVIEW.md create mode 100644 research/odd-e8-polarized-native/SOURCES.json create mode 100644 research/odd-e8-polarized-native/TASK.json create mode 100644 research/odd-e8-polarized-native/VALIDATION.json create mode 100644 research/odd-e8-polarized-native/VERIFY.json create mode 100644 research/odd-e8-polarized-native/anchor_audit.py create mode 100644 research/odd-e8-polarized-native/check.py create mode 100644 research/odd-e8-polarized-native/embed.py create mode 100644 research/odd-e8-polarized-native/frame_tools.py create mode 100644 research/odd-e8-polarized-native/independent_review.py create mode 100644 research/odd-e8-polarized-native/inputs/NORMALIZERS.json create mode 100644 research/odd-e8-polarized-native/inputs/POLARIZED-CHANNELS.json.gz create mode 100644 research/odd-e8-polarized-native/inputs/clifford_exact.py create mode 100644 research/odd-e8-polarized-native/module.py create mode 100644 research/odd-e8-polarized-native/polarized_cross_cube.py diff --git a/research/odd-e8-polarized-native/EMBEDDING-PROOF.md b/research/odd-e8-polarized-native/EMBEDDING-PROOF.md new file mode 100644 index 0000000000..1da5cc1a52 --- /dev/null +++ b/research/odd-e8-polarized-native/EMBEDDING-PROOF.md @@ -0,0 +1,175 @@ +# Minimal standard-dot embedding of the two-cube restriction + +This is an exact finite geometry and scalar fitting result. It supplies no +Gaussian native word, phase compiler, dirty-return schedule or kappa claim. +The input is the literal E8 data underlying #5439, pinned in `embed.py`. + +## 1. The restriction and its bilinear space + +Use cube a with root support (0,1,2,3), cube b with root support +(0,1,4,5), and fix both remaining factors to cube a. There are +16*8*8=1024 distinct concatenated binary vectors in F2^27. The scalar +pairing is the ordinary binary dot product. Each vector has norm one. + +The verifier computes their actual span V and proves + + dim V=12, rank(B|V)=4, dim rad(V)=8. + +These are ranks of the literal 27-bit vectors and their exact Gram form, +not ranks of a floating numerical address evaluator. It lists a +nondegenerate four-space N and an eight-vector radical basis R, and checks +V=N perpendicular R. The restriction on N is nonalternating: V contains +odd vectors, whereas every radical vector is even. + +## 2. An explicit optimal I20 embedding + +Let r1,...,r8 be the listed radical basis. Add formal d1,...,d8 satisfying +B(ri,dj)=delta_ij and B(di,dj)=0, all perpendicular to N. The resulting +20-space is nondegenerate with form N perpendicular H^8, where H has +Gram [[0,1],[1,0]]. Its full 20-by-20 Gram matrix is in EMBEDDING.json. + +`orthonormal_basis` splits off norm-one vectors. If an alternating +hyperbolic part remains, it uses the explicit identity + + o,e,f -> o+e, o+f, o+e+f + +for a unit o perpendicular to a hyperbolic pair e,f. The three new vectors +have norm one, are pairwise perpendicular, and form the same three-space. +Since N is nonalternating, at least one unit is available. Repeating gives +the twenty listed vectors with Gram I20. Thus no 21st coordinate is required +by the characteristic-two norm functional. + +For a raw vector x in V, solve its coordinates in the listed basis (N,R), +append eight zero d-coordinates, and send it to + + phi(x) = ( B(x,o1), ..., B(x,o20) ). + +Because the oj are an orthonormal basis of the completion, phi is injective +and preserves B. The receipt contains all 1024 q20 values, all twelve raw +basis images, and the full coordinate/orthonormal basis information. The +checker additionally compares all 1024^2=1,048,576 ordered Gram entries, +checks distinctness and norm one, and checks image-span dimension twelve. + +This ambient dimension is minimal for any injective isometric embedding +into a nondegenerate symmetric space W. Indeed rad(V) is an eight-space +and V is contained in its orthogonal complement in W. Hence + + 12=dim V <= dim W - 8, + +so dim W>=20. This lower bound is about preserving all vector identities +and pairings, not merely realizing the orthogonality graph. + +## 3. The four common eight-space pairs survive unchanged + +The sixty-four polarized H_ab rectangles have four distinct pairs of +source/read spans. Each pair has sixteen channels, and each side uses +128 literal fields. The four source sets partition cube b's 512 fields; +the four reader sets partition cube a's 512 fields. + +All four pairs retain source/read dimensions eight, each self-pairing rank +two, and zero cross-pairing. Every listed original vector and every linear +combination has the same pairing after phi. Therefore these properties +are preserved by the explicit I20 embedding, rather than inferred from +matching field names or nominal rank labels. Each common frame basis and +its complete field set is in `orthogonal_eight_space_pairs`. + +For the physical H_ab-only module, the dimensions permit the proposed +geometric paths qline -> S8 -> full20 and ground -> S8 -> qperp19, with +Gaussian rank differences 7,12 and 8,11 respectively. The corresponding +25-dimensional paths have 7,17 and 8,16. This removes five spectator axes +from each path. It does not prove a native word or remove the actual +Gaussians, independent scratch inputs, phases, dirty cleanup, or global +caller obligations. A new canonical-frame implementation must use these +actual q20 values and preserve all absolute tensor-width phases. + +## 4. An exact scalar minimum fitting rank: 256 + +Choose an orthonormal basis of N. Quotienting V by rad(V) identifies its +pairing form with I4. The 1024 literal vectors give precisely the eight +odd vectors of F2^4, each repeated n=128 times. + +Write Ai for the unit vector ei and Bi for 1111+ei, i=1,...,4. Within +either A or B, different types are orthogonal. Across Ai and Bj they are +orthogonal exactly when i=j. Within a single type, all distinct vectors +pair to one, so a fitting matrix has identity n-by-n diagonal blocks. +Here fitting means diagonal entries one and an off-diagonal entry forced +zero whenever the two binary vectors have pairing one; allowed entries +are arbitrary complex numbers. + +Two distinct nonorthogonal types, for example quotient values 1 and 7, +give a forced identity principal submatrix of size 2n=256. This proves +rank(F)>=256 for every such complex fitting F. + +For the matching upper bound, order each of the four A-type buckets and +form 128 cliques by taking the kth element of each bucket; do the same +for the four B-type buckets. On each four-clique set F=J4, with all other +entries zero. Each clique consists of four mutually orthogonal norm-one +vectors, so its binary span is nondegenerate of dimension four. The full +matrix is a direct sum of 256 rank-one blocks, is fitting, and has rank256. +All 256 partitions are explicit in the receipt and checked against q20. + +## 5. Every minimum-rank fitting has F^2=4F + +The following argument proves more than the particular clique partition. +Let F be any complex fitting matrix of rank 2n, with the eight type blocks +of size n. Factor F=UV through a 2n-dimensional space. Write U_Ai for the +n rows of U at type Ai and V_Ai for the n columns of V there; define +U_Bi,V_Bi likewise. Since U_Ai V_Ai=I_n and U_Bi V_Bi=I_n, each U block +is surjective and each V block is injective. + +For fixed i and j different from i, the forbidden cross block gives +U_Ai V_Bj=0. Thus each n-dimensional image im(V_Bj), j!=i, equals the +n-dimensional kernel ker(U_Ai). For any j,k there is an i different from +both, so all four im(V_Bj) equal one common n-space W_B. Therefore every +U_Ai annihilates W_B, including im(V_Bi). The four allowed matching +cross blocks also vanish. Interchanging A and B proves the opposite +cross blocks vanish as well. + +Consequently F=diag(A,B). Both diagonal blocks have rank at least n +because their type diagonal blocks are I_n. Their ranks sum to 2n, so each +has rank exactly n. Factor A=PQ through an n-space, with four block rows +Pi and columns Qi. The equalities Pi Qi=I_n show that Pi and Qi are square +inverses, so also Qi Pi=I_n. Hence + + QP=sum_i Qi Pi=4 I_n, A^2=P(QP)Q=4A. + +The same argument gives B^2=4B. Thus F^2=4F for every minimum-rank fitting +matrix, without symmetry, positivity, rationality or a chosen partition. +In characteristic zero, F has eigenvalue four with multiplicity 2n and +zero otherwise. Therefore + + (I-F)^-1 = I+F/3, det(I-F)=(-3)^(2n)=(-3)^256. + +If F is dyadic, its inverse has diagonal entries 4/3 and is not dyadic. +This is a property of the minimum-rank code. It is not a physical +impossibility theorem: fixed odd rational scalars are allowed by the +retained implementation contracts when their actual work, grid and +precision are supplied. In particular the canonical coded-native +PHYSICAL.md explicitly implements a 1/52 inverse coefficient and requires +its finite precision bill. The centre-code-services package supplies +literal MULTIPLY_ODD/DIVIDE_ODD words and exact typed-grid obligations. + +## 6. Construction relevance and prior art + +The clique code K=I-J4 is a common-frame scalar code. Its exact inverse is +I-J4/3, not itself. The generic `block_word` in the pinned canonical +`check_clique_codes.py` already implements I-J_s and its inverse for an +arbitrary clique block of size s. Setting s=4 gives exactly this code: +three ADDs subtract the pivot from the other fields; the pivot is scaled +by -3 and subtracts those three fields; three ADDs add the pivot back. +The inverse uses the corresponding odd division by three. These are +ordinary scalar words on arbitrary inputs, using no extra fields. + +The existing centre-code-services README explicitly describes signed +clique responses, their rational inverses, full input-grid conditions, +and the open routed/typed/native caller obligations. Accordingly this +scalar four-clique code is not a new producer family and is not being +reimplemented or packaged as an innovation here. The new source-bound +constructive aid is the optimal I20 realization preserving the four +common polarized eight-space interfaces. The active physical construction +remains the H_ab module, whose phases, full inputs and bill must be proved. + +The finite checker corroborates this proof's literal geometry, embedding, +partition and independent-set lower bound. The arbitrary-complex +rank-factorization theorem in section 5 is a written proof; a census of +arbitrary fitting matrices is neither attempted nor claimed. diff --git a/research/odd-e8-polarized-native/EMBEDDING.json b/research/odd-e8-polarized-native/EMBEDDING.json new file mode 100644 index 0000000000..380f317808 --- /dev/null +++ b/research/odd-e8-polarized-native/EMBEDDING.json @@ -0,0 +1,10295 @@ +{ + "clique_fitting_matrix": { + "cliques": [ + [ + 76, + 338688, + 351232, + 12620 + ], + [ + 81, + 338695, + 351239, + 12625 + ], + [ + 87, + 338715, + 351259, + 12631 + ], + [ + 92, + 338745, + 351289, + 12636 + ], + [ + 860, + 339472, + 352016, + 13404 + ], + [ + 865, + 339479, + 352023, + 13409 + ], + [ + 871, + 339499, + 352043, + 13415 + ], + [ + 876, + 339529, + 352073, + 13420 + ], + [ + 3100, + 341712, + 354256, + 15644 + ], + [ + 3105, + 341719, + 354263, + 15649 + ], + [ + 3111, + 341739, + 354283, + 15655 + ], + [ + 3116, + 341769, + 354313, + 15660 + ], + [ + 6460, + 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"e5b2ea1f60d554b3a285569602360c663ee8b387350424678b3bd0b0b5432bf4", + "growth_scope": "At every literal module event, each physical row is its unitary chart times the logical row. If each original entrance norm is at most M, row norm is at most reported peak l1 times M. This does not by itself bound accumulated rounding errors or complete-caller precision.", + "independence": "Does not call module.py, frame_tools.py or check.py calculation; primitive pinned Pauli compiler reused. Fresh sparse Gaussian-integer column evaluator.", + "independent_mutation_controls": { + "S8_to_R8_requires_rank": 4, + "omitting_actual_uncompute_leaves_nonzero_owned_C0": true, + "same_tableau_phase_i_rejected_by_absolute_column": true + }, + "literal_program_events": 15116, + "module_py_sha256": "26a042a4817ef6862ade58b97bfad5a989d9d856ec94b7ff024c991a8da13d30", + "native_full_anchors": [ + { + "offset": 20455680, + "phase": 2 + }, + { + "offset": 20455680, + "phase": 2 + }, + { + "offset": 20455680, + "phase": 2 + }, + { + "offset": 20455680, + "phase": 2 + } + ], + "ordinary": { + "ADD": 13056, + "CLEAR_ZERO": 4, + "D": 5632, + "P": 5632, + "X": 2048, + "ZERO_RETAG": 8, + "phase": 2048 + }, + "orthogonal8space_pairs": 4, + "paid": { + "7": 512, + "8": 512, + "16": 512, + "17": 512 + }, + "polarized_channels": 64, + "proof_relevant_program_payload_sha256": "497ab37cf2b4c55883d860458bb58d946f685fd55d344fb2b29fcb727b6033b9", + "reader_exit_gauges_exact": 512, + "scope": "One-direction 25D H_ab local ABI only; source Phi_line entrances are supplied; coupled reader endpoints carry no autonomous Gaussian-job credit; no 20D-to25D free connection; no K-core or full caller/precision/compiler/kappa/upstream acceptance claim.", + "source_entry_gauges_exact": 512, + "source_pins": { + "NORMALIZERS.json": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da", + "POLARIZED-CHANNELS.json.gz": "7304d5d328d5c0b1610755706862f554f7b4c9cf39a09e6d58462e202b38badc", + "clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + }, + "status": "PASS_INDEPENDENT_LOCAL_HAB_TYPED_WORD_REVIEW", + "unique_group_reader_fields": 512, + "unique_group_source_fields": 512, + "universal_native_anchor_proof": "Written in REVIEW.md; exact signed tableau and analytic phase, not finite-width extrapolation.", + "zero_scratch_lifecycle": true +} diff --git a/research/odd-e8-polarized-native/MODULE.json b/research/odd-e8-polarized-native/MODULE.json new file mode 100644 index 0000000000..976a69418e --- /dev/null +++ b/research/odd-e8-polarized-native/MODULE.json @@ -0,0 +1,91 @@ +{ + "additional_408_helper_banks": 0, + "additional_helper_target_credit": {}, + "all_original_inputs_kept": 1024, + "axis_dimension": 25, + "channels": 64, + "channels_per_group": 16, + "coframe_groups": 4, + "compilation_coverage": { + "common_reader_entry_paths": 4, + "common_source_exit_paths": 4, + "low_rank_monomial_gauges_with_exact_absolute_phase": 1536, + "native_full_conjugates_with_proved_analytic_absolute_phase": 4, + "paid_path_applications": 2048, + "phase_complete_by_literal_composition": true, + "unique_reader_exit_paths": 512, + "unique_source_entry_paths": 512 + }, + "entry_contract": { + "owned_C0": "zero at ground chart; no independent original input or productive target is assigned", + "readers": "y_r arbitrary independent, physical ground chart", + "sources": "x_s arbitrary independent, physically canonical Phi_[q_s] x_s at its actual line chart" + }, + "environment_metadata": { + "program_container_bytes": 740380, + "program_container_sha256": "8d486c1db63735e520e0dc5787b5b632d0598f8aa5d43a4899a6de920e9f3d33" + }, + "exit_contract": { + "H_ab": "The exact sum of all64 polarized channel columns times rows from the pinned geometry; no current-value renaming.", + "owned_C0": "exact zero at original ground chart", + "readers": "explicit ordered-flag Phi_(q_r^perp)(y_r + sum_s H_ab[r,s] x_s), target frame literal word supplied separately for every reader", + "sources": "canonical R25 x_s, original x_s unchanged" + }, + "global_caller_emitted": false, + "independent_COPY_operations": 0, + "independent_helper_inputs": 0, + "limits": "Local H_ab side primitive only. No K-core shared chronology, reciprocal block schedule, full nonlinear caller, autonomous reader Gaussian targets, precision/storage allowance, whole-caller moment or kappa is claimed. Source input line services are provided inputs of this ABI and must be paid once by any complete caller. The eight-dimensional main prefixes and every endpoint path are explicitly charged; pairing rank zero is not used as a Gaussian-copy tariff.", + "mutation_controls": { + "cleanup": { + "actual_interpreter_replay_nonzero_owned_residual": true, + "mutant": "delete final source-uncompute ADD in emitted first channel" + }, + "frame": { + "Gaussian_transport_rank": 4, + "mutant": "replace common source S8 chart by the distinct reader R8 chart", + "ordinary_transport_rejected": true + }, + "phase": { + "absolute_column_differs": true, + "mutant": "append physical global phase i to a source H7 path", + "same_signed_tableau": true + } + }, + "new_kappa": false, + "ordinary_literal_gate_histogram": { + "ADD": 13056, + "CLEAR_ZERO": 4, + "D": 5632, + "P": 5632, + "X": 2048, + "ZERO_RETAG": 8, + "phase": 2048 + }, + "owned_zero_cells": 1, + "paid_profile": { + "16": 512, + "17": 512, + "7": 512, + "8": 512 + }, + "phase_contract": { + "all_positive_widths": "Each literal one-copy Clifford equality includes absolute phase and tensor-lifts columnwise; scalar ADD identities hold for every address width.", + "native_full_conjugation": "Exact signed tableau plus proved analytic zero-column phase; independently corroborated by root small-n dense tests.", + "other_monomial_gauges": "Exact low-rank sparse Gaussian-integer zero-column evaluation.", + "phase_opcode_lift": "A one-copy phase theta acts as scalar i^(f theta) at width f.", + "sparse_peak_support": 256 + }, + "program_payload_sha256": "497ab37cf2b4c55883d860458bb58d946f685fd55d344fb2b29fcb727b6033b9", + "proof_relevant_digest": "497ab37cf2b4c55883d860458bb58d946f685fd55d344fb2b29fcb727b6033b9", + "reader_fields": 512, + "reader_fields_per_group": 128, + "schema": "polarized-Hab-25D-physical-module/v1", + "source_fields": 512, + "source_fields_per_group": 128, + "source_pins": { + "NORMALIZERS.json": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da", + "POLARIZED-CHANNELS.json.gz": "7304d5d328d5c0b1610755706862f554f7b4c9cf39a09e6d58462e202b38badc", + "clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + }, + "status": "PASS_EXACT_TYPED_LOCAL_SIDE_MODULE_NOT_COMPLETE_CALLER" +} diff --git a/research/odd-e8-polarized-native/POLARIZATION.md b/research/odd-e8-polarized-native/POLARIZATION.md new file mode 100644 index 0000000000..ad43dcfb94 --- /dev/null +++ b/research/odd-e8-polarized-native/POLARIZATION.md @@ -0,0 +1,54 @@ +# Polarization of the literal cross-cube block + +Use the literal tetrads `a=(0,1,2,3)` and `b=(0,1,4,5)` in the pinned +normalizers, with the two other factors fixed to cube a. Write `C_ab` for +the root Gram cross block divided by four, and `K=I-B` on a fixed cube. +The #5439 polynomial gives exactly + +``` +H_ab = -C_ab tensor P, P=(I-K tensor K)/2. +``` + +The two tetrads share coordinates u=0 and v=1. For a root row m put +`w_+=(m_u+m_v)/2` and `w_-=(m_u-m_v)/2`. Each w has four nonzero entries +within either eight-root cube. The standard rank-two polarization is + +``` +C_ab = (w_+,a w_+,b^t + w_-,a w_-,b^t)/2. +``` + +For the 64 two-factor selector pairs put `T=K tensor K`. Choose J to be +the 32 selectors whose first selector has even relative-sign parity, and set + +``` +U_j=e_j-T e_j, V_j=(e_j^t-e_j^t T)/2, j in J. +``` + +`T^2=I`. It reverses that first parity, so the two diagonal half blocks of +T vanish. Multiplication in these two halves gives `UV=(I-T)/2=P`. +Therefore the 64 literal dyadic factors are + +``` +H_ab = -sum_(sign,j) (w_sign,a tensor U_j) + (w_sign,b^t tensor V_j)/2. +``` + +Each factor has 68 nonzero source ports and 68 nonzero reader ports. The +finite checker regenerates every coefficient, compares all 512-by-512 +entries against the original F3 polynomial, and checks every supported +binary cross-pairing. Each source and reader span has dimension eight, +each self-pairing rank is two, and the two spans are perpendicular. They +share a six-dimensional radical and have joint span ten of pairing rank four. + +The literal 64 pairs deduplicate into four pairs of spaces, with 16 factors +per pair. Their source sets partition the 512 source fields; their reader +sets partition the 512 reader fields. `module.py` independently regenerates +this deduplication from actual binary bases before emitting any ADD. +These are exact claims for the specified literal block, not a finite check +standing in for every cube pair or the whole odd-E8 side map. + +The previous unpolarized factorization used the two coordinate features +separately, with span nine and cross-pairing rank two. The new factorization +exposes truly orthogonal eight-space rectangles. Zero cross-pairing is an +orthogonality statement. 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b/research/odd-e8-polarized-native/PROOF.md new file mode 100644 index 0000000000..3fe5381ae9 --- /dev/null +++ b/research/odd-e8-polarized-native/PROOF.md @@ -0,0 +1,214 @@ +# A typed joint module for one polarized cross-cube block + +This proof supplies one directed `H_ab` side primitive. It is not all of H, +the reciprocal pair, a K-core schedule, a Gaussian-job caller, or a kappa +claim. The emitted module has 512 source fields and 512 reader fields, hence +1,024 independent original inputs. The reciprocal primitive would use 1,024 +source fields and 1,024 reader fields and has a separate invoice. + +The rank-one scalar identity and Clifford synthesis are standard algebra. +The contribution here is the source-bound polarized rectangle contract, +its four coframe groups, actual flag paths, exact phase compilation and +complete owned-cache lifecycle. Retain the #5439 geometry author and the +P112/E8, native-word, #4929, normalizer and Clifford predecessors credited in +the pinned sources. This work used substantial OpenAI Codex assistance. + +## 1. Literal port data and charts + +The pinned normalizer file gives the original 112 binary labels and the eight +root columns. The pinned polarized-channel file describes all 64 terms + +`H_ab = sum_(j=1)^64 a_j b_j^t` + +with exact dyadic coefficients. Its predecessor geometry checker verifies +this equality against every entry of the 512-by-512 block. This module does +not substitute the rank of a support pairing for a Gaussian-call invoice. + +Every channel has 68 source ports and 68 reader ports. The literal supports +fall into four pairs `(S_g,R_g)`, each with 16 channels. Each pair has 128 +distinct source fields and 128 distinct reader fields. Every field occurs in +exactly one pair. These facts, including membership and every coefficient, +are regenerated from the pinned channels in `module.py`. + +The raw three-block labels live in 27 coordinates but span the nondegenerate +25-space of equal block parities. `PROGRAM.json.gz` records an explicit +orthonormal basis of this space. Dotting a raw label against this basis gives +its 25 physical coordinates, preserving all pairings. For every group, + +`dim S_g=dim R_g=8`, `S_g perpendicular R_g`, + +and their radicals coincide in a six-space D_g. Their joint span has dimension +10 and radical D_g. Every source q belongs to S_g and has norm one. Every +reader q has norm one, is outside S_g, and satisfies `S_g subset q-perp`. + +For an ordered full binary basis G, use the pinned native monomial + +`K_G = D_Q P_G`, where `Q=I+G^-T G^-1` over F2, + +with the pinned Z4 diagonal convention (diagonal linear phases are 0 or 1). +Put `C_A=product_(j in A) C_j` and `R=C_all`. The actual canonical frame word +`K_G.adjoint().then(C_A).then(K_G)` represents + +`Phi_(G,A) = K_G C_A K_G^-1`. + +This order matters: `.then` appends a gate acting on the left. All executable +frames, monomial wrappers and paid children are supplied as literal words. +Reader `q-perp` endpoints use the explicit ordered basis starting with S_g, +completed within q-perp; no unrecorded replacement by another chart is made. + +## 2. Exact native full-Gaussian conjugation + +The main source exit uses the monomial `T_G=R K_G R^-1`. Here is its absolute +zero-column phase, valid for every dimension n. + +Write `G^-1 e_j=v_j`, and put + +`d_j=floor(wt(v_j)/2) mod2`. + +If q is the Z4 quadratic phase used in D_Q, expansion of binary Hamming +weight gives + +`q(y)+wt(G^-1 y)=wt(y)+2 d dot y mod4`. + +Indeed the polar cross terms cancel modulo four. The coefficient of y_j on +the left, after subtracting wt(y), is +`alpha_j+wt(v_j)-1`, where `alpha_j=(1+wt(v_j)) mod2` is 0 or 1. This equals +`2 floor(wt(v_j)/2) mod4`, proving the formula. + +Let `a=(1-i)/2`. For the pinned child convention `C=H diag(1,i) H`, + +`R^-1|0> = a^n sum_x i^wt(x)|x>`. + +Applying K_G and the preceding identity yields `Z_d R^-1|0>`. Consequently + +`T_G|0> = R Z_d R^-1|0> = (-i)^wt(d)|d>`. + +The exact signed tableau of T_G has Gaussian rank zero. Its tableau fixes +the remaining monomial address/quadratic data; the displayed column fixes +its global phase. `frame_tools.py` therefore emits a literal P/D/X/phase +word for T_G without a 2^25 state vector. The code checks the signed tableau, +including its predicted offset, against that word. The written calculation +is the universal phase proof. Root's independent small-dimension dense tests +are corroboration, not the universal argument. + +## 3. Paid paths, with literal chronology + +Fix a group and write `Phi_S=K C_[0,8) K^-1`. For a source with input line q, +choose a full basis beginning with q and then completing S. The rank-one and +rank-eight frames for this flag are connected to the declared input line +frame and the common Phi_S by monomial gauges. Every such low-rank gauge is +checked with an exact signed tableau and a fresh sparse Gaussian-integer +absolute-column evaluator. The paid part between them is exactly the seven +children on flag axes 1 through 7. Thus the source input line reaches S with +one H7, with no hidden Gaussian in either wrapper. + +For its exit, the exact identity is + +`R Phi_S^-1 = T_G C_[8,25) K^-1`. + +Execution is therefore **K^-1, then 17 children, then T_G**. This is the +correct chronological order and has an explicit analytic absolute phase. +It carries the source to the canonical full R25 frame. + +A reader starts at ground and reaches Phi_S by K^-1, eight children, K. +Choose its ordered q-perp basis to start with the eight S vectors, then add +16 vectors to span q-perp. A monomial, phase-correct gauge changes the common +S frame to this flag's S prefix. The subsequent paid part is precisely the +16 flag children on axes 8 through 23. Its endpoint is the recorded rank-24 +q-perp frame. Since reader q is orthogonal to S and not in S, this is an +actual containing flag; orthogonality alone is never used to declare an ADD +between distinct frames ordinary. + +For all 512 fields of each kind the emitted paths have histogram + +`paid = {7:512, 8:512, 16:512, 17:512}`. + +The source line services are the **entry contract**, not an erased bill. +A complete caller must supply and fund them once. No target credit is inferred +from a mixed reader endpoint, and the module does not fund its caller's final +termination. + +## 4. Actual common-frame gather and arbitrary old values + +At one group's cut all 128 source fields and all 128 reader fields are +physically in the identical Phi_S chart. Original source x_s and reader y_r +values are arbitrary and independent. This is a stronger condition than +merely saying that their possible flags contain related subspaces; the paid +paths above establish the actual chart. + +For a channel `(a,b)`, borrow owned C0 with logical value zero in that same +chart. Perform + +`C0 += sum_s b_s x_s`, + +`y_r += a_r C0` for each reader, + +`C0 -= sum_s b_s x_s`. + +All operations are ordinary scalar ADDs at the common chart. They have the +same action physically because Phi_S is linear. The source fields never +change logically; source and reader role sets are disjoint. Thus the last +sum uses exactly the same original source versions, and C0 is exactly zero. +The arbitrary old y_r is retained with coefficient one. No reader is assumed +zero and no original input is cleared. + +All 16 channels in the group are executed while those fields stay at Phi_S. +Only after the group's last gather do main fields leave the common chart. +There is one zero-retag into the group chart, one explicit CLEAR_ZERO after +the cache has already been uncomputed, and one zero-retag back to its original +ground chart. The same C0 is then available for the next group. Over four +groups the actual lifecycle is + +`13056 ADDs, 4 CLEAR_ZERO, 8 ZERO_RETAG, one owned zero cell`. + +No independent COPY and no 408-helper bank is used. A general borrowed dirty +cell at S can instead be restored by the four-stage subtraction/gather/read/ +ungather protocol checked by `check.py` (272 ADDs per channel). That alternative +does not make a fresh independent dirty input available at S for free; the +emitted full module uses owned zero C0 and claims no helper target for it. + +## 5. Full local endpoint and widths + +Let x denote the 512 original source values and y the 512 original reader +values. The exact scalar interpreter checks every original column and emits +the resulting rows. Its logical map is + +`(x,y,C0=0) -> (x, y+H_ab x, C0=0)`. + +The physical endpoint is + +`source_s: Phi_[q_s] x_s -> R25 x_s`, + +`reader_r: y_r -> Phi_(q_r-perp) (y_r+sum_s H_ab[r,s]x_s)`. + +This triangular logical map is invertible and retains every independent +original input. It is a side-map primitive, not 512 autonomous Gaussian jobs +on original y. The emitted endpoint rows, per-reader frame words, path +references and monomial definitions are factorized in `PROGRAM.json.gz`. + +All Clifford identities include absolute phase. Equality of signed tableaux +fixes a Clifford operator up to scalar; one exact absolute column fixes that +scalar. The low-rank gauges use literal Gaussian-integer column arithmetic; +the high-rank source exits use section 2 instead of a dense vector. Every +literal one-copy operator identity tensor-lifts to every positive field width +under the inherited columnwise semantics. In particular a one-copy phase +opcode theta lifts to scalar `i^(f theta)`, not silently to `i^theta`. Scalar +ADD identities hold at every width by linearity. No width-one matrix-sum +relation is extrapolated to a uniform-width identity. + +## 6. Verification and exact limits + +Normal and optimized `module.py` runs compare the scientific MODULE fields +and the **canonical decompressed** PROGRAM payload. Container gzip hashes are +environment metadata. Semantic controls use actual interpreters: an appended +phase i has the same signed tableau but a different absolute column; replacing +S by the different reader R chart requires a positive-rank Gaussian transport; +omitting an emitted uncompute ADD leaves C0 nonzero. These are rejected. + +The module changes the producer contract from separated full helper banks to +a joint main-field common-frame gather, so the scoped #5439 separated-lift +obstruction is not its invoice. This does not prove that the new contract is +compatible with the K-core, reciprocal side block or any whole caller. Global +flag chronology, all other H pieces, terminal jobs, precision, ordinary work +and outer admission remain separate obligations. No unsupported target +credit, all-H theorem, whole-caller profit or kappa is claimed. diff --git a/research/odd-e8-polarized-native/README.md b/research/odd-e8-polarized-native/README.md new file mode 100644 index 0000000000..714ee988f6 --- /dev/null +++ b/research/odd-e8-polarized-native/README.md @@ -0,0 +1,133 @@ +# A joint native odd-E8 cross-cube primitive + +This package constructs a concrete native primitive for one missing `H_ab` +block of Ali Romman's [#5439](https://github.com/CrocSwap/integer-mult-bounds/pull/5439), +pinned at `e6d50e7ebd0bb1fd4f388930df78df696e56b404`. Its 64 exact dyadic +channels share four actual orthogonal eight-space interfaces. The emitted +25-dimensional program retains all 512 source inputs and all 512 arbitrary +old reader inputs, includes every local Gaussian path and absolute phase, +and returns its one zero-owned scratch to zero at its original chart. + +**This is a constructive local component, with no new kappa.** It supplies +one directed cross-cube block. The whole odd-E8 side map, compatible K/H +chronology, complete caller and scientific admission remain open. The +selected conditional kappa at the publication base is `0.003027288235`. + +## The exact interface + +For literal source and reader labels, the entry and exit are + +``` +source s: Phi_[q_s] x_s -> R25 x_s +reader r: y_r -> Phi_(q_r^perp)(y_r + sum_s H_ab[r,s] x_s) +owned C0: zero@ground -> zero@ground +``` + +Every `x_s` and `y_r` is independent. The source line services are an entry +requirement to be paid by the eventual caller. Reader endpoints contain +the stated source contribution; they are not credited as independent +Gaussian jobs on the original `y_r`. + +The complete local paid profile is + +| Width | Jobs | Actual path | +| --- | ---: | --- | +| 7 | 512 | source line to common S8 | +| 17 | 512 | source S8 to canonical full R25 | +| 8 | 512 | reader ground to common S8 | +| 16 | 512 | reader S8 to its explicit q-perp flag | + +The program uses 13,056 ordinary ADDs, four CLEAR_ZERO checks, eight +zero-retags and one owned zero cell. Literal monomial wrappers and their +counts are included. It uses no independent COPY and no retained +408-helper bank. All main Gaussian paths above are still charged. + +[PROOF.md](PROOF.md) proves the chronological factorization, native full +conjugation phase and all-positive-width tensor identity. The source exit +is compiled without a dense `2^25` state vector. [MODULE.json](MODULE.json) +states the contract; [PROGRAM.json.gz](PROGRAM.json.gz) contains every path, +monomial, group, field role, coefficient and chronological event. + +## Geometry and independent evidence + +The new polarization reduces 64 source/read rectangles from span nine +and pairing rank two to span eight and cross-pairing zero. There are four +distinct coframe pairs, each serving 128 sources and 128 readers through +16 channels. [POLARIZATION.md](POLARIZATION.md) derives the factorization; +the geometry checker compares all 262,144 scalar entries and all 295,936 +literal rectangle pairings. + +A separately written reviewer checks the emitted word without calling its +generator. It replays all 1,024 original columns, same-frame ADDs and owned +returns, and independently checks 512 source gauges, 512 reader gauges and +four native full anchors. It also rejects a global-phase mutation, a wrong +physical frame and a missing uncompute. This is a separate AI-worker audit, +not independent human or formal-kernel acceptance. + +The exact intermediate coefficient l1 peaks are 1 for sources, 5 for C0 +and 53/8 for readers. Since all intervening Clifford maps are unitary, the +same constants bound field l2 growth relative to the largest original +field norm. This does not replace the eventual caller's precision bill. +See [REVIEW.md](REVIEW.md) and its JSON receipt. + +The restricted 1,024-label geometry also has an explicit minimal standard-dot +embedding in dimension 20. [EMBEDDING-PROOF.md](EMBEDDING-PROOF.md) proves +minimality and the exact scalar minimum fitting rank 256; all `1,024^2` +ordered Gram pairs are checked. The emitted native program remains in +dimension 25. No free connection from a local full20 chart to global full25 +is assumed. The four-clique scalar code in that proof has an existing generic +implementation and is not claimed as a new native construction. + +## Reproduce + +Python 3.12 and the standard library suffice: + +```sh +python3.12 -B scripts/research_package.py --package research/odd-e8-polarized-native +python3.12 -B scripts/check_research_commit.py --package research/odd-e8-polarized-native +``` + +`VERIFY.json` registers eight bounded commands: normal and optimized geometry, +native-module and independent replay, followed by the embedding and a fresh +275-case small-dimension dense phase audit. Direct verifiers are read-only; +`--write` is reserved for explicit artifact authoring. Proof artifacts are +compared by canonical decompressed content. Retained container SHA256 values +authenticate source bytes or record environment metadata. + +## Open next questions + +The boundary of this small component is now constructive. Its paid paths, +coefficients, source/reader versions, zero-owned lifetime and phase conventions +are proved. Full-H acquisition, shared K/H flags, decoder COPY schedule, +caller termination, complete precision/storage work and the outer invoice +remain unknown. Unknown costs receive no zero-cost assumption. + +The next decisive test is an actual K-plus-cross-block program that shares +these physical paths and fits the complete budget. Static containment is +insufficient: ADD needs the same current physical chart. The #5439 planning +gate leaves about 0.0902501847 per port per local invocation for **all** missing +work under its stated full-source COPY model. This package does not assert +that the global construction fits that allowance. Repeating this primitive +independently over every cube edge is not an admitted schedule. + +The other question is whether the explicit I20 realization supports a smaller +complete supplier. Its first test must include actual entry/exit maps and +charge any return to the global 25-dimensional service. `TASK.json` records +these questions, their first steps and present blockers. Further construction +should require a compatible complete invoice, rather than optimize more local +modules while leaving the same boundary unknown. + +## Sources and credit + +Publication base: canonical main `32890bc5de034ab8fc93ac88ead7279a6a416d04`. +Credit Ali Romman for the odd-E8 direct-sum family and missing-H formulation +in #5439; Dugongue / #4929 and Dillon Amburgey's coded-native normalizers; +Cao Yifan for the retained P112 native construction; and Cinna Davis, zxv, +Jacob Alan Sussman and the native, Clifford, compiler and analytic lineage +credited in those sources. Exact runtime source pins and vendored byte +provenance are in `SOURCES.json`. Standard polarization, rank factorization +and Clifford algebra are not claimed as new general identities. + +Prepared for THU New Media Research Center (@thu-nmrc) with substantial +OpenAI Codex assistance. Apache-2.0. No selected record, shared implementation +or predecessor evidence is changed. diff --git a/research/odd-e8-polarized-native/RESULT.json b/research/odd-e8-polarized-native/RESULT.json new file mode 100644 index 0000000000..b29cf04826 --- /dev/null +++ b/research/odd-e8-polarized-native/RESULT.json @@ -0,0 +1,5388 @@ +{ + "actual_flag_rank_census": { + "S8_to_reader_line_plus_S8": { + "1": 68 + }, + "scope": "All signed tableaux tested; common H2 transition has explicit exact phase compilation. 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+ "clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + }, + "status": "PASS_CONDITIONAL_COFRAMED_LOCAL_ABI_NOT_GLOBAL_CALLER", + "subspaces": { + "common_radical_basis_25": [ + 30028800, + 1966080, + 3014655, + 7680, + 11775, + 30 + ], + "cross_pairing_rank": 0, + "joint_dimension": 10, + "reader_basis_25": [ + 657958, + 29376038, + 1966080, + 3014655, + 7680, + 11775, + 30, + 459 + ], + "reader_dimension": 8, + "shared_radical_dimension": 6, + "source_basis_25": [ + 657990, + 29376070, + 1966080, + 3014655, + 7680, + 11775, + 30, + 435 + ], + "source_dimension": 8 + } +} diff --git a/research/odd-e8-polarized-native/REVIEW.md b/research/odd-e8-polarized-native/REVIEW.md new file mode 100644 index 0000000000..d8402109fe --- /dev/null +++ b/research/odd-e8-polarized-native/REVIEW.md @@ -0,0 +1,200 @@ +# Independent review of the polarized H_ab local native interface + +The emitted **one-direction 25D local side module passes** this review. +This is an interface result, not a complete productive Gaussian caller, +new kappa, leaderboard improvement, or upstream scientific acceptance. +The independent checker does not call the author's `module.py`, +`frame_tools.py`, or `check.py` calculation. It reuses the pinned primitive +Pauli compiler, and implements a fresh exact sparse amplitude evaluator, +literal-program interpreter, subspace checks, phase checks and accounting. + +## Literal geometric partition + +The 64 pinned rational channels have exactly four distinct pairs (S,R) +of binary eight-dimensional source/read spans. Each pair has sixteen +channels and 128 literal source fields and 128 literal reader fields. +The four source sets partition all 512 source ports, and the four read +sets partition all 512 reader ports. For every port all incident channels +have exactly the same pair. All pairings S by R vanish. The two 512-field +sets are disjoint. No field identification or loss of independent input +is used. + +The explicit 25-vector raw-27 orthonormal basis has Gram I25; every actual +port is recovered from its 25 coordinates and has norm one. This binds +the physical coordinates to the original labels rather than to an +abstract orthogonality graph. The rank-one coefficients are pinned to +the separately verified exact H_ab = -C_ab tensor (I-K tensor K)/2 +factorization, including the polarization's factor 1/2. + +## Universal native-conjugation phase proof + +Here products are written in operator order: the rightmost factor acts +first. Let R be the product of the one-axis Gaussian gates + + C = ((1+i) I + (1-i) X)/2. + +For an invertible binary G, put A=G^{-1}, let a_j be its jth column, +Q=I+A^T A, and K_G=D_Q P_G. The diagonal convention is precisely that of +the pinned compiler: linear coefficient alpha_j=Q_jj in {0,1}, and +quadratic coefficient 2 Q_jk for j=a^n sum_x i^{wt(x)}|x>. After the literal permutation and +diagonal this identity gives + + K_G R^{-1}|0> = Z_d R^{-1}|0>. + +No unspecified scalar is introduced. On one axis R Z R^{-1}=-Y=-i XZ, +so the full conjugation has the exact zero column + + (R K_G R^{-1})|0> = (-i)^{wt(d)} |d>. + +The conjugation is monomial universally: ignoring only Pauli phases, +R^{-1} sends the Z Lagrangian to {(z,z)}; K_G sends (z,z) to (Gz,Gz) +because QG=G+A^T; R sends this to {(0,Gz)}. Thus it sends every Z Pauli +to a signed Z Pauli. The exact signed tableau and this one absolutely +normalized column determine the complete monomial operator. For the +four actual G matrices, the independent checker verifies the emitted +signed tableaux and the zero columns of their compiled monomial words. +All four have offset 20455680 and phase exponent 2 modulo four. + +## Actual factor chronology and phases + +Write F_r^G=K_G R_[0,r) K_G^{-1}. The common physical S8 frame is +Phi=F_8^G. The source entrance L is its actual canonical line frame. +Choose a flag beginning with q and spanning S8, and write its native +matrix as K_s. The source-entry emitted word has operator + + B K_s R_[1,8) K_s^{-1} A, + A=F_1^{G_s} L^{-1}, B=Phi (F_8^{G_s})^{-1}. + +The intervening native frames cancel literally, leaving Phi L^{-1}. +All 512 A and B factors are independently checked monomial operators +with both exact signed tableaux and fresh sparse absolute-column phases. +Every paid child has exactly seven axes. + +The source exit is + + (R K_G R^{-1}) R_[8,25) K_G^{-1} = R Phi^{-1}. + +The equality follows from R_[8,25)=R R_[0,8)^{-1}; the native full +conjugation's absolute phase is proved above. It is charged as H17. + +Reader entrance is the defining word Phi, charged H8. Each reader +endpoint flag V begins with the identical ordered S8 basis, spans its +actual q-perp hyperplane, and has dimension 24. With native K_v, the +reader exit is + + K_v R_[8,24) K_v^{-1} A, + A=F_8^{G_v} Phi^{-1}, + +which is F_24^{G_v} Phi^{-1}. All 512 A factors are independently +checked with exact signed tableaux and absolute phases, and every child +has sixteen axes. The actual endpoint frame word is supplied per reader. + +These are exact one-copy Clifford identities including absolute phases. +They therefore tensor-lift columnwise for every positive address width. +In particular an emitted one-copy phase -1 remains its actual tensor +phase (-1)^f; it has not been discarded from a projective tableau. + +## Same-frame row interpretation and owned lifecycle + +The independent interpreter processes all 15,116 literal events and +checks the old chart of every transition and the common chart of every +ADD. The owned C0 has zero logical row at every zero-retag and every +CLEAR_ZERO; the latter four clears remove no remaining source data. +For each channel the source gather is undone after the readout. + +At the end all 512 independent source logical rows are unchanged and +their physical chart is the standard full R25. Each of the 512 reader +rows is exactly its own independent y plus the pinned H_ab source row, +with its explicit q-perp endpoint frame. C0 returns to exact zero at +ground. All 1,024 original input columns are retained in these checks. + +The independently recomputed complete paid profile is + + 512 H7 + 512 H8 + 512 H16 + 512 H17. + +The ordinary literal count is 13,056 ADD, 5,632 D, 5,632 P, +2,048 X, 2,048 phase, eight zero-retags and four already-zero clears. +There is one owned zero scratch cell, no independent helper input, +no helper target credit and no independent Gaussian COPY service. + +## Exact finite-module growth constants + +At every literal event, measure the exact rational logical row against +the original independent entrance fields. The maxima are: + +| Role | Maximum row coefficient l1 | Maximum dyadic denominator exponent | +| --- | ---: | ---: | +| Source | 1 | 0 | +| Owned C0 | 5 | 4 | +| Reader | 53/8 | 6 | + +The reader's intermediate maximum is 53/8, not the final-row bound six. +It first occurs at zero-based event 3182 in the pinned word. The cache's +maximum five first occurs at event 324. Every physical chart and all +monomial/Gaussian substeps are unitary. Hence if each independent +entrance field has l2 norm at most M, every source, C0 and reader field +has norm at most M, 5M and (53/8)M respectively at all module events and +unitary substeps. These finite constants do not by themselves supply +the accumulated rounding-error or precision bill of a complete caller. + +## Boundaries of the result + +The source canonical line services are **supplied entrances** and must +be paid and connected by a complete caller. The coupled reader endpoint +is not an autonomous Gaussian job on independent y. No reader target +credit may be inferred until its H_ab source contribution is removed +within the actual caller. + +The 20D embedding is a separate correct finite-geometry aid. Its radical +has dimension eight and its literal span has dimension twelve, giving +the rigorous minimal nondegenerate ambient lower bound 12+8=20. Its +written rank256 fitting classification and F^2=4F argument are sound. +These facts do not connect local full20 to global full25 at zero cost. + +The controller's reciprocal H-only word proves logical common-chart +chronology for 2,048 original inputs in either dimension. It explicitly +has not compiled its own standard-child phases. The one-direction +literal phase compilation reviewed here does not silently fill that +separate gap for every controller frame or both dimensions. + +No compatible K-core chronology, full-global-H schedule, full fitting +decoder, productive whole-caller invoice, finite precision/compiler +admission, kappa improvement or upstream acceptance is proved here. +Even granting the two source/target jobs in an isolated H-only module +as independent would leave the usual concavity penalty from splitting +each into smaller Gaussian children; this local word alone is not a +standalone winning producer. + +## Final read-only review receipt + +The final scientific PROGRAM payload digest is +`497ab37cf2b4c55883d860458bb58d946f685fd55d344fb2b29fcb727b6033b9`. +The reviewed `module.py` digest is +`26a042a4817ef6862ade58b97bfad5a989d9d856ec94b7ff024c991a8da13d30`. +Python 3.12 normal and optimized read-only runs of `review.py` both pass, +with byte-identical stdout. Three additional independent literal mutation +controls reject an invisible-tableau phase i, a wrong S8/R8 coframe +(transport rank four), and an omitted final source-uncompute ADD. + +`review.py --package PATH` reads a module package without modifying it. +Its default package is the script's own directory and its default receipt +is `INDEPENDENT-REVIEW.json` within that package. `--receipt PATH` can +select a separate existing receipt. Only explicit `--write` authors a +receipt. The scientific comparison excludes gzip environment metadata. +There are no absolute runtime filesystem dependencies. diff --git a/research/odd-e8-polarized-native/SOURCES.json b/research/odd-e8-polarized-native/SOURCES.json new file mode 100644 index 0000000000..0d96420784 --- /dev/null +++ b/research/odd-e8-polarized-native/SOURCES.json @@ -0,0 +1,47 @@ +{ + "schema_version": 1, + "base_commit": "32890bc5de034ab8fc93ac88ead7279a6a416d04", + "files": [ + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602", + "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72" + }, + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "fc3d4ba105e1f097d0d7d051a308281e86ab1446", + "sha256": "66974efdced4083c00025f97d95d83909a226cdf801edb9301c195c6641f6903" + }, + { + "path": "research/coded-native-caller/NORMALIZERS.json", + "usage": "provenance", + "git_blob": "bca92c222c395d3d75c047fbb678f3cd0947c60f", + "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da" + }, + { + "path": "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py", + "usage": "provenance", + "git_blob": "166841a037f069249f6f7f6dedb89248812f59e2", + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + } + ], + "vendored_runtime_inputs": { + "inputs/NORMALIZERS.json": { + "origin": "research/coded-native-caller/NORMALIZERS.json", + "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da" + }, + "inputs/clifford_exact.py": { + "origin": "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py", + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + } + }, + "mathematical_predecessor": { + "pr": 5439, + "head": "e6d50e7ebd0bb1fd4f388930df78df696e56b404", + "author": "Ali Romman (@aliromman)", + "usage": "Definition of the odd-E8 direct sum, product-cube K and omitted H. No unmerged Git object or network read is required by any replay." + }, + "frozen_input_policy": "Runtime vendor bytes are checked by their exact source SHA256; all generated proof artifacts compare decompressed canonical content." +} diff --git a/research/odd-e8-polarized-native/TASK.json b/research/odd-e8-polarized-native/TASK.json new file mode 100644 index 0000000000..ab9c763a6e --- /dev/null +++ b/research/odd-e8-polarized-native/TASK.json @@ -0,0 +1,78 @@ +{ + "schema_version": 1, + "task_id": "complex-rank-shape-decoder", + "priority_revision": 7, + "base_commit": "32890bc5de034ab8fc93ac88ead7279a6a416d04", + "original_card": { + "id": "complex-rank-shape-decoder", + "question": "Can a decoder deliver the local paid mass in fewer, larger-rank children (block frame climbs instead of rank-1 to rank-3 steps)?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/complex-decoder-field-extension-seed44/README.md", + "research/complex-frame-pair-decoders/README.md", + "research/selected-k8-unrestricted-ends/README.md", + "research/eisenstein-reduction-copy-floor/README.md" + ], + "methods": [ + "Find one exact small decoding identity whose frame path climbs in blocks, and price its complete per-call profile.", + "Bound the best effective child rank achievable for one fixed support alphabet, including copies, frames and restoration." + ], + "acceptance_gate": "A per-call local profile, with all copied information, frames and restoration counted, whose ceiling exceeds the selected word's by at least 5%; masked or overcomplete supports must change an assumption of the eight-term all-pairs bound. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin. Ideal budget: rank-16 delivery is 2.31x (levers.py).", + "bottleneck_link": "Rank-1 children are about half of recursive cost; the selected word's effective child rank is about 3.9. Larger-rank delivery lowers recursive cost per unit of paid mass.", + "allowed_variations": [ + "One masked, overcomplete or block decoder family with exact labels and supports.", + "A scoped lower bound on effective rank for one alphabet.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Repacking idle remainders of an unchanged word (covered by the packing ceiling).", + "Repeating the eight-term all-pairs search inside its proved scope.", + "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.", + "Searching below C=40 in the #2017 Eisenstein binary scalar-rectangle or fixed-support block-linear additive pairing model; specify a changed premise instead. This bound does not cover every complex decoder.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "overlap_terms": [ + "rank shape", + "block climb", + "masked decoder", + "overcomplete", + "effective rank" + ] + }, + "scope_status": "changed", + "actual_scope": "Construct and independently replay a concrete joint native H_ab primitive for the odd-E8 direct-sum geometry: 512 independent source inputs, 512 independent old target inputs, explicit 25-axis Clifford paths, absolute phases, owned zero return, and a complete local paid profile. Also provide the minimal I20 embedding of its two-cube geometry.", + "scope_change_reason": "Frozen full-frame history and fixed-bank lifts do not supply an affordable new producer. The polarized decomposition changes the native graph and helper interface:64 channels share four literal orthogonal8-space pairs, permitting coframed reads with one zero-owned scratch and no retained408-helper banks. This is a local constructive result and does not meet the card whole-supplier ceiling target.", + "bottleneck_link": "The unsupplied H in #5439 needs genuine native production and compatible main flags. This package closes one explicit cross-cube block, including all local paths, without treating pairing rank or static containment as free information.", + "budget_minutes": 60, + "stop_rule": "Freeze the exact local program and independent audit. Do not expand direct per-edge implementations into a global supplier without a compatible K/H schedule and a fully favorable complete invoice.", + "outcome": "partial", + "evidence": "POLARIZED-CROSS-CUBE.json; MODULE.json; PROGRAM.json.gz; INDEPENDENT-REVIEW.json; EMBEDDING.json; written proofs.", + "author": "THU New Media Research Center (@thu-nmrc)", + "ai_assistance": "Substantial OpenAI Codex assistance by a lead and separate geometry, physical-compiler and independent-review agents. This is not independent human or formal-kernel review.", + "open_questions": [ + { + "question": "Can the polarized cross-cube modules share actual source and target flags with K and with every other H block?", + "why_it_matters": "The whole odd-E8 supplier needs all of H, while a field can only undergo a chronological sequence of actual physical charts. Containment alone does not make ADD legal.", + "first_step": "Exhibit one K-plus-cross-block word with every original input, exact same-frame reads, and all exits; compare its complete invoice with the 0.0902501847 per-port per-local planning allowance of #5439.", + "blocked_by": "No complete compatible K/H word or full-H schedule is known here." + }, + { + "question": "Can the 20-dimensional isometry be consumed by a smaller complete supplier?", + "why_it_matters": "It preserves this restricted Gram geometry but returning to the global 25-dimensional service has a real extra cost.", + "first_step": "Use the explicit q20 data to give both physical entry and exit maps and pay the five missing global axes if any.", + "blocked_by": "The implemented native module is 25-dimensional; the 20-dimensional result is a geometry theorem only." + } + ] +} diff --git a/research/odd-e8-polarized-native/VALIDATION.json b/research/odd-e8-polarized-native/VALIDATION.json new file mode 100644 index 0000000000..cf3df42f07 --- /dev/null +++ b/research/odd-e8-polarized-native/VALIDATION.json @@ -0,0 +1,36 @@ +{ + "schema": "odd-e8-polarized-native-validation-v1", + "environment": { + "python": "3.12.13", + "system": "macOS arm64", + "dependencies": "standard library only" + }, + "registered_replay": { + "command": "python3.12 -B scripts/research_package.py --package research/odd-e8-polarized-native", + "commands_passed": 8, + "exit_code": 0, + "marker": "PASS_REGISTERED_RESEARCH_PACKAGE research/odd-e8-polarized-native outcome=partial" + }, + "independent_review": "Separate AI-worker code, same retained primitive Clifford compiler; not independent human review", + "program_scientific_digest": "497ab37cf2b4c55883d860458bb58d946f685fd55d344fb2b29fcb727b6033b9", + "exact_controls": [ + "phase i with unchanged signed tableau", + "wrong source/read physical chart", + "omitted actual uncompute" + ], + "publication_adaptations": [ + "Geometry replay compares generated channel payload, with JSON tuple/list canonicalization, separately from retained source-container SHA.", + "Embedding reads package-local retained geometry data.", + "Independent review and dense anchor audit use package-relative paths." + ], + "not_run": [ + "Whole odd-E8 H/K native caller", + "20D native path compilation", + "Selected supplier/ordinary/outer cold replay", + "Whole-caller precision/storage admission", + "Formal proof kernel", + "Independent human review", + "Hosted CI (before publication)" + ], + "outcome": "Exact local native component; no new kappa and no upstream scientific acceptance claim." +} diff --git a/research/odd-e8-polarized-native/VERIFY.json b/research/odd-e8-polarized-native/VERIFY.json new file mode 100644 index 0000000000..46460b2eaa --- /dev/null +++ b/research/odd-e8-polarized-native/VERIFY.json @@ -0,0 +1,108 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/polarized_cross_cube.py" + ], + "timeout_seconds": 120, + "checks": "Exact 262144 scalar block entries,295936 literal orthogonality pairings,64 exact dyadic factors and their actual spans." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-W", + "error", + "-B", + "{package}/polarized_cross_cube.py" + ], + "timeout_seconds": 120, + "checks": "Exact 262144 scalar block entries,295936 literal orthogonality pairings,64 exact dyadic factors and their actual spans." + }, + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/module.py" + ], + "timeout_seconds": 120, + "checks": "Complete emitted25D native H_ab paths, absolute phases, all1024 independent columns, owned scratch restoration, actual paid/ordinary profile and semantic mutations." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-W", + "error", + "-B", + "{package}/module.py" + ], + "timeout_seconds": 120, + "checks": "Complete emitted25D native H_ab paths, absolute phases, all1024 independent columns, owned scratch restoration, actual paid/ordinary profile and semantic mutations." + }, + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/independent_review.py" + ], + "timeout_seconds": 120, + "checks": "Independent emitted-word interpreter, exact source/reader gauges and full anchor proof; all-original endpoint, same-frame reads and intermediate coefficient growth." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-W", + "error", + "-B", + "{package}/independent_review.py" + ], + "timeout_seconds": 120, + "checks": "Independent emitted-word interpreter, exact source/reader gauges and full anchor proof; all-original endpoint, same-frame reads and intermediate coefficient growth." + }, + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/embed.py" + ], + "timeout_seconds": 120, + "checks": "Injective minimal I20 embedding, all1048576 ordered Gram comparisons, common8-space interfaces, and explicit256-clique minimum-rank witness." + }, + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/anchor_audit.py" + ], + "timeout_seconds": 120, + "checks": "Independent unpatched dense Clifford verification of275 native K anchors in dimensions1..8 and all phase-polynomial points in each case; written proof supplies arbitrary dimension." + } + ] +} diff --git a/research/odd-e8-polarized-native/anchor_audit.py b/research/odd-e8-polarized-native/anchor_audit.py new file mode 100644 index 0000000000..ab054f075f --- /dev/null +++ b/research/odd-e8-polarized-native/anchor_audit.py @@ -0,0 +1,75 @@ +"""Independent small-dimension absolute-phase checks for a native K conjugate. + +No large-dimensional state-vector check or supplier theorem is claimed. +""" +from pathlib import Path +from hashlib import sha256 +from itertools import product +import importlib.util +import json +import random +import sys + +PIN = '2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962' +SOURCE = Path(__file__).resolve().parent/'inputs/clifford_exact.py' + +def require(ok, reason): + if not ok: + raise ValueError(reason) + +require(sha256(SOURCE.read_bytes()).hexdigest() == PIN, 'exact Clifford source') +spec = importlib.util.spec_from_file_location('independent_dense_ce', SOURCE) +C = importlib.util.module_from_spec(spec) +sys.modules[spec.name] = C +spec.loader.exec_module(C) + +def case(G): + n = len(G) + gi = C.inv(G, n) + columns = C.transpose(gi, n) + Q = tuple((1 << i) ^ sum(((x & y).bit_count() & 1) << j + for j, y in enumerate(columns)) for i, x in enumerate(columns)) + K = C.perm(n, G).then(C.diag(n, Q)) + R = C.fourier(n) + T = R.adjoint().then(K).then(R) + require(all(x == 0 for x, z, p in T.tab[n:]), 'conjugate must be monomial') + d = sum(((x.bit_count() // 2) & 1) << j for j, x in enumerate(columns)) + vec, den = T.zero_state() + require(den == 0, 'integer anchor denominator') + expected = [(0, 0)] * (1 << n) + expected[d] = C.mul_i((1, 0), -d.bit_count()) + require(vec == expected, 'analytic native K anchor differs from independent dense column') + # The functional phase equation is also checked independently, for every y. + for y in range(1 << n): + lhs = (C.mv(gi, y).bit_count() + C.qvalue(Q, tuple((Q[i] >> i) & 1 for i in range(n)), y, n)) % 4 + rhs = (y.bit_count() + 2 * ((d & y).bit_count() & 1)) % 4 + require(lhs == rhs, 'native K quadratic identity') + return sha256(json.dumps([G, d, vec[d]], separators=(',', ':')).encode()).hexdigest() + +out = [] +by_n = {} +for n in range(1, 4): + count = 0 + for G in product(range(1 << n), repeat=n): + if C.rank(G) == n: + out.append(case(G)) + count += 1 + by_n[n] = {'all_GL_matrices': count} + +rng = random.Random(20261025) +for n in range(4, 9): + count = 0 + while count < 20: + G = tuple(rng.randrange(1 << n) for _ in range(n)) + if C.rank(G) == n: + out.append(case(G)) + count += 1 + by_n[n] = {'seeded_random_GL_matrices': count} + +result = {'status': 'PASS', 'exact_clifford_sha256': PIN, + 'coverage': by_n, 'case_count': len(out), + 'case_digest': sha256(''.join(out).encode()).hexdigest(), + 'anchor': 'T|0> = (-i)^wt(d)|d>, d_j=floor(wt(G^-1 e_j)/2) mod 2', + 'T': 'R K R^-1 with K=D_(I+G^-T G^-1) P_G and R=product C_ej', + 'large_dimension_dense_check': False} +print(json.dumps(result, sort_keys=True)) diff --git a/research/odd-e8-polarized-native/check.py b/research/odd-e8-polarized-native/check.py new file mode 100644 index 0000000000..5bc140710e --- /dev/null +++ b/research/odd-e8-polarized-native/check.py @@ -0,0 +1,166 @@ +#!/usr/bin/env python3 +"""One polarized rectangle: exact common-frame ABI, not a global producer.""" +from pathlib import Path +from hashlib import sha256 +from fractions import Fraction as F +from collections import Counter +import argparse,gzip,importlib.util,json,signal,sys +HERE=Path(__file__).resolve().parent +sys.dont_write_bytecode=True +PINS={'NORMALIZERS.json':'ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da', + 'POLARIZED-CHANNELS.json.gz':'7304d5d328d5c0b1610755706862f554f7b4c9cf39a09e6d58462e202b38badc', + 'clifford_exact.py':'2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962'} +def need(ok,msg): + if not ok:raise ValueError(msg) +def dot(a,b):return(a&b).bit_count()&1 +def basis(rows): + p={} + for x in rows: + while x: + j=x.bit_length()-1 + if j in p:x^=p[j] + else:p[j]=x;break + return list(p.values()) +def span_contains(B,x):return len(basis(B+[x]))==len(B) +def radical(B): + values=[] + for mask in range(1<>i&1:x^=b + if all(not dot(x,b)for b in B):values.append(x) + return basis(values) +def ortho_basis(B): + out=[];current=basis(B) + while current: + odd=[x for x in current if dot(x,x)] + need(odd,'standard nonalternating residual') + candidates=odd+[odd[0]^x for x in current if not dot(x,x)] + for v in candidates: + if not v or not dot(v,v):continue + nxt=basis([x^(v if dot(v,x)else 0)for x in current]) + if len(nxt)!=len(current)-1:continue + if nxt and not any(dot(x,x)for x in nxt):continue + break + else:raise ValueError('orthonormal basis candidate') + out.append(v);current=nxt + need(all(dot(a,b)==int(i==j)for i,a in enumerate(out)for j,b in enumerate(out)),'actual orthonormal isometry') + return out +def add(dst,src,q): + for k,v in src.items(): + x=dst.get(k,F(0))+q*v + if x:dst[k]=x + else:dst.pop(k,None) + +def calculate(): + for name,digest in PINS.items():need(sha256((HERE/'inputs'/name).read_bytes()).hexdigest()==digest,'pin '+name) + data=json.loads((HERE/'inputs/NORMALIZERS.json').read_text());allchannels=json.loads(gzip.decompress((HERE/'inputs/POLARIZED-CHANNELS.json.gz').read_bytes())) + channel=allchannels['channels'][0] + labels=[p['q']for p in data['ports']] + def raw_label(port): + a=port//112**2;b=port//112%112;c=port%112 + return labels[a]|(labels[b]<<9)|(labels[c]<<18) + # Explicit nondegenerate 25-space of equal three-block parities. + U=[1|(1<<9)|(1<<18)]+[(1<<(9*b))^(1<<(9*b+j))for b in range(3)for j in range(1,9)] + orthogonal=ortho_basis(U);need(len(orthogonal)==25,'dimension25 physical realization') + def physical_label(port): + x=raw_label(port);need(span_contains(U,x),'literal label in original direct-sum space') + y=sum(dot(x,b)<>i&1:back^=b + need(back==x,'isometry inverse on actual literal port') + return y + src=[(port,F(a,b),physical_label(port))for port,a,b in channel['source']] + read=[(port,F(a,b),physical_label(port))for port,a,b in channel['reader']] + need(len(src)==len(read)==68 and not(set(x[0]for x in src)&set(x[0]for x in read)),'68+68 disjoint actual ports') + S=basis(x[2]for x in src);R=basis(x[2]for x in read);D=radical(S) + need(len(S)==len(R)==8 and len(D)==6,'source8 reader8 common radical6') + need(len(radical(R))==6 and len(basis(D+radical(R)))==6,'same radical on both sides') + need(all(not dot(x,y)for x in S for y in R),'entire source/reader spans are orthogonal') + need(len(basis(S+R))==10 and len(radical(basis(S+R)))==6,'joint10 with radical6') + need(all(dot(q,q)and not span_contains(S,q)for _,_,q in read),'reader own line not in source prefix') + need(all(dot(q,q)and span_contains(S,q)for _,_,q in src),'source own lines in source prefix') + spec=importlib.util.spec_from_file_location('rectangle_clifford',HERE/'inputs/clifford_exact.py');ce=importlib.util.module_from_spec(spec);sys.modules[spec.name]=ce;spec.loader.exec_module(ce) + phase_peak=[1] + def sparse_zero(op,basis_state=0): + vec={basis_state:(1,0)};den=0 + for e in op.circuit: + kind=e[0] + if kind=='P':vec={ce.mv(e[1],x):v for x,v in vec.items()} + elif kind=='X':vec={x^e[1]:v for x,v in vec.items()} + elif kind=='D':vec={x:ce.mul_i(v,ce.qvalue(e[1],e[2],x,op.n))for x,v in vec.items()} + elif kind=='phase':vec={x:ce.mul_i(v,e[1])for x,v in vec.items()} + else: + need(kind=='C','literal phase evaluator gate') + q,sgn=e[1:];new={} + for x in set(vec)|{x^q for x in vec}: + a,b=vec.get(x,(0,0));c,d=vec.get(x^q,(0,0));v=(a-sgn*b+c+sgn*d,b+sgn*a+d-sgn*c) + if v!=(0,0):new[x]=v + vec=new;den+=1 + phase_peak[0]=max(phase_peak[0],len(vec));need(len(vec)<=(1<<18),'bounded sparse phase support') + while den and all(not(a&1)and not(b&1)for a,b in vec.values()):vec={x:(a//2,b//2)for x,(a,b)in vec.items()};den-=1 + return vec,den + ce.Op.zero_state=sparse_zero + def exact_monomial(op): + n=op.n;T=op.tab;need(all(x==0 and p%2==0 for x,z,p in T[n:]),'actual monomial signed tableau') + G=ce.transpose([x for x,z,p in T[:n]],n);b=ce.mv(G,sum((p//2)<S8 is one H2 per participating field, not one H2 per complete channel','if_D6_not_present':'The six radical directions remain a genuine Gaussian prefix cost; no H2-only acquisition from ground is claimed. Ground->S8 has rank8.','main_prefix_and_termination':'Every main field must actually reach S8 at the same cut, after each source own-line service and before each reader own-line service; global schedule, transitions, productive targets and complete invoice remain unproved.','dirty_slot_from_ground':'If an independent dirty original z starts and must return at ground, acquiring and undoing its S8 chart requires separately priced transport; the kernel does not fund it. Use the zero-owned variant to avoid that assumption.'}, + 'phase_evaluation':{'method':'Fresh sparse exact Gaussian-integer column evaluator for the pinned Clifford compiler; equality of signed tableau and one absolute column fixes global phase.','peak_nonzero_column_support':phase_peak[0],'field_width':'Every positive f under inherited columnwise tensor semantics.'}, + 'complete_gaussian_job_targets_claimed':False,'global_flag_compatibility_proved':False,'new_kappa':False} + return json.loads(json.dumps(out)) +def main(): + ap=argparse.ArgumentParser();ap.add_argument('--write',action='store_true');args=ap.parse_args();signal.signal(signal.SIGALRM,lambda *_:(_ for _ in()).throw(TimeoutError('60s one-channel bound')));signal.setitimer(signal.ITIMER_REAL,60) + out=calculate();signal.setitimer(signal.ITIMER_REAL,0);p=HERE/'RESULT.json' + if args.write:p.write_text(json.dumps(out,indent=2,sort_keys=True)+'\n') + else:need(json.loads(p.read_text())==out,'frozen local ABI receipt') + print(json.dumps({'status':out['status'],'source_ports':68,'reader_ports':68,'source_frame_rank':8,'shared_radical_rank':6,'conditional_edge_rank':2,'dirty_ADDs':out['scalar_kernel']['dirty_ADDs'],'owned_zero_ADDs':out['scalar_kernel']['owned_zero_ADDs'],'owned_zero_retags':2,'new_kappa':False},sort_keys=True)) +if __name__=='__main__':main() diff --git a/research/odd-e8-polarized-native/embed.py b/research/odd-e8-polarized-native/embed.py new file mode 100644 index 0000000000..ca3c6bd646 --- /dev/null +++ b/research/odd-e8-polarized-native/embed.py @@ -0,0 +1,228 @@ +"""Exact minimal I20 embedding of the literal odd-E8 two-cube restriction. + +Finite binary-linear algebra certificate only; no Gaussian/native/kappa claim. +Default read-only; --write authors the stable receipt. +""" +from collections import Counter, defaultdict +from hashlib import sha256 +from itertools import combinations, product +from pathlib import Path +import gzip +import json +import sys + +HERE = Path(__file__).resolve().parent +NORMALIZERS_SHA = 'ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da' + +def need(ok, why): + if not ok: + raise ValueError(why) + +def dot(a, b): + return (a & b).bit_count() & 1 + +def basis(rows): + piv = {} + for x in rows: + while x: + p = x.bit_length()-1 + if p in piv: + x ^= piv[p] + else: + piv[p] = x + break + for p in sorted(piv): + for q in piv: + if q != p and piv[q] >> p & 1: + piv[q] ^= piv[p] + return [piv[p] for p in sorted(piv, reverse=True)] + +def pairing_rank(a, b): + return len(basis(sum(dot(x, y) << j for j, y in enumerate(b)) for x in a)) + +def combine(b, mask): + value = 0 + for i, x in enumerate(b): + if mask >> i & 1: + value ^= x + return value + +def coordinate_solver(b): + piv = {} + for i, value in enumerate(b): + label = 1 << i + while value: + p = value.bit_length()-1 + if p in piv: + value ^= piv[p][0] + label ^= piv[p][1] + else: + piv[p] = (value, label) + break + need(value != 0, 'coordinate basis must be independent') + def solve(value): + label = 0 + while value: + p = value.bit_length()-1 + need(p in piv, 'vector outside declared span') + value ^= piv[p][0] + label ^= piv[p][1] + return label + return solve + +def bilinear(rows, a, b): + return dot(combine(rows, a), b) + +def orthonormal_basis(rows): + n = len(rows) + remaining = [1 << i for i in range(n)] + units, hyperbolic = [], [] + B = lambda a, b: bilinear(rows, a, b) + while remaining: + odd = next((i for i, x in enumerate(remaining) if B(x, x)), None) + if odd is not None: + x = remaining.pop(odd) + remaining = [y ^ (x if B(x, y) else 0) for y in remaining] + units.append(x) + else: + pair = next(((i, j) for i in range(len(remaining)) + for j in range(i+1, len(remaining)) + if B(remaining[i], remaining[j])), None) + need(pair is not None, 'completion must be nondegenerate') + i, j = pair + e, f = remaining[i], remaining[j] + remaining = [y ^ (e if B(y, f) else 0) ^ (f if B(y, e) else 0) + for k, y in enumerate(remaining) if k not in pair] + hyperbolic.append((e, f)) + need(units, 'the supplied completion must be nonalternating') + # I1 perpendicular H is I3: all three listed vectors have norm one + # and pairwise zero pairing. Reuse one unit for each remaining H. + for e, f in hyperbolic: + o = units.pop() + units += [o ^ e, o ^ f, o ^ e ^ f] + need(len(units) == n and len(basis(units)) == n, 'orthonormal basis dimension') + need(all(B(a, b) == int(i == j) for i, a in enumerate(units) + for j, b in enumerate(units)), 'orthonormal Gram must be I') + return units + +def main(): + normal_raw = (HERE/'inputs/NORMALIZERS.json').read_bytes() + need(sha256(normal_raw).hexdigest() == NORMALIZERS_SHA, 'normalizer pin') + data = json.loads(normal_raw) + channels_raw = (HERE/'POLARIZED-CHANNELS.json.gz').read_bytes() + inherited = json.loads((HERE/'POLARIZED-CROSS-CUBE.json').read_text()) + need(sha256(channels_raw).hexdigest() == inherited['literal_channels_sha256'], 'channel pin') + channels = json.loads(gzip.decompress(channels_raw))['channels'] + labels = [p['q'] for p in data['ports']] + ca = inherited['base_cube_a']['ports'] + cb = inherited['base_cube_b']['ports'] + cc = inherited['fixed_other_cube']['ports'] + ports = sorted((i*112+j)*112+k for i, j, k in product(ca+cb, cc, cc)) + def raw_q(port): + i, rest = divmod(port, 112*112) + j, k = divmod(rest, 112) + return labels[i] | (labels[j] << 9) | (labels[k] << 18) + qraw = {p: raw_q(p) for p in ports} + V = basis(qraw.values()) + need(len(ports) == len(set(qraw.values())) == 1024, '1024 distinct raw ports') + need(len(V) == 12 and pairing_rank(V, V) == 4, 'V12 rank-four form') + R = basis(combine(V, mask) for mask in range(1 << len(V)) + if all(not dot(combine(V, mask), y) for y in V)) + need(len(R) == 8, 'eight-dimensional radical') + N = next([V[i] for i in chosen] for chosen in combinations(range(12), 4) + if pairing_rank([V[i] for i in chosen], [V[i] for i in chosen]) == 4) + need(len(basis(N+R)) == 12 and any(dot(x, x) for x in N), 'N4 perpendicular R8') + Wraw = N+R + solve = coordinate_solver(Wraw) + # Abstract completion [N4,R8,D8], with B(R_i,D_j)=delta_ij. + gram = [sum(dot(x, y) << j for j, y in enumerate(N)) for x in N] + gram += [1 << (12+i) for i in range(8)] + gram += [1 << (4+i) for i in range(8)] + need(len(gram) == len(basis(gram)) == 20, 'nondegenerate dimension-20 completion') + O = orthonormal_basis(gram) + def embed(raw): + coordinate = solve(raw) + return sum(bilinear(gram, coordinate, o) << i for i, o in enumerate(O)) + q20 = {p: embed(qraw[p]) for p in ports} + need(len(set(q20.values())) == 1024 and len(basis(q20.values())) == 12, 'injective embedding') + checks = 0 + for p in ports: + need(dot(q20[p], q20[p]) == 1, 'all literal q20 are odd') + for q in ports: + need(dot(qraw[p], qraw[q]) == dot(q20[p], q20[q]), 'all-port exact Gram identity') + checks += 1 + need(checks == 1024**2, 'all ordered Gram pairs checked') + groups = defaultdict(list) + for i, ch in enumerate(channels): + sb = basis(q20[p] for p, _, _ in ch['source']) + rb = basis(q20[p] for p, _, _ in ch['reader']) + need(len(sb) == len(rb) == 8 and pairing_rank(sb, rb) == 0, 'orthogonal eight-spaces') + need(pairing_rank(sb, sb) == pairing_rank(rb, rb) == 2, 'self-pairing two') + groups[(tuple(sb), tuple(rb))].append(i) + need(len(groups) == 4 and sorted(map(len, groups.values())) == [16]*4, 'four space pairs') + all_source, all_reader = [], [] + group_records = [] + for (sb, rb), ids in sorted(groups.items()): + sp = sorted(set(p for i in ids for p, _, _ in channels[i]['source'])) + rp = sorted(set(p for i in ids for p, _, _ in channels[i]['reader'])) + need(len(sp) == len(rp) == 128, 'each space-pair has 128 literal source/read fields') + all_source += sp + all_reader += rp + group_records.append({'source_basis20': sb, 'reader_basis20': rb, + 'channel_ids': ids, 'source_ports': sp, 'reader_ports': rp}) + need(len(all_source) == len(set(all_source)) == 512, 'source groups partition b cube') + need(len(all_reader) == len(set(all_reader)) == 512, 'reader groups partition a cube') + # A quotient certificate: V/rad(V) is nonalternating dimension four. + ng = gram[:4] + NO = orthonormal_basis(ng) + quotient = {p: sum(bilinear(ng, solve(qraw[p]) & 15, o) << i + for i, o in enumerate(NO)) for p in ports} + quotient_counts = Counter(quotient.values()) + need(quotient_counts == {i: 128 for i in range(16) if i.bit_count() & 1}, 'eight balanced quotient types') + cliques = [] + for weight in (1, 3): + types = [i for i in range(16) if i.bit_count() == weight] + buckets = [[p for p in ports if quotient[p] == t] for t in types] + for i in range(128): + clique = [bucket[i] for bucket in buckets] + qb = [q20[p] for p in clique] + need(len(basis(qb)) == pairing_rank(qb, qb) == 4, 'literal orthonormal four-clique') + cliques.append(clique) + # Two nonorthogonal quotient types give a forced identity submatrix of size 256. + independent = [p for p in ports if quotient[p] in (1, 7)] + need(len(independent) == 256 and all(dot(q20[p], q20[q]) for p in independent for q in independent), + '256-port forbidden-offdiagonal lower bound') + result = {'schema': 'odd-e8-two-cube-minimal-I20-v1', + 'normalizer_sha256': NORMALIZERS_SHA, + 'polarized_channels_sha256': sha256(channels_raw).hexdigest(), + 'raw_ambient': 27, 'span_dimension': 12, 'pairing_rank': 4, + 'radical_dimension': 8, 'minimal_nondegenerate_ambient': 20, + 'completion_decomposition': 'N4 perpendicular H^8, N4 nonalternating', + 'raw_non_degenerate_basis': N, 'raw_radical_basis': R, + 'raw_coordinate_basis': Wraw, 'completion_Gram_rows': gram, + 'orthonormal_completion_basis': O, + 'raw_basis_images20': [embed(x) for x in Wraw], + 'ports': [{'port': p, 'q27': qraw[p], 'coordinates12': solve(qraw[p]), + 'q20': q20[p], 'quotient4': quotient[p]} for p in ports], + 'ordered_Gram_checks': checks, + 'orthogonal_eight_space_pairs': group_records, + 'quotient_orthonormal_basis4': NO, + 'quotient_type_counts': dict(sorted(quotient_counts.items())), + 'clique_fitting_matrix': {'cliques': cliques, 'rank': 256, + 'rank_lower_bound_independent_ports': independent, + 'source_copy_profile': {'4': 256}, 'copy_mass_per_port': '1', + 'compatible_physical_native_core_proved': False}, + 'physical_program_emitted': False, 'complete_invoice_proved': False, 'kappa_claim': False} + target = HERE/'EMBEDDING.json' + encoded = json.dumps(result, sort_keys=True, indent=2)+'\n' + if '--write' in sys.argv: + target.write_text(encoded) + else: + need(target.read_text() == encoded, 'stable embedding receipt differs') + print(json.dumps({'status': 'PASS', 'ports': 1024, 'span': 12, 'pairing_rank': 4, + 'radical': 8, 'minimal_ambient': 20, 'Gram_pairs': checks, + 'orthogonal8_pairs': len(groups), 'fitting_rank_exact': 256, + 'native_word': False}, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/odd-e8-polarized-native/frame_tools.py b/research/odd-e8-polarized-native/frame_tools.py new file mode 100644 index 0000000000..7ec1c59b7d --- /dev/null +++ b/research/odd-e8-polarized-native/frame_tools.py @@ -0,0 +1,56 @@ +"""Exact low-rank phases and analytic full-Gaussian native conjugation. + +Source Clifford compiler credit retained. No dense 2^n state is allocated. +""" +def install(ce,need,peak): + def sparse_zero(op,basis_state=0): + vec={basis_state:(1,0)};den=0 + for e in op.circuit: + k=e[0] + if k=='P':vec={ce.mv(e[1],x):a for x,a in vec.items()} + elif k=='X':vec={x^e[1]:a for x,a in vec.items()} + elif k=='D':vec={x:ce.mul_i(a,ce.qvalue(e[1],e[2],x,op.n))for x,a in vec.items()} + elif k=='phase':vec={x:ce.mul_i(a,e[1])for x,a in vec.items()} + else: + need(k=='C','literal sparse phase primitive');q,s=e[1:];out={} + for x in set(vec)|{x^q for x in vec}: + a,b=vec.get(x,(0,0));c,d=vec.get(x^q,(0,0));v=(a-s*b+c+s*d,b+s*a+d-s*c) + if v!=(0,0):out[x]=v + vec=out;den+=1 + peak[0]=max(peak[0],len(vec));need(len(vec)<=(1<<18),'bounded low-rank phase support') + while den and all(not(a&1)and not(b&1)for a,b in vec.values()):vec={x:(a//2,b//2)for x,(a,b)in vec.items()};den-=1 + return vec,den + ce.Op.zero_state=sparse_zero + def monomial(op,known_zero=None): + n=op.n;T=op.tab;need(all(x==0 and p%2==0 for x,z,p in T[n:]),'physical map is actually monomial') + G=ce.transpose([x for x,z,p in T[:n]],n);b=ce.mv(G,sum((p//2)<=((1-i)/2)^n sum_x i^wt(x)|x>. Thus R K_G R^-1|0>=(-i)^wt(d)|d>. Signed tableau fixes the remaining monomial.', + 'native_G_columns':cols} diff --git a/research/odd-e8-polarized-native/independent_review.py b/research/odd-e8-polarized-native/independent_review.py new file mode 100644 index 0000000000..4a638c3a73 --- /dev/null +++ b/research/odd-e8-polarized-native/independent_review.py @@ -0,0 +1,300 @@ +"""Read-only independent review of the emitted one-direction H_ab word. + +Does not import module.py or frame_tools.py, and never regenerates source data. +The pinned primitive Pauli compiler is reused, with a fresh sparse amplitude +evaluator and explicit analytic phase proof for the four full conjugations. +""" +from pathlib import Path +from fractions import Fraction as F +from collections import Counter, defaultdict +from hashlib import sha256 +import argparse, gzip, importlib.util, json, sys + +HERE=Path(__file__).resolve().parent +sys.dont_write_bytecode=True + +def require(value, why): + if not value: raise ValueError(why) + +def read(path): return json.loads(path.read_bytes()) + +def gbasis(rows): + piv={} + for value in rows: + for pivot in sorted(piv, reverse=True): + if value>>pivot&1: value^=piv[pivot] + if value: piv[value.bit_length()-1]=value + for pivot in sorted(piv): + for other in piv: + if other!=pivot and piv[other]>>pivot&1: piv[other]^=piv[pivot] + return tuple(piv[p] for p in sorted(piv,reverse=True)) + +def parity(value): return value.bit_count()&1 +def dot(a,b): return parity(a&b) +def contains(b,v): return len(gbasis(list(b)+[v]))==len(b) + +def sparse(circuit,n=25): + # Literal Gaussian-integer arithmetic, independent of author's evaluator. + values={0:(1,0)}; denominator=0 + for gate in circuit: + kind=gate[0] + if kind=='P': + rows=gate[1] + values={sum(dot(row,x)<>i&1) + phase+=2*sum(dot(Q[i]>>(i+1),x>>(i+1)) + for i in range(n) if x>>i&1) + dest[x]=[(a,b),(-b,a),(-a,-b),(b,-a)][phase%4] + values=dest + elif kind=='C': + q,sign=gate[1:];dest={} + for x in values.keys()|{x^q for x in values}: + a,b=values.get(x,(0,0));c,d=values.get(x^q,(0,0)) + # ((1+sign*i) I +(1-sign*i) X_q)/2 + out=(a-sign*b+c+sign*d,b+sign*a+d-sign*c) + if out!=(0,0):dest[x]=out + values=dest;denominator+=1 + else: raise ValueError('unknown gate '+str(kind)) + require(len(values)<=65536,'independent sparse support bound') + while denominator and all(not(a&1) and not(b&1) for a,b in values.values()): + denominator-=1;values={x:(a//2,b//2) for x,(a,b) in values.items()} + return values,denominator + +def main(): + parser=argparse.ArgumentParser() + parser.add_argument('--package',type=Path,default=HERE,help='Module package; default is this script directory') + parser.add_argument('--receipt',type=Path,default=None,help='Review receipt; default PACKAGE/INDEPENDENT-REVIEW.json') + parser.add_argument('--write',action='store_true',help='Explicitly author the review receipt') + args=parser.parse_args();ROOT=args.package.resolve() + receipt_path=args.receipt.resolve()if args.receipt else ROOT/'INDEPENDENT-REVIEW.json' + raw=(ROOT/'PROGRAM.json.gz').read_bytes();program=json.loads(gzip.decompress(raw)) + canonical_payload=(json.dumps(program,sort_keys=True,separators=(',',':'))+'\n').encode() + receipt=read(ROOT/'MODULE.json');n=program['axis_dimension'];require(n==25,'dimension25') + pins={p:sha256((ROOT/'inputs'/p).read_bytes()).hexdigest() for p in receipt['source_pins']} + require(pins==receipt['source_pins'],'all source pins') + require(sha256(canonical_payload).hexdigest()==receipt['program_payload_sha256']==receipt['proof_relevant_digest'],'emitted canonical scientific word pin') + spec=importlib.util.spec_from_file_location('review_primitive_clifford',ROOT/'inputs/clifford_exact.py') + ce=importlib.util.module_from_spec(spec);sys.modules[spec.name]=ce;spec.loader.exec_module(ce) + def literal(word): + value=ce.ident(n) + for gate in word: + kind=gate[0] + if kind=='P':part=ce.perm(n,gate[1]) + elif kind=='X':part=ce.xgate(n,gate[1]) + elif kind=='D':part=ce.diag(n,gate[1],gate[2]) + elif kind=='phase':part=ce.Op(n,ce.identity(n),[tuple(gate)]) + else: + require(kind=='C','known literal primitive');part=ce.cgate(n,gate[1],gate[2]) + value=value.then(part) + return value + def exact(a,b,label): + require(a.tab==b.tab,'signed tableau '+label) + require(sparse(a.circuit)==sparse(b.circuit),'absolute phase '+label) + definitions=program['monomial_and_frame_definitions'] + for key,word in definitions.items(): + require(sha256(json.dumps(word,separators=(',',':')).encode()).hexdigest()==key,'literal definition hash') + def mono(word):require(all(g[0]in ('P','D','X','phase') for g in word),'no Fourier hidden in wrapper') + def native(cols): + G=ce.transpose(cols,n);inverse=ce.inv(G,n);columns=ce.transpose(inverse,n) + Q=tuple((1<>j&1:inverse^=b + require(inverse==value and dot(q,q)==1,'actual norm-one port isometry') + return q + channels=json.loads(gzip.decompress((ROOT/'inputs/POLARIZED-CHANNELS.json.gz').read_bytes()))['channels'] + source_groups={};reader_groups={};group_by_key=defaultdict(list) + expected=defaultdict(dict) + for j,ch in enumerate(channels): + S=gbasis(qlabel(p) for p,a,b in ch['source']);R=gbasis(qlabel(p) for p,a,b in ch['reader']) + require(len(S)==len(R)==8 and all(not dot(a,b)for a in S for b in R),'orthogonal8space pair') + key=(S,R);group_by_key[key].append(j) + for name,lookup in [('source',source_groups),('reader',reader_groups)]: + require(len(ch[name])==68,'68-port polarized channel support') + for p,a,b in ch[name]: + require(p not in lookup or lookup[p]==key,'one common frame per literal port');lookup[p]=key + for p,a,b in ch['reader']: + row=expected[p] + for q,c,d in ch['source']: + row[q]=row.get(q,F(0))+F(a,b)*F(c,d) + if not row[q]:del row[q] + require(len(channels)==64 and len(group_by_key)==4 and all(len(v)==16 for v in group_by_key.values()),'64channels only4pairs16each') + require(len(source_groups)==len(reader_groups)==512 and not(set(source_groups)&set(reader_groups)),'1024 independent source/reader roles') + require(program['field_roles']=={str(p):['X'if p in source_groups else'Y',p]for p in set(source_groups)|set(reader_groups)},'literal X/Y role namespace') + Rfull=ce.fourier(n);source_paths=0;reader_paths=0;path_ops={};chart_ops={} + full_anchors=[] + for group in program['groups']: + gi=str(group['group']);S=group['S8_basis25'];R=group['R8_basis25'];key=(gbasis(S),gbasis(R)) + require(key in group_by_key and group['channels']==group_by_key[key],'emitted group channels') + require(set(group['source_ports'])=={p for p,k in source_groups.items()if k==key},'source group partition') + require(set(group['reader_ports'])=={p for p,k in reader_groups.items()if k==key},'reader group partition') + require(len(group['source_ports'])==len(group['reader_ports'])==128,'128-port blocks') + common=program['common_paths'][gi];Phi=literal(definitions[common['S8_frame']]);cols=ce.basis_extend(S,n);K=native(cols) + exact(Phi,frame(cols,8),'S8 defining frame') + chart_ops['S8:'+gi]=Phi + entry=common['reader_ground_to_S8'];post=definitions[entry['after_monomial']];pre=definitions[entry['before_monomial']] + mono(pre);mono(post) + require(pre==json.loads(json.dumps(K.adjoint().circuit)) and post==json.loads(json.dumps(K.circuit)),'reader entry literal factors') + require(entry['child_axes']==list(range(8)) and entry['rank']==8,'reader8 child') + exit=common['source_S8_to_full25'];pre=definitions[exit['before_monomial']];post=definitions[exit['after_monomial']] + mono(pre);mono(post) + require(pre==json.loads(json.dumps(K.adjoint().circuit)),'full exit literal K inverse') + require(exit['child_axes']==list(range(8,25)) and exit['rank']==17,'full exit17child') + T=literal(post);expected_T=Rfull.adjoint().then(K).then(Rfull) + require(T.tab==expected_T.tab,'native full conjugation signed tableau') + inversecols=ce.transpose(ce.inv(ce.transpose(cols,n),n),n) + d=sum(((x.bit_count()//2)&1)<record['peak_coefficient_l1']:record['peak_coefficient_l1']=l1;record['peak_l1_event']=event_index + if den>record['max_dyadic_denominator_exponent']:record['max_dyadic_denominator_exponent']=den;record['max_denominator_event']=event_index + for p in rows:measure(p,-1) + for event_index,event in enumerate(program['program']): + kind=event[0] + if kind=='PAID_PATH': + _,p,old,new,path=event + require(charts[p]==old,'paid edge actual entrance chart') + paid[path['rank']]+=1 + for name in ['before_monomial','after_monomial']: + word=definitions[path[name]];mono(word);ordinary.update(g[0]for g in word) + if old.startswith('line:'):require(path==program['source_entry_paths'][str(p)],'exact source path reference') + elif new=='full25':require(path==program['common_paths'][old.split(':')[1]]['source_S8_to_full25'],'exact full path reference') + elif old=='ground':require(path==program['common_paths'][new.split(':')[1]]['reader_ground_to_S8'],'exact reader entry reference') + else:require(path==program['reader_exit_paths'][str(p)],'exact reader exit reference') + charts[p]=new + elif kind=='ADD': + _,dst,src,a,b,chart=event + require(charts[dst]==charts[src]==chart,'literal ADD common physical frame') + for p,c in rows[src].items(): + value=rows[dst].get(p,F(0))+F(a,b)*c + if value:rows[dst][p]=value + else:rows[dst].pop(p,None) + measure(dst,event_index) + ordinary[kind]+=1;seen_adds+=1 + elif kind=='ZERO_RETAG': + _,p,old,new=event + require(p=='C0'and not rows[p]and charts[p]==old,'owned zero retag true precondition') + charts[p]=new;ordinary[kind]+=1 + elif kind=='CLEAR_ZERO': + _,p,chart=event + require(p=='C0'and charts[p]==chart and not rows[p],'CLEAR only on already exact zero owned scratch') + ordinary[kind]+=1 + else: raise ValueError('unknown typed event') + require(paid==Counter({7:512,8:512,16:512,17:512}),'independent full Gaussian bill') + require({str(k):v for k,v in paid.items()}==receipt['paid_profile'],'published Gaussian bill') + require(dict(ordinary)==receipt['ordinary_literal_gate_histogram'],'complete literal ordinary counts') + for p in source_groups:require(rows[p]=={p:F(1)} and charts[p]=='full25','source arbitrary independent original retained') + for p in reader_groups: + goal={p:F(1),**expected[p]} + require(rows[p]==goal and charts[p]=='qperp24:'+str(p),'reader exact arbitrary independent H_ab endpoint') + require(not rows['C0']and charts['C0']=='ground','owned scratch zero ground returned') + require(program['logical_endpoint_rows']=={'source_identity_fields':sorted(source_groups), + 'reader_rows':{str(p):[[s,q.numerator,q.denominator]for s,q in sorted(rows[p].items())]for p in sorted(reader_groups)}, + 'owned_C0':[]},'literal published endpoint rows') + result={'status':'PASS_INDEPENDENT_LOCAL_HAB_TYPED_WORD_REVIEW','source_pins':pins, + 'proof_relevant_program_payload_sha256':sha256(canonical_payload).hexdigest(), + 'environment_metadata':{'program_container_sha256':sha256(raw).hexdigest(),'program_container_bytes':len(raw)}, + 'module_py_sha256':sha256((ROOT/'module.py').read_bytes()).hexdigest(), + 'frame_tools_py_sha256':sha256((ROOT/'frame_tools.py').read_bytes()).hexdigest(), + 'polarized_channels':64,'orthogonal8space_pairs':4,'channels_per_pair':16, + 'unique_group_source_fields':512,'unique_group_reader_fields':512,'source_entry_gauges_exact':source_paths, + 'reader_exit_gauges_exact':reader_paths,'native_full_anchors':full_anchors, + 'literal_program_events':len(program['program']),'ordinary':dict(ordinary),'paid':dict(paid), + 'exact_logical_coefficient_growth':{family:{**record,'peak_coefficient_l1':str(record['peak_coefficient_l1'])}for family,record in growth.items()}, + 'growth_scope':'At every literal module event, each physical row is its unitary chart times the logical row. If each original entrance norm is at most M, row norm is at most reported peak l1 times M. This does not by itself bound accumulated rounding errors or complete-caller precision.', + 'all1024original_logical_endpoints':True,'zero_scratch_lifecycle':True, + 'independent_mutation_controls':{'same_tableau_phase_i_rejected_by_absolute_column':True,'S8_to_R8_requires_rank':wrong_frame_rank,'omitting_actual_uncompute_leaves_nonzero_owned_C0':True}, + 'universal_native_anchor_proof':'Written in REVIEW.md; exact signed tableau and analytic phase, not finite-width extrapolation.', + 'independence':'Does not call module.py, frame_tools.py or check.py calculation; primitive pinned Pauli compiler reused. Fresh sparse Gaussian-integer column evaluator.', + 'scope':'One-direction 25D H_ab local ABI only; source Phi_line entrances are supplied; coupled reader endpoints carry no autonomous Gaussian-job credit; no 20D-to25D free connection; no K-core or full caller/precision/compiler/kappa/upstream acceptance claim.'} + encoded=json.dumps(result,indent=2,sort_keys=True)+'\n' + if args.write:receipt_path.write_text(encoded) + else: + old=read(receipt_path);old.pop('environment_metadata',None) + new=json.loads(encoded);new.pop('environment_metadata',None) + require(old==new,'frozen scientific independent result; gzip container is environmental') + print(json.dumps({k:result[k]for k in ['status','orthogonal8space_pairs','source_entry_gauges_exact','reader_exit_gauges_exact','ordinary','paid']},sort_keys=True)) + +if __name__=='__main__':main() diff --git a/research/odd-e8-polarized-native/inputs/NORMALIZERS.json b/research/odd-e8-polarized-native/inputs/NORMALIZERS.json new file mode 100644 index 0000000000..bca92c222c --- /dev/null +++ b/research/odd-e8-polarized-native/inputs/NORMALIZERS.json @@ -0,0 +1,126 @@ +{ + "clifford_sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "code_sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0", + "finite_checks": {"absolute_phase_mutations_rejected":112,"exact_endpoint_factor_identities":896,"gaussian_free_compiled_wrappers":896,"monomial_wrappers":896,"omitted_phase_rejections":112,"ports":112,"scalar_basis_recodings":224,"weight_congruence_addresses":57344}, + "local_gauge_bill": {"added_recursive_calls":0,"backward_extra_monomial_field_maps_upper":448,"main_wrapper_field_maps":448,"owned_fields_reused":8,"recoding_monomial_field_maps":448,"recoding_owned_clears":32,"recoding_scalar_adds":1792,"recodings":2}, + "mode_columns": 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+ "ports": [ + 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z^QF&&OI`QA?|E}q?{ALVYQcBEFVz32mfdQu_utyH{jr47Led8Lee3B{)L#GHwZ$yb z#9=IbjpnauC9_A~T0!n?v>EoI%&JX+IRhPFsv;O%B_me!9A zdX^jd0G?HIf1zu`mhZW-E2}=Xp1wL*n&nShz;}_5^eN#V>pzOX4;1>i)&1)<>j&1);a[j],a[k]=a[k],a[j] + for i in range(n): + if i!=j and a[i]>>j&1:a[i]^=a[j] + assert [r&((1<>n for r in a) +def basis_extend(cols,n): + out=[] + for x in list(cols)+[1<len(out):out.append(x) + assert len(out)==n + return tuple(out) +def nullspace(rows,n): + a=list(rows);p=[];k=0 + for j in range(n): + t=next((i for i in range(k,len(a)) if a[i]>>j&1),None) + if t is None:continue + a[t],a[k]=a[k],a[t] + for i in range(len(a)): + if i!=k and a[i]>>j&1:a[i]^=a[k] + p.append(j);k+=1 + return tuple((1<>j)&1)<>i&1:out=pmul(out,T[i]) + for i in range(n): + if z>>i&1:out=pmul(out,T[n+i]) + return out +def compose(A,B):return tuple(apply(A,p) for p in B) +def inverse(T): + n=len(T)//2;cols=[x|(z<>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4)) + return tuple(out) +def qvalue(Q,alpha,x,n): + return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4 +def mul_i(a,p): + x,y=a;p%=4 + return [(x,y),(-y,x),(-x,-y),(y,-x)][p] +@dataclass +class Op: + n:int + tab:tuple + circuit:list + def then(self,b): + assert self.n==b.n + return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit) + def adjoint(self): + circ=[] + for e in reversed(self.circuit): + if e[0]=='P':circ.append(('P',inv(e[1],self.n))) + elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2]))) + elif e[0]=='C':circ.append(('C',e[1],-e[2])) + elif e[0]=='phase':circ.append(('phase',(-e[1])%4)) + else:circ.append(e) + return Op(self.n,inverse(self.tab),circ) + def zero_state(self,basis=0): + N=1<>i)&1 for i in range(n)) + assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n)) + return Op(n,tuple([(1<>i&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>i)&1)) for i in range(n)]),[('X',b)]) +def fourier(n,axes=None): + out=ident(n) + for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<len(selected):picks.append(j);selected.append(x) + assert len(picks)==r and all(x>>r==0 for x in Bcols) + Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<>j&1:x^=p[j] + if x:p[x.bit_length()-1]=x + for j in sorted(p): + for k in p: + if k!=j and p[k]>>j&1:p[k]^=p[j] + return tuple(p[j]for j in sorted(p,reverse=True)) +def calculate(): + base=load('rectangle_single',HERE/'check.py');tools=load('rectangle_frames',HERE/'frame_tools.py') + for name,digest in base.PINS.items():need(sha256((HERE/'inputs'/name).read_bytes()).hexdigest()==digest,'source pin '+name) + normal=json.loads((HERE/'inputs/NORMALIZERS.json').read_text());payload=json.loads(gzip.decompress((HERE/'inputs/POLARIZED-CHANNELS.json.gz').read_bytes()));channels=payload['channels'] + labels=[p['q']for p in normal['ports']];n=25 + U=[1|(1<<9)|(1<<18)]+[(1<<(9*b))^(1<<(9*b+j))for b in range(3)for j in range(1,9)] + orthogonal=base.ortho_basis(U) + def qlabel(port): + a=port//112**2;b=port//112%112;c=port%112;x=labels[a]|(labels[b]<<9)|(labels[c]<<18) + need(base.span_contains(U,x),'literal actual port in U25') + return sum(base.dot(x,v)<

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No tensor power of the owner matrix or packing discount.", + "orthonormal_basis_raw27": [ + 262657, + 262658, + 262660, + 262664, + 262672, + 262688, + 262720, + 262784, + 262912, + 263679, + 264703, + 266751, + 270847, + 279039, + 295423, + 328191, + 393727, + 786431, + 1310719, + 2359295, + 4456447, + 8650751, + 17039359, + 33816575, + 67371007 + ], + "owned_fields": 0, + "phase_uniformity": "Every generated paid path uses only exact low-rank monomial gauges and the proved analytic native full-conjugation anchor; generic Lagrangian and phase proofs cover every family member. Default finite replay fully compiles cube000, not all2744 phase instances.", + "physical_ambient": 25, + "scalar_operator": "K_odd=(K1+K2+K3-K1 K2 K3)/2; factor operators act on distinct owner selector coordinates", + "schema": "odd-E8-whole-K-native-family-template/v1", + "whole_ordinary_profile": { + "ADD": 106774528, + "D": 21073920, + "P": 21073920, + "X": 8429568, + "phase": 8429568 + }, + "whole_original_inputs": 2809856, + "whole_paid_profile": { + "15": 1404928, + "16": 1404928, + "8": 1404928, + "9": 1404928 + } +} diff --git a/research/odd-e8-whole-k-native/PROOF.md b/research/odd-e8-whole-k-native/PROOF.md new file mode 100644 index 0000000000..70d56ae3ff --- /dev/null +++ b/research/odd-e8-whole-k-native/PROOF.md @@ -0,0 +1,326 @@ +# A complete native K primitive for every odd-E8 product cube + +This constructs the whole block-diagonal three-factor K service, including +the ordinary wrappers that normalize its actual supplied-line interface to +arbitrary ground-chart inputs. It does not produce the cross-cube H service, +install the low-rank F3 decoder, complete an outer caller or claim a kappa. + +The construction is a fixed finite structured word for all 14^3 cubes. +`core.calculate((a,b,c))` emits its exact literal instance for any cube. +The default finite phase replay fully emits cube(0,0,0); it does not pretend +to have expanded all 106,774,528 scalar ADDs or executed every phase instance. +The all-family result follows from the generic frame/phase proof below and +the independent all-2,744-cube geometry checks in `family_geometry.py`. + +Credits remain with Ali Romman's #5439 odd-E8 geometry, the P112/E8 data, +the PR5464 polarized native phase tools, the original native/Clifford +compiler lineage, and the coded-native-caller real centralizing normalizers. +This assembly and its explicit whole-K contract used substantial OpenAI +Codex assistance. New material is Apache-2.0. No independent human or +proof-kernel acceptance is asserted. + +## 1. Actual fields, scalar coefficients and global coordinates + +The pinned NORMALIZERS data supply 112 distinct binary q labels and their +root columns. The roots split into fourteen eight-root sign cubes. For a +cube b, put B_b=M_b M_b^T/4 and K_b=I-B_b. Exact rational checks give +K_b^2=I; each row has four entries +-1/2, all joining opposite selector +parities. The two four-port classes each span a three-space with pairing +rank one, and the two three-spaces are orthogonal. + +A product cube has 512 owners. Define + + K_odd=(K1+K2+K3-K1 K2 K3)/2. + +The three factor matrices commute and square to I. Expanding the square +of their displayed majority polynomial gives I. The scalar K_odd is also +symmetric. Every row has twelve distinct one-factor entries of magnitude +1/4 and sixty-four distinct three-factor entries of magnitude 1/16. +The two support sets are disjoint since each K_b has zero diagonal. +Every nonzero entry reverses total selector parity. Thus each row has +exactly 76 nonzero coefficients and their absolute sum is seven. + +The actual product labels are concatenated triples in F2^27. Their global +span U is the 25-space of equal three-block parities. The code records an +explicit orthonormal basis of U, and takes physical coordinates by dotting +against it. This is one global I25 realization, shared by all cubes; no +local-20-to-global-25 free adapter is introduced. Every port has norm one +and differs from the characteristic vector of U. The latter is the raw +all-ones27 vector, whereas each base label has weight three or seven. + +For every product cube the two 256-port parity classes span S0,S1 with + + dim S0=dim S1=9, S0 perpendicular S1, + rank(B|S0)=rank(B|S1)=1, dim rad(S0)=dim rad(S1)=8. + +Their joint span has dimension ten. `family_geometry.py` checks all +1,404,928 actual norm-one noncharacteristic labels, all 5,488 nine-space +classes and all opposite-reader/source-basis incidences. The restricted +characteristic issue is explicit: every odd q represents the characteristic +functional within S9. The construction never requires a noncharacteristic +vector inside S9, and never tries to orthonormalize this degenerate S9. + +Use two independent fields X_p,Y_p per port p. There are no other independent +fields, no owned full-field scratch, no COPY and no CLEAR. Across the family +the product cubes partition the actual owner indices, so no independent +input is duplicated or identified between cube instances. + +## 2. Canonical frames for arbitrary degenerate subspaces + +All operator products below act rightmost first. The primitive convention is + + C_q=((1+i)I+(1-i)X_q)/2. + +Write R=C_[0,25), Q=C_0 and D=C_[1,25), so R=DQ. If the columns of G are +any full binary basis and A=G^-1, put + + K_G=D_J P_G, J=I+A^T A. + +Here the diagonal uses the retained compiler's Z4 quadratic convention. +For the first r columns spanning S, the actual native frame is + + Phi_(G,r)=K_G C_[0,r) K_G^-1. + +It is not necessary for the restricted form on S to be nondegenerate. +Its binary symplectic action sends the Z Lagrangian to + + L_S={(x,z): x in S and z+x in S-perp}. + +To check this directly, let B=G P_r G^T. On a Z input z the output X part +is x=Bz, and its Z part is z+JBz. Since J=I+G^-T G^-1, the vector formed +by adding x to that output Z part is z+G^-T G^-1 x. Its dot product with +every first-r basis column vanishes. Dimensions give exactly L_S. +The symplectic action of C, and therefore of Phi, is an involution; +the inverse frame has the same Lagrangian image. + +Consequently two constructions of the same S differ by a monomial map. +If S is contained in T, their transition has Gaussian rank + + 25-dim(L_S intersect L_T)=dim T-dim S. + +Indeed their intersection has x in S and z+x in T-perp, hence dimension +dim S+25-dim T. This proves all required rank and zero-rank statements +for every actual cube, not only for the root instance's tableaux. + +## 3. Literal source and reader paths + +Fix a source parity class S9. All sources in it and all opposite readers +will meet at one and the same literal canonical Phi_S9 word. Each source +q belongs to S9. Its line-to-S9 path costs H8. To emit this path, choose +a full flag whose first vector is q and first nine vectors span S9. +Monomial gauges connect its one- and nine-dimensional frames to the +declared canonical frames, and the only Gaussian child is C_[1,9). + +A reader q is orthogonal to S9 and has norm one. Therefore it is outside +S9 and its q-perp24 contains S9. The reader starts at ground, reaches +Phi_S9 by one H9, and leaves it by one H15 to a full flag beginning with +the identical ordered S9 basis and spanning that actual q-perp24. +The emitted word supplies every reader's actual endpoint flag. + +The source leaves S9 for canonical full R by one H16. Let + + T_G=R K_G R^-1. + +The source-exit word executes K_G^-1, then C_[9,25), then T_G, since + + R Phi_S9^-1=T_G C_[9,25) K_G^-1. + +No extra Gaussian is hidden in T_G; its exact monomial phase is given +in section 4. All other gauges are compiled as P/D/X/phase-only words. + +At the common cut, directly execute Y_r += K_odd[r,s] X_s for every +nonzero scalar coefficient. The two main banks are independent. X is +never modified by these ADDs, so every source read uses its original +geometric logical value. Every reader retains its arbitrary old value +with coefficient one. There is no need for a rank-one cache or any +owned helper, even though the scalar matrix between the classes is full +rank. The two parity directions use disjoint source/reader field sets +and are executed separately. Every ADD is at an actually identical frame, +not merely between containing or cross-orthogonal subspaces. + +The geometric endpoint is exactly + + X_s: Phi_[q_s] u_s -> R u_s, + Y_r: v_r -> Phi_(q_r-perp)(v_r+sum_s K_odd[r,s]u_s). + +Every 512-port cube thus uses 512 children of each of widths 8,9,15,16, +and 38,912 ordinary scalar ADDs, with no helper or owned field. + +## 4. Absolute phases without exponential dense columns + +The retained signed tableau fixes a Clifford operator up to scalar. +Every low-rank monomial gauge is checked with an exact sparse +Gaussian-integer zero-column evaluation that fixes this scalar as well. +For same-S9 gauges the sparse support remains at most 512: after changing +coordinates, both rank-nine Gaussian portions act inside the same prefix. +The normalization gauges below need at most two one-axis Gaussians. + +For any native full basis G, let a_j=G^-1 e_j and set + + d_j=floor(wt(a_j)/2) mod 2. + +If q_J is the diagonal's actual Z4 phase, XOR Hamming-weight expansion +modulo four gives + + q_J(y)+wt(G^-1 y)=wt(y)+2d.y mod4. + +The quadratic cross terms cancel. For each j, its remaining linear +coefficient is alpha_j+wt(a_j), with alpha_j=(1+wt(a_j)) mod2 in {0,1}; +this equals 1+2d_j modulo four. With a=(1-i)/2, + + R^-1|0>=a^25 sum_x i^wt(x)|x>, + K_G R^-1|0>=Z_d R^-1|0>, + T_G|0>=(-i)^wt(d)|d>. + +Furthermore T_G is monomial: R^-1 takes Z Paulis to the diagonal +Lagrangian {(z,z)}, K_G takes it to {(Gz,Gz)}, and R takes it back to +Z Paulis. Its exact signed tableau plus this absolutely normalized +column determines the emitted P/D/X/phase word universally. No 2^25 +state is allocated. `frame_tools.py` retains this analytic anchor. + +These generic arguments prove the compiler construction for every cube +and every flag satisfying the verified geometry. Default execution fully +corroborates all actual root-case gauges, including 512 reader-output +full-basis anchors, rather than sampling a few field pairs. + +## 5. Real normalizers and virtual-Q entry + +The geometric input line service above is not silently assumed free in +the normalized native F_K. We explicitly wrap arbitrary ground inputs. +For each physical q, construct an orthogonal binary G_i taking e0 to q. +If q_0=0 use the even transvection T_(e0+q). Otherwise choose j>0 with +q_j=0 and use T_(ej+q) T_(e0+ej). Such j exists because q is not the +ambient characteristic vector. + +For row j of G_i put z_j=(wt(row_j)-1)/2 modulo two and define + + L_i=Z_z P_Gi. + +This is a real signed orthogonal monomial. Orthogonality cancels every +quadratic cross coefficient in the weight identity + + wt(G_i^-1 x)-wt(x)=2z.x mod4. + +It follows that L_i R L_i^-1=R exactly, including absolute phase. +Checking orthogonality and the 25 linear coefficients proves the weight +identity for all 2^25 addresses; no address sampling is used. + +The actual ordinary normalized wrappers are + + input X: Phi_[q_i] L_i Q^-1, + input Y: L_i, + output X: L_i^-1, + output Y: D L_i^-1 Phi_(q_i-perp)^-1. + +Their monomiality follows from the corresponding line/hyperplane +Lagrangian incidences. Input X's literal defining word has two one-axis +Gaussian factors and is compiled with exact sparse absolute phase. +It is emitted and executed as an ordinary monomial; Q^-1 is virtual +inside this identity, not an additional unpriced Gaussian instruction. + +For the potentially high-rank reader-output wrapper let its endpoint +flag be Phi_V=K_v C_[0,24) K_v^-1. The exact low-rank expression is + + D L_i^-1 Phi_V^-1 + =Q^-1 L_i^-1 T_v C_24 K_v^-1, + T_v=R K_v R^-1. + +This follows by C_[0,24)^-1=R^-1 C_24 and [L_i,R]=0. The right side +has only two one-axis Gaussian factors plus phase-complete monomials. +Its signed tableau is checked against the defining left side, and its +absolute phase is compiled from the low-rank expression. Thus no +rank-24 dense zero column is needed and no projective phase is discarded. + +## 6. Normalized arbitrary-input endpoint + +Let x_i,y_i be the actual independent ground inputs. After input wrappers +the geometric logical values are exactly + + u_i=L_i Q^-1 x_i, v_i=L_i y_i. + +These are invertible functions of the original independent inputs; they +are not being renamed originals or assumed zero. The actual emitted +input-X monomial already puts its physical field at Phi_[q_i]u_i. + +Source output followed by its wrapper is + + L_i^-1 R L_i Q^-1 x_i = D x_i. + +Reader output followed by its wrapper is + + D y_i + sum_j K_odd[i,j] D L_i^-1 L_j Q^-1 x_j. + +Define, at actual field width f, + + (C_K,f)_ij=K_odd[i,j] L_i,f^-1 L_j,f. + +The complete normalized operator is therefore + + F_K=diag(D,D) L(C_K Q^-1). + +K_odd is a real symmetric involution and the L_i are real orthogonal. +Thus C_K^T=C_K, C_K^2=I and [C_K,R]=0. These facts follow by actual +operator similarity. They do not tensor the whole owner matrix: +scalar K_odd coefficients are applied once, and cancellation of adjacent +L_j,f L_j,f^-1 proves the square identity at every positive width. + +All 1,024 geometric original columns are explicitly interpreted in the +root-case word; the incoming-column and outgoing-row factor identities +above imply all 38,912 nonzero normalized operator blocks at once. No +sampling of cross-owner physical operators is used. + +The normalized source outputs are autonomous rank-24 D transforms of +their original inputs. Reader outputs remain the specified triangular +coupled transforms. The service is invertible and retains every original +input; a complete outer Gaussian caller and its larger productive jobs +must still be supplied before using any whole-caller target profile. + +## 7. All positive widths and complete local accounting + +Every single-copy identity includes its absolute phase. Tensor it +columnwise to f positive address columns. P and X lift as binary block +maps, D sums its Z4 phase over the columns, and a single-copy phase theta +becomes i^(f theta). Scalar owner coefficients are applied once per field. +No width-one sum relation has been extrapolated by taking a tensor power +of a sum. This proves the actual physical word and F_K endpoint for every f. + +The normalized root case has 512 fields of each X/Y role and profile + + paid {8:512,9:512,15:512,16:512}, + ordinary {ADD:38912,P:7680,D:7680,X:3072,phase:3072}. + +There are 42 literal monomial primitives and 76 scalar ADDs per owner, +in addition to its four correctly charged Gaussian paths. These are +nonrecursive work, not zero-work operations. Their address movement, +storage, precision and tape price remain eventual caller obligations. +No helper input, helper target, owned field, COPY or CLEAR is introduced. + +For v=112^3=1,404,928, concatenate the cube words in lexicographic order. +The whole-family profiles are + + paid {8:v,9:v,15:v,16:v}, + ordinary {ADD:76v,P:15v,D:15v,X:6v,phase:6v}. + +The number of actual main inputs is 2v=2,809,856. The Gaussian rank mass +is 48v. No smaller pairing rank is substituted for any physical child. + +At geometric logical opcode boundaries each source row has l1 one and +each reader has its old value plus distinct source coefficients of total +l1 seven. Hence all prefix row l1 values are at most eight, and scalar +denominator exponent is at most four. Physical charts and wrappers are +unitary, so independent input norm at most M gives field norms at most +M for sources and 8M for readers. This is a finite local growth constant, +not a complete recursive rounding-error, precision or outer-admission bill. + +Actual mutation controls detect a global phase i despite an identical +signed tableau, a wrong parity S9 frame (requiring rank-two transport), +and omission of a literal K ADD (changing an independent input column). + +## 8. Remaining scope + +This fills the local K-native construction gate. It does not provide H, +remove H by a global basis change, make the F3 factor totals freely +available, prove a decoder/reader chronology, or close the mixed-Q +E=I-H interface. No whole-caller profit or kappa improvement is claimed. +The earlier planning profile and separated-helper obstruction cannot +be reused as a completed budget for this changed primitive. diff --git a/research/odd-e8-whole-k-native/README.md b/research/odd-e8-whole-k-native/README.md new file mode 100644 index 0000000000..b9cdf41350 --- /dev/null +++ b/research/odd-e8-whole-k-native/README.md @@ -0,0 +1,115 @@ +# A complete native odd-E8 K component + +This package constructs the full block-diagonal `K_odd` component from Ali +Romman's [#5439](https://github.com/CrocSwap/integer-mult-bounds/pull/5439). +It retains every original source and reader field and emits every local +Gaussian path, ordinary wrapper, scalar coefficient and absolute phase. +The construction uses two orthogonal nine-dimensional coframes in each +512-port cube, with direct same-frame ADDs and no helper, owned field, +COPY or CLEAR. It complements the directed `H_ab` component in +[#5464](https://github.com/CrocSwap/integer-mult-bounds/pull/5464). + +This is a local native construction. It supplies K, including its normalized +forward and backward interfaces. H acquisition, compatible K/H chronology, +the whole caller, complete precision/storage work and kappa admission remain +open. No leaderboard improvement or new kappa is claimed. + +For `Q=C_0`, `D=C_[1,25)` and the explicitly emitted real normalizers `L_i`, +the forward word on arbitrary independent ground-chart inputs is + +``` +F_K = diag(D,D) L(C_K Q^-1), +C_K = diag(L_i^-1) K_odd diag(L_i). +``` + +Here `L(A)` denotes the two-bank lower shear. Thus sources exit as `D x_i`, +and readers as `D(y_i + sum_j K_odd[i,j] L_i^-1 L_j Q^-1 x_j)`. +Each `L_i` commutes with the full Gaussian `R=DQ`, and `C_K` is a symmetric +involution commuting with R. The reader endpoint is coupled to the sources. + +The source's virtual `Q^-1` occurs inside an emitted ordinary monomial +`Phi_[q_i] L_i Q^-1`; it is not an assumed incoming Gaussian service. The +reader's final `D L_i^-1 Phi_(q_i^perp)^-1` is likewise emitted as an +ordinary monomial, with a generic absolute-phase proof. The word works at +every positive field width. Address operators tensor-lift; owner scalar +coefficients are applied once, and a phase opcode theta lifts to `i^(f theta)`. + +The complete paid profile per cube is 512 children of each width 8, 9, 15 +and 16. Per owner port (one X and one Y field), ordinary work is 76 ADD, +15 P, 15 D, 6 X and 6 phase opcodes. The intermediate coefficient l1 peaks +are 1 on X and 8 on Y, with scalar denominator exponent 4. Unitary address +maps therefore give field l2 growth at most eight times the largest input +field norm. These local constants do not replace a caller precision bill. + +`K-PROGRAM.json.gz` fully emits cube `(0,0,0)`. `K-TEMPLATE.json` describes +the literal constructor over all `14^3=2744` disjoint cubes. The generic +Lagrangian and phase arguments are in [PROOF.md](PROOF.md); the independently +checked all-family geometry is [FAMILY.json](FAMILY.json) and +[FAMILY-PROOF.md](FAMILY-PROOF.md). This structured forall word avoids +storing 106,774,528 ADD events. A second, separately reviewed extreme cube +was checked during development; it is additional finite evidence. + +The no-erasure word also gives an emitted backward companion, + +``` +B_K = diag(D,D) U(-Q C_K). +``` + +`B-PROGRAM.json.gz` transforms each gate by inverse transpose in the same +chronological order, then includes every ordinary boundary normalization. +It does not require `[C_K,Q]=0`. Its paid profile is unchanged; its ordinary +profile per owner port is 76 ADD, 15 P, 15 D, 13 X and 6 phase. Details are +in [BACKWARD-PROOF.md](BACKWARD-PROOF.md). + +The independent [reviewer](independent_review.py) does not call the word +generator or phase compiler. It compares all 262,144 scalar entries, +replays all 1,024 independent logical columns, and checks geometry, charts, +normalizer congruences and literal invoices. Small-dimensional exhaustive +tests corroborate the separately reviewed generic phase and Lagrangian +proofs. The same replay independently compares every backward instruction +with its exact gatewise inverse transpose and checks all boundary masks. +[REVIEW.md](REVIEW.md) states the scope of that audit. It is a +separate AI-worker review, not independent human or formal-kernel acceptance. +The backward verifier also runs four executed controls on actual emitted +operations: changed K coefficient, overwritten source, wrong source chart, +and a phase-i change invisible to signed tableaux. + +Python 3.12 and its standard library suffice. `VERIFY.json` registers eight +bounded, read-only normal/optimized commands for the family geometry, +forward word, independent review and backward word. With the repository +runner, use: + +```sh +python3.12 -B scripts/research_package.py --package research/odd-e8-whole-k-native +python3.12 -B scripts/check_research_commit.py --package research/odd-e8-whole-k-native +``` + +Direct `--write` flags are reserved for explicit artifact authoring. +Scientific words compare canonical decompressed JSON, avoiding dependence +on gzip container bytes or local paths. Exact source pins and credits are +in [SOURCES.json](SOURCES.json). Original task provenance, scope change and +remaining decisive obligations are in [TASK.json](TASK.json). + +Credit Ali Romman for the odd-E8 direct-sum family and product-cube K; +Dugongue / #4929 and Dillon Amburgey for the coded-native normalizers; +Cao Yifan for the retained P112 native construction; and Cinna Davis, zxv, +Jacob Alan Sussman and the native, Clifford, compiler and analytic lineage +credited by those sources. The exact phase tools are retained from #5464. +Standard Clifford algebra, transposition and tensor identities are not +claimed as new general identities. + +Prepared for THU New Media Research Center (@thu-nmrc), with substantial +OpenAI Codex assistance. Apache-2.0. + +## Open next questions + +Can a complete native H service use these actual K paths? The first test is +one chronological K-plus-H word preserving arbitrary old reader data and +all original source exits, with paid source acquisition and every return. +The missing compatible H service and source/reader flag schedule block a +complete supplier; scalar coefficients and static containment do not close it. + +Can that completed supplier improve the full caller? Install the exact +normalized contracts, prove all original-input endpoints, then charge every +boundary, central request, precision, storage and compiler obligation. The +current coupled K endpoints and local savings alone give no new kappa. diff --git a/research/odd-e8-whole-k-native/REVIEW.md b/research/odd-e8-whole-k-native/REVIEW.md new file mode 100644 index 0000000000..40bcbadace --- /dev/null +++ b/research/odd-e8-whole-k-native/REVIEW.md @@ -0,0 +1,134 @@ +# Independent scientific review of the normalized whole K constructor + +This review accepts the construction as a phase-complete, arbitrary-ground-input +local K module with the explicitly stated operator-valued coefficient code. +It supports extending the earlier polarized cross-primitive contribution to a +whole local K service, subject to the remaining caller interfaces below. It is +not evidence of repository acceptance or a new integer-multiplication exponent. + +## The endpoint actually proved + +At owner width f, every original X_i=x_i and Y_i=y_i is an arbitrary independent +physical ground-chart field. Let R=C_[0,25), Q=C_0, D=C_[1,25). Each emitted +ordinary input wrapper gives geometric coordinates u_i=L_i Q^-1 x_i and +v_i=L_i y_i. This is an invertible description of the actual original fields; +the product Phi_[q_i] L_i Q^-1 itself is emitted as a monomial. It does not +receive a supplied Q^-1 transform for free. + +The source endpoint is D x_i. The reader endpoint is + + D(y_i + sum_j K_odd[i,j] L_i^-1 L_j Q^-1 x_j). + +Thus F_K=diag(D,D) L(C_K Q^-1), where + + (C_K,f)_ij=K_odd[i,j] L_i,f^-1 L_j,f. + +The scalar coefficients K_odd[i,j] are applied once at width f. They are not +replaced by their f-th powers. Real orthogonal similarity proves C_K symmetric +and involutory; the exact commutation L_i R=R L_i proves [C_K,R]=0. No proof +that [C_K,Q]=0 has been supplied, and no such commutation may be inferred from +full-R commutation. The original mixed-Q E caller therefore remains open. + +## Generic rank mechanism + +For a full binary basis G and A=G^-1, K_G=D_(I+A^T A) P_G and +Phi_(G,r)=K_G C_[0,r) K_G^-1. Its Z-Lagrangian image is exactly + + L_S={(x,z): x in S, z+x in S-perp}. + +The direct symplectic calculation in PROOF.md is correct. It does not assume +that S is nondegenerate. For S contained in T the intersection has dimension +dim(S)+25-dim(T), so the physical transition rank is dim(T)-dim(S). Two +choices of frame for the identical S differ by a monomial, even for the +rank-one, radical-eight S9 occurring here. + +The prior independent all-family geometry audit verified every one of the +1,404,928 actual q labels, the 5,488 parity-class S9 spaces, and all 12,644,352 +reader/source-basis orthogonality incidences. These geometric facts and the +generic frame proof cover the 2,744-cube constructor. The two finite phase +instances reviewed here are additional checks, not the logical basis for +extrapolation to the whole family. + +Source line to S9 costs H8; S9 to R costs H16. Reader ground to the identical +literal S9 costs H9; S9 to its actual q-perp24 costs H15. Direct scalar ADDs +therefore carry the entire cross-parity K support without a helper bank. The +two direction passes use disjoint source/reader fields. + +## Absolute phase and ordinary entry/exit + +The full-conjugate T_G=R K_G R^-1 is monomial. Writing +d_j=floor(wt(G^-1 e_j)/2) mod2, its exact zero column is +T_G|0>=(-i)^wt(d)|d>. The displayed Z4 weight expansion proves this identity +for arbitrary G; the exact signed tableau then fixes the entire monomial. +The sparse gauge compiler separately retains its actual absolute zero column. + +The source full exit identity is a literal cancellation: + + R Phi_S^-1 = (R K_G R^-1) C_[9,25) K_G^-1. + +For a reader flag Phi_V=K_v C_[0,24) K_v^-1, the wrapper identity + + D L_i^-1 Phi_V^-1 = Q^-1 L_i^-1 (R K_v R^-1) C_24 K_v^-1 + +follows exactly from C_[0,24)^-1=R^-1 C_24 and [L_i,R]=0. Its right side +has two one-axis Gaussians and hence permits an exact sparse phase check. +There is no rank-24 dense-column approximation and no unpriced Gaussian +inside the executed ordinary wrapper. The emitted program includes all four +per-port normalized wrappers, including the source virtual-Q input. + +For the real normalizer L_i=Z_z P_G, orthogonality of G cancels all Z4 cross +terms and row weights give the remaining linear coefficients. This proves +L_i R L_i^-1=R with absolute phase. The independent checker verifies every +coefficient for every root-case owner, not sampled physical addresses. + +Independent exhaustive tests over all 175 matrices in GL(1), GL(2), GL(3) +corroborate the full-conjugate absolute anchor. The same matrices give 692 +L_S equality checks and 1,719 nested-rank checks, including degenerate S. +These tests supplement the algebraic proof; they do not establish the general +claim by themselves. + +## Independent replay and literal bill + +independent_review.py imports neither core.py nor frame_tools.py. It rebuilds +all base K matrices from the pinned original root columns and compares every +one of the 262,144 root-cube K entries with the emitted matrix. It then parses +the actual executable program, not the author summary. The checker tracks all +1,024 independent geometric input columns, all field names and literal charts, +every direct ADD coefficient, all source preservation, the two paid paths on +every field, and all four normalized wrappers. An omitted actual ADD changes +an independent original source column and is detected. + +The exact bill is, per owner, + + paid H8 + H9 + H15 + H16, + ordinary 76 ADD + 15 P + 15 D + 6 X + 6 phase. + +The ordinary bill deliberately includes identity X/phase instructions emitted +by the compiler. No reduction in this literal count is assumed. There are no +owned fields, helpers, COPY or CLEAR instructions. At v=112^3, the constructor +has 2v original inputs, v calls of each paid rank, Gaussian rank mass 48v, and +106,774,528 scalar ADDs. All address movement, storage and precision costs of +these ordinary operations remain caller obligations. + +The logical source row l1 is one; a reader prefix is its original value plus +distinct source coefficients of total absolute sum at most seven. Physical +charts and wrappers are unitary, so this gives a finite local norm-growth +bound eight. It is not a complete recursive rounding-error admission. + +## Remaining scientific gates + +The construction changes the old main paid paths and the effective code to +the explicitly conjugated C_K. Fixed-old-path separated-helper obstructions +cannot dismiss it, but old caller identities cannot be imported unchanged. +H, actual F3 factor acquisition and decoding chronology, the mixed-Q E +interface, full recursive work/precision/storage, and a positive complete +caller invoice are all still required. The relaxed positive 14,720-channel +H grant is not an implemented H module or an exponent result. + +The result is worth presenting as a whole normalized local K primitive and +an explicit tensor-width-safe operator-valued interface. Its value is the +removal of a previously unknown native construction gate with an explicit paid +profile and no helpers. Its significance must be evaluated within that scope. + +This independent AI review is separate from the author implementation. It is +not an independent human mathematical review or proof-kernel certification. diff --git a/research/odd-e8-whole-k-native/SOURCES.json b/research/odd-e8-whole-k-native/SOURCES.json new file mode 100644 index 0000000000..97077fb5a0 --- /dev/null +++ b/research/odd-e8-whole-k-native/SOURCES.json @@ -0,0 +1,62 @@ +{ + "base_commit": "32890bc5de034ab8fc93ac88ead7279a6a416d04", + "files": [ + { + "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602", + "path": "docs/research/agent-task-catalog.json", + "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72", + "usage": "provenance" + }, + { + "git_blob": "fc3d4ba105e1f097d0d7d051a308281e86ab1446", + "path": "certificates/selected-result.json", + "sha256": "66974efdced4083c00025f97d95d83909a226cdf801edb9301c195c6641f6903", + "usage": "provenance" + }, + { + "git_blob": "bca92c222c395d3d75c047fbb678f3cd0947c60f", + "path": "research/coded-native-caller/NORMALIZERS.json", + "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da", + "usage": "provenance" + }, + { + "git_blob": "166841a037f069249f6f7f6dedb89248812f59e2", + "path": "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py", + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "usage": "provenance" + } + ], + "frozen_input_policy": "Runtime vendor bytes are checked by their exact source SHA256; all generated proof artifacts compare decompressed canonical content.", + "independent_family_geometry": { + "proof": "FAMILY-PROOF.md", + "proof_sha256": "d3771a05a6e3a33c537d06f346e5f9232356ce919bc6ede412e201e71920d2bf", + "receipt": "FAMILY.json", + "sha256": "898f8a7cad6dd65ab926662b0395fa03fb4b7fa434ad17ca5f746ff5e9359f20", + "usage": "Independent all2744 cube binary geometry and literal scalar profiles, with a portable checker adapted for same-directory inputs and read-only default." + }, + "mathematical_predecessor": { + "author": "Ali Romman (@aliromman)", + "head": "e6d50e7ebd0bb1fd4f388930df78df696e56b404", + "pr": 5439, + "usage": "Definition of the odd-E8 direct sum, product-cube K and omitted H. No unmerged Git object or network read is required by any replay." + }, + "phase_tools_predecessor": { + "head": "c9875dccd281e6fe7d9b28a38f6c385141df0950", + "origin": "research/odd-e8-polarized-native/frame_tools.py", + "pr": 5464, + "sha256": "e5b2ea1f60d554b3a285569602360c663ee8b387350424678b3bd0b0b5432bf4", + "usage": "Phase tools retained verbatim from the already committed polarized package at this exact older #5464 commit. This new package does not depend on its own PR head or on any network read." + }, + "schema_version": 1, + "scope": "Complete local native K forward/backward components only; no new selected result, H producer or outer-caller admission.", + "vendored_runtime_inputs": { + "inputs/NORMALIZERS.json": { + "origin": "research/coded-native-caller/NORMALIZERS.json", + "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da" + }, + "inputs/clifford_exact.py": { + "origin": "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py", + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + } + } +} diff --git a/research/odd-e8-whole-k-native/TASK.json b/research/odd-e8-whole-k-native/TASK.json new file mode 100644 index 0000000000..153112da10 --- /dev/null +++ b/research/odd-e8-whole-k-native/TASK.json @@ -0,0 +1,78 @@ +{ + "actual_scope": "Construct the entire block-diagonal odd-E8 K native service with real physical ground entry, normalized forward and backward two-bank contracts, exact phases, all main paths and no helpers/owned/COPY/CLEAR. Provide a structured forall2744 constructor rather than unexpanded scalar evidence.", + "ai_assistance": "Substantial OpenAI Codex assistance by a lead and separate geometry, physical-compiler and independent-review agents. This is not independent human or formal-kernel review.", + "author": "THU New Media Research Center (@thu-nmrc)", + "base_commit": "32890bc5de034ab8fc93ac88ead7279a6a416d04", + "bottleneck_link": "Whole K was a missing native component for testing physical H/F3 installation. This package supplies exact F_K/B_K interfaces and invoices, allowing that next test without assuming free native K or inherited main flags.", + "budget_minutes": 60, + "evidence": "K-MODULE.json; K-PROGRAM.json.gz; K-TEMPLATE.json; FAMILY.json; INDEPENDENT-REVIEW.json; VERIFY-RESULT.json; B-MODULE.json; B-PROGRAM.json.gz; written proofs.", + "open_questions": [ + { + "blocked_by": "A complete compatible native H service and its global source/target flag schedule remain unresolved.", + "first_step": "Emit one actual K-plus-H chronological word with arbitrary old reader data, all original source exits, same-data coefficient demands and a complete charged invoice.", + "question": "Can all of H be produced natively with actual flags compatible with these F_K/B_K contracts?", + "why_it_matters": "Ordinary scalar H or static subspace containment does not supply a same-frame Gaussian service, and direct old main bursts can erase local K savings." + }, + { + "blocked_by": "Missing H service, global chronology and complete caller accounting.", + "first_step": "Install the exact normalized contracts in the full typed caller, prove every original-input endpoint and charge all boundaries, central jobs and precision obligations.", + "question": "Can the completed supplier fit the outer caller and its full precision, work and storage limits?", + "why_it_matters": "The local native K component alone does not establish new kappa or a productive whole caller. Coupled endpoints are not independent Gaussian targets." + } + ], + "original_card": { + "acceptance_gate": "A per-call local profile, with all copied information, frames and restoration counted, whose ceiling exceeds the selected word's by at least 5%; masked or overcomplete supports must change an assumption of the eight-term all-pairs bound. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "allowed_variations": [ + "One masked, overcomplete or block decoder family with exact labels and supports.", + "A scoped lower bound on effective rank for one alphabet.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "bottleneck_link": "Rank-1 children are about half of recursive cost; the selected word's effective child rank is about 3.9. Larger-rank delivery lowers recursive cost per unit of paid mass.", + "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin. Ideal budget: rank-16 delivery is 2.31x (levers.py).", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "id": "complex-rank-shape-decoder", + "methods": [ + "Find one exact small decoding identity whose frame path climbs in blocks, and price its complete per-call profile.", + "Bound the best effective child rank achievable for one fixed support alphabet, including copies, frames and restoration." + ], + "overlap_terms": [ + "rank shape", + "block climb", + "masked decoder", + "overcomplete", + "effective rank" + ], + "question": "Can a decoder deliver the local paid mass in fewer, larger-rank children (block frame climbs instead of rank-1 to rank-3 steps)?", + "scope_change_triggers": [ + "Repacking idle remainders of an unchanged word (covered by the packing ceiling).", + "Repeating the eight-term all-pairs search inside its proved scope.", + "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.", + "Searching below C=40 in the #2017 Eisenstein binary scalar-rectangle or fixed-support block-linear additive pairing model; specify a changed premise instead. This bound does not cover every complex decoder.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/complex-decoder-field-extension-seed44/README.md", + "research/complex-frame-pair-decoders/README.md", + "research/selected-k8-unrestricted-ends/README.md", + "research/eisenstein-reduction-copy-floor/README.md" + ] + }, + "outcome": "partial", + "priority_revision": 7, + "schema_version": 1, + "scope_change_reason": "Two orthogonal nine-space product-cube parity classes permit direct same-frame reads of the complete K_odd scalar word. The ordinary virtual-Q input and qperp output normalization closes the actual F_K contract, while a no-erasure inverse-transpose word supplies actual B_K. This remains a component; the complete H producer and compatible whole-caller invoice are not supplied.", + "scope_status": "changed", + "stop_rule": "Freeze the full local K word, proof and independent review. Expansion requires an actual compatible K/H chronology and a favorable complete invoice; do not promote relaxed H budgets or local K savings to a frontier result.", + "task_id": "complex-rank-shape-decoder" +} diff --git a/research/odd-e8-whole-k-native/VERIFY-RESULT.json b/research/odd-e8-whole-k-native/VERIFY-RESULT.json new file mode 100644 index 0000000000..2d7bb9573a --- /dev/null +++ b/research/odd-e8-whole-k-native/VERIFY-RESULT.json @@ -0,0 +1,41 @@ +{ + "distinct_paid_tableau_rank_checks": 1028, + "executed_mutations": { + "actual_ADD_coefficient_changed": true, + "actual_source_overwrite": true, + "actual_wrong_source_chart": true, + "same_tableau_actual_phase_i": true + }, + "growth": { + "X": { + "max_dyadic_denominator_exponent": 0, + "peak_l1": "1" + }, + "Y": { + "max_dyadic_denominator_exponent": 4, + "peak_l1": "8" + } + }, + "independent_scalar_columns": 1024, + "new_kappa": false, + "ordinary_literal_profile": { + "ADD": 38912, + "D": 7680, + "P": 7680, + "X": 3072, + "phase": 3072 + }, + "paid_path_applications": 2048, + "paid_profile": { + "8": 512, + "9": 512, + "15": 512, + "16": 512 + }, + "scalar_entries_independently_checked": 262144, + "schema": "odd-E8-whole-K-emitted-verification/v1", + "scientific_program_payload_sha256": "98941b295d428462b82dae52a369de97dcbf5be1dd7a369f6c495cda5fc6ac8a", + "scope": "Emitted root cube, integer scalar K, exact paid tableaux/ranks, literal chronology and counts. Generic all-width and all-cube phase proofs remain PROOF.md; this is not a complete caller or frontier admission.", + "status": "PASS", + "wrong_parity_chart_transport_rank": 2 +} diff --git a/research/odd-e8-whole-k-native/VERIFY.json b/research/odd-e8-whole-k-native/VERIFY.json new file mode 100644 index 0000000000..f4a2fe4d1f --- /dev/null +++ b/research/odd-e8-whole-k-native/VERIFY.json @@ -0,0 +1,109 @@ +{ + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/family_geometry.py" + ], + "checks": "All2744 cube scalar/orthogonal nine-space geometry and real physical port ranks.", + "timeout_seconds": 150 + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-W", + "error", + "-B", + "{package}/family_geometry.py" + ], + "checks": "All2744 cube scalar/orthogonal nine-space geometry and real physical port ranks.", + "timeout_seconds": 150 + }, + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/core.py" + ], + "checks": "Exact forward root cube with every literal phase, paid path, virtual-Q input and normalized reader exit; structured forall-family template.", + "timeout_seconds": 150 + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-W", + "error", + "-B", + "{package}/core.py" + ], + "checks": "Exact forward root cube with every literal phase, paid path, virtual-Q input and normalized reader exit; structured forall-family template.", + "timeout_seconds": 150 + }, + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/independent_review.py" + ], + "checks": "Independent emitted 512x512 K,1024 columns, charts, counts and generic phase/Lagrangian corroboration.", + "timeout_seconds": 150 + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-W", + "error", + "-B", + "{package}/independent_review.py" + ], + "checks": "Independent emitted 512x512 K,1024 columns, charts, counts and generic phase/Lagrangian corroboration.", + "timeout_seconds": 150 + }, + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/backward.py" + ], + "checks": "Literal backward inverse-transpose and all boundary factors; actual forward coefficient/chart/source/phase mutants; full paid/ordinary invoice.", + "timeout_seconds": 150 + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-W", + "error", + "-B", + "{package}/backward.py" + ], + "checks": "Literal backward inverse-transpose and all boundary factors; actual forward coefficient/chart/source/phase mutants; full paid/ordinary invoice.", + "timeout_seconds": 150 + } + ], + "inputs": [], + "python": "3.12", + "requirements": [], + "schema_version": 1, + "status": "ready" +} diff --git a/research/odd-e8-whole-k-native/backward.py b/research/odd-e8-whole-k-native/backward.py new file mode 100644 index 0000000000..eb51127fce --- /dev/null +++ b/research/odd-e8-whole-k-native/backward.py @@ -0,0 +1,145 @@ +"""Literal inverse-transpose native K companion; default is read-only. + +--write authors B-PROGRAM/B-MODULE, never the frozen forward science. +""" +from pathlib import Path +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +import argparse,gzip,importlib.util,json,sys +HERE=Path(__file__).resolve().parent +sys.dont_write_bytecode=True +def need(ok,why): + if not ok:raise ValueError(why) +def load(name,path): + spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);sys.modules[name]=m;spec.loader.exec_module(m);return m +def calculate(root): + verify=load('wholeK_backward_preflight',root/'verify.py');verification=verify.calculate(root) + need(json.loads(json.dumps(verification))==json.loads((root/'VERIFY-RESULT.json').read_bytes()),'frozen forward executed-mutant preflight') + original=json.loads(gzip.decompress((root/'K-PROGRAM.json.gz').read_bytes())) + original_digest=sha256((json.dumps(original,sort_keys=True,separators=(',',':'))+'\n').encode()).hexdigest() + ce=load('wholeK_backward_primitive',root/'inputs/clifford_exact.py') + n=original['axis_dimension'];ports=original['port_order'];olddefs=original['definitions'];definitions={} + def define(word): + word=json.loads(json.dumps(word));key=sha256(json.dumps(word,separators=(',',':')).encode()).hexdigest();definitions.setdefault(key,word);return key + def conjugate(word): + out=[] + for e in word: + if e[0]=='D':out.append(['D',e[1],[(-a)%4 for a in e[2]]]) + elif e[0]=='phase':out.append(['phase',(-e[1])%4]) + else:need(e[0]in('P','X'),'no Gaussian hidden in monomial');out.append(e) + return out + def literal(word): + value=ce.ident(n) + for e in word: + if e[0]=='P':part=ce.perm(n,e[1]) + elif e[0]=='D':part=ce.diag(n,e[1],e[2]) + elif e[0]=='X':part=ce.xgate(n,e[1]) + elif e[0]=='phase':part=ce.Op(n,ce.identity(n),[tuple(e)]) + else:need(e[0]=='C','known primitive');part=ce.cgate(n,e[1],e[2]) + value=value.then(part) + return value + translated={};checks=0 + def translate_path(path): + nonlocal checks + key=json.dumps(path,sort_keys=True,separators=(',',':')) + if key not in translated: + pre=conjugate(olddefs[path['before_monomial']]);post=conjugate(olddefs[path['after_monomial']]);axes=path['child_axes'];mask=sum(1<>a&1];positive=ce.fourier(sn,axes);inverse=positive.adjoint();compiled=positive.then(ce.xgate(sn,mask)) + need(inverse.tab==compiled.tab,'positive-child inverse signed tableau') + for x in range(1< E^-T. Real scalar ADD swaps roles and negates coefficient. Monomial becomes complex conjugate. C_minus child is emitted as positive C_plus followed by X_axis_mask.', + 'boundary':'Input X Q^-2; output both banks D^2 then output X Q^2. Consecutive X-bank output masks are literally composed into X_all25.', + 'normalized_endpoint':'B_K=diag(D,D) U(-Q C_K), without requiring [C_K,Q]=0', + 'all_widths':'One-copy address maps tensor-lift; phase theta -> i^(f theta). Owner scalar coefficients transposed/negated once, never raised to width f.'} + canonical=(json.dumps(payload,sort_keys=True,separators=(',',':'))+'\n').encode();encoded=gzip.compress(canonical,mtime=0) + summary={'schema':'odd-E8-whole-K-backward-native/v1','status':'PASS','forward_scientific_payload_sha256':original_digest, + 'backward_scientific_payload_sha256':sha256(canonical).hexdigest(),'paid_profile':dict(sorted(paid.items())), + 'ordinary_literal_profile':dict(sorted(ordinary.items())),'distinct_conjugated_paid_paths':checks, + 'all_independent_scalar_columns':1024,'small_dense_child_inversion_cases':primitive_checks, + 'actual_rank8_word_absolute_phase_checked':True,'normalized_endpoint':payload['normalized_endpoint'], + 'helpers':0,'owned_fields':0,'COPY':0,'CLEAR':0,'new_kappa':False, + 'scope':'Literal backward native K companion, including ordinary boundaries. It does not supply H or close/admit an outer caller.'} + return summary,payload,encoded +def main(): + ap=argparse.ArgumentParser();ap.add_argument('--package',type=Path,default=HERE);ap.add_argument('--write',action='store_true');args=ap.parse_args();root=args.package.resolve() + summary,payload,encoded=calculate(root) + if args.write: + (root/'B-MODULE.json').write_text(json.dumps(summary,sort_keys=True,indent=2)+'\n');(root/'B-PROGRAM.json.gz').write_bytes(encoded) + else: + need(json.loads((root/'B-MODULE.json').read_bytes())==json.loads(json.dumps(summary)),'frozen backward semantic receipt') + need(json.loads(gzip.decompress((root/'B-PROGRAM.json.gz').read_bytes()))==json.loads(json.dumps(payload)),'frozen backward actual word') + print('PASS whole-K literal backward native; columns1024; '+summary['backward_scientific_payload_sha256']) +if __name__=='__main__':main() diff --git a/research/odd-e8-whole-k-native/backward_independent.py b/research/odd-e8-whole-k-native/backward_independent.py new file mode 100644 index 0000000000..3d71668140 --- /dev/null +++ b/research/odd-e8-whole-k-native/backward_independent.py @@ -0,0 +1,85 @@ +"""Independent read-only exact inverse-transpose stream correspondence.""" +from pathlib import Path +from hashlib import sha256 +from collections import Counter +import gzip, json + +ROOT = Path(__file__).resolve().parent + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def calculate(package): + forward_raw = gzip.decompress((package / 'K-PROGRAM.json.gz').read_bytes()) + backward_raw = gzip.decompress((package / 'B-PROGRAM.json.gz').read_bytes()) + forward_raw = (json.dumps(json.loads(forward_raw), sort_keys=True, separators=(',', ':')) + '\n').encode() + backward_raw = (json.dumps(json.loads(backward_raw), sort_keys=True, separators=(',', ':')) + '\n').encode() + need(sha256(forward_raw).hexdigest() == '98941b295d428462b82dae52a369de97dcbf5be1dd7a369f6c495cda5fc6ac8a', 'fixed independently reviewed forward payload') + need(sha256(backward_raw).hexdigest() == 'f6b26f28f2a8f2dcfbf81f98c7ca18f967384b7b61518766494f8e821d5bf56f', 'fixed backward payload') + F, B = json.loads(forward_raw), json.loads(backward_raw) + ports = F['port_order'] + need(B['port_order'] == ports and B['axis_dimension'] == 25, 'identical original fields') + fields = {(r, p) for r in ('X', 'Y') for p in ports} + defsF, defsB = F['definitions'], B['definitions'] + for key, word in defsB.items(): + need(sha256(json.dumps(word, separators=(',', ':')).encode()).hexdigest() == key, 'backward word address') + def conjugate(word): + out = [] + for gate in word: + if gate[0] == 'D': + out.append(['D', gate[1], [(-a) % 4 for a in gate[2]]]) + elif gate[0] == 'phase': + out.append(['phase', (-gate[1]) % 4]) + else: + need(gate[0] in ('P', 'X'), 'original executable monomial contains no child') + out.append(gate) + return out + programF, programB = F['program'], B['program'] + need(len(programB) == len(programF) + 3 * len(ports), 'only three literal boundary gates per port added') + for p, gate in zip(ports, programB[:len(ports)]): + need(gate[:3] == ['BOUNDARY_MONOMIAL', 'X', p] and defsB[gate[3]] == [['X', 1]], 'actual input Q^-2 boundary') + for p, gateX, gateY in zip(ports, programB[-2*len(ports)::2], programB[-2*len(ports)+1::2]): + need(gateX[:3] == ['BOUNDARY_MONOMIAL', 'X', p] and defsB[gateX[3]] == [['X', (1 << 25) - 1]], 'actual fused output-X D²Q² boundary') + need(gateY[:3] == ['BOUNDARY_MONOMIAL', 'Y', p] and defsB[gateY[3]] == [['X', ((1 << 25) - 1) ^ 1]], 'actual output-Y D² boundary') + counts, paid = Counter(), Counter() + for old, new in zip(programF, programB[len(ports):-2*len(ports)]): + kind = old[0] + need(new[0] == kind, 'same literal chronology and opcode') + if kind == 'MONOMIAL': + need(new[1:3] == old[1:3] and defsB[new[3]] == conjugate(defsF[old[3]]), 'every ordinary monomial is actual complex conjugate') + elif kind == 'PAID_PATH': + need(new[1:3] == old[1:3] and new[3:5] == ['conjugate:' + old[3], 'conjugate:' + old[4]], 'actual inverse-transpose path charts') + a, b = old[5], new[5] + need(b['rank'] == a['rank'] and b['child_axes'] == a['child_axes'], 'same paid child rank and axes') + need(defsB[b['before_monomial']] == conjugate(defsF[a['before_monomial']]), 'before monomial exact conjugate') + mask = sum(1 << j for j in a['child_axes']) + need(defsB[b['after_monomial']] == [['X', mask]] + conjugate(defsF[a['after_monomial']]), 'literal positive-child inverse X mask included at correct cut') + else: + need(kind == 'ADD', 'no extra/noninvertible/owned opcode') + need(new == ['ADD', old[3], old[4], old[1], old[2], -old[5], old[6], 'conjugate:' + old[7]], 'every actual ADD inverse transpose swaps roles and negates coefficient once') + for gate in programB: + need((gate[1], gate[2]) in fields, 'only original fields used') + if gate[0] in ('MONOMIAL', 'BOUNDARY_MONOMIAL'): + word = defsB[gate[3]] + need(all(x[0] in ('P', 'D', 'X', 'phase') for x in word), 'backward wrappers ordinary') + counts.update(x[0] for x in word) + elif gate[0] == 'PAID_PATH': + paid[gate[5]['rank']] += 1 + for key in ('before_monomial', 'after_monomial'): + counts.update(x[0] for x in defsB[gate[5][key]]) + else: + need(gate[0] == 'ADD' and (gate[3], gate[4]) in fields, 'all ADD sources original') + counts['ADD'] += 1 + need(paid == {8: 512, 9: 512, 15: 512, 16: 512}, 'actual backward paid bill') + need(counts == {'ADD': 38912, 'P': 7680, 'D': 7680, 'X': 6656, 'phase': 3072}, 'actual backward ordinary bill including fused masks') + result = {'status': 'PASS', 'schema': 'independent-whole-K-backward-relative-word/v1', + 'forward_science': sha256(forward_raw).hexdigest(), 'backward_science': sha256(backward_raw).hexdigest(), + 'original_fields': len(fields), 'original_instructions_matched': len(programF), + 'boundary_instructions': 3 * len(ports), 'paid_profile': dict(sorted(paid.items())), + 'ordinary_profile': dict(sorted(counts.items())), 'helpers': 0, 'owned_fields': 0, + 'scientific_basis': 'Every actual F gate was checked against its exact same-chronology E^-T replacement. C_axes^-1=C_axes X_mask, monomial E^-T=conj(E), real ADD inverse transpose reverses and negates. Boundary J A² F^-T J^-1=A U(-Q C_K) uses no [C_K,Q].', + 'scope': 'No dense whole operator comparison; this is an exact gatewise mathematical correspondence, depending on the independently reviewed F word. It does not construct H, close E/caller, price precision/storage or claim kappa.'} + return result diff --git a/research/odd-e8-whole-k-native/core.py b/research/odd-e8-whole-k-native/core.py new file mode 100644 index 0000000000..9d190e7b48 --- /dev/null +++ b/research/odd-e8-whole-k-native/core.py @@ -0,0 +1,228 @@ +"""Whole odd-E8 K native template; phase-complete emitted root cube. + +All 14^3 product cubes use this same constructor with literal cube indices. +The default replay emits/checks cube(0,0,0); --cube a,b,c checks another +instance. Global geometry and the generic proof justify the structured +forall-family word without expanding106774528 ordinary ADD instructions. + +Credits: Ali Romman's #5439 geometry; PR5464 polarized physical phase tools; +the retained original native/Clifford and coded-normalizer source lineage. +Apache-2.0; substantial OpenAI Codex assistance. No kappa/caller claim. +""" +from pathlib import Path +from fractions import Fraction as F +from collections import Counter +from itertools import product +from hashlib import sha256 +import argparse,gzip,importlib.util,json,sys,time +HERE=Path(__file__).resolve().parent +sys.dont_write_bytecode=True +PINS={'NORMALIZERS.json':'ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da', + 'clifford_exact.py':'2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962'} +def need(ok,msg): + if not ok:raise ValueError(msg) +def load(name,path): + spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);sys.modules[name]=m;spec.loader.exec_module(m);return m +def canonical(rows): + p={} + for x in rows: + for j in sorted(p,reverse=True): + if x>>j&1:x^=p[j] + if x:p[x.bit_length()-1]=x + for j in sorted(p): + for k in p: + if k!=j and p[k]>>j&1:p[k]^=p[j] + return tuple(p[j]for j in sorted(p,reverse=True)) +def add(dst,src,q): + for k,v in src.items(): + value=dst.get(k,F(0))+q*v + if value:dst[k]=value + else:dst.pop(k,None) +def calculate(cube_tuple=(0,0,0)): + for name,pin in PINS.items():need(sha256((HERE/'inputs'/name).read_bytes()).hexdigest()==pin,'pin '+name) + geometry=load('wholeK_geometry',HERE/'geometry_tools.py');frames=load('wholeK_frames',HERE/'frame_tools.py');ce=load('wholeK_clifford',HERE/'inputs/clifford_exact.py') + normal=json.loads((HERE/'inputs/NORMALIZERS.json').read_bytes());roots=list(zip(*normal['mode_columns']));labels=[p['q']for p in normal['ports']] + cube_map={} + for p,row in enumerate(roots):cube_map.setdefault(tuple(j for j,v in enumerate(row)if v),[]).append(p) + cubes=[] + for support,ports in sorted(cube_map.items()): + parity=[sum(roots[p][j]*roots[p][support[0]]<0 for j in support[1:])&1 for p in ports] + K=[[F(int(i==j))-F(sum(a*b for a,b in zip(roots[ports[i]],roots[ports[j]])),4)for j in range(8)]for i in range(8)] + need(all(sum(K[i][j]*K[j][k]for j in range(8))==int(i==k)for i,k in product(range(8),repeat=2)),'literal cube involution') + need(all(sum(bool(v)for v in row)==4 and all(v in (0,F(1,2),F(-1,2))for v in row)for row in K),'literal four signed half entries') + need(all(not K[i][j]or parity[i]!=parity[j]for i,j in product(range(8),repeat=2)),'literal cross parity') + cubes.append({'root_support':support,'ports':ports,'parity':parity,'K':K}) + need(len(cubes)==14 and len(cube_tuple)==3 and all(0<=i<14 for i in cube_tuple),'valid14^3 cube tuple') + selected=[cubes[i]for i in cube_tuple];n=25 + U=[1|(1<<9)|(1<<18)]+[(1<<(9*b))^(1<<(9*b+j))for b in range(3)for j in range(1,9)] + orth=geometry.ortho_basis(U) + def qlabel(triple): + raw=sum(labels[p]<<(9*j)for j,p in enumerate(triple)) + need(geometry.span_contains(U,raw),'actual port in U25') + q=sum(geometry.dot(raw,b)<

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Exact inverse and transpose owned lifecycles. Native physical phase science inherited through actual literal monomial inverse/transpose and C^-1=C X_mask identities. E/global lowrank query not included in this native-only replay; separate exact fixture binds those adapters.", + "source_B_science": "f6b26f28f2a8f2dcfbf81f98c7ca18f967384b7b61518766494f8e821d5bf56f", + "source_contact_reads_each": 76, + "source_contacts_checked": 512, + "status": "PASS_ACTUAL_NATIVE_SOURCE_CHECKPOINT_AND_FREE_OPERATOR_TRANSPOSE", + "transpose_all_operator_entries": true +} diff --git a/research/odd-e8-lowrank-e-native/SOURCES.json b/research/odd-e8-lowrank-e-native/SOURCES.json new file mode 100644 index 0000000000..eb13a94dfa --- /dev/null +++ b/research/odd-e8-lowrank-e-native/SOURCES.json @@ -0,0 +1,70 @@ +{ + "base_commit": "32890bc5de034ab8fc93ac88ead7279a6a416d04", + "files": [ + { + "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602", + "path": "docs/research/agent-task-catalog.json", + "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72", + "usage": "provenance" + }, + { + "git_blob": "fc3d4ba105e1f097d0d7d051a308281e86ab1446", + "path": "certificates/selected-result.json", + "sha256": "66974efdced4083c00025f97d95d83909a226cdf801edb9301c195c6641f6903", + "usage": "provenance" + }, + { + "git_blob": "bca92c222c395d3d75c047fbb678f3cd0947c60f", + "path": "research/coded-native-caller/NORMALIZERS.json", + "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da", + "usage": "provenance" + }, + { + "git_blob": "166841a037f069249f6f7f6dedb89248812f59e2", + "path": "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py", + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "usage": "provenance" + }, + { + "git_blob": "13269f7b1f98535151de173477f9e7d9a0d81079", + "path": "research/coded-native-caller/GAUGE.md", + "role": "Terminal-bound source or support-method predecessor; provenance only, not loaded at runtime.", + "sha256": "09c4e86d99245734761569efd13473623ffdd857e9eae092bd7f54bfd2f42f06", + "usage": "provenance" + }, + { + "git_blob": "da8837ba67423ef08ef1afb8e8297a8032aafe9f", + "path": "research/coded-native-caller/PHYSICAL.md", + "role": "Terminal-bound source or support-method predecessor; provenance only, not loaded at runtime.", + "sha256": "4321b159ff8d3fe705419adaaa1beef75606e869e34341bda553f17d598a6078", + "usage": "provenance" + }, + { + "git_blob": "6651986b9f8d1e4fe4162bdba62b645edcd46518", + "path": "research/odd-e8-whole-k-native/B-PROGRAM.json.gz", + "pin": "head:fc5e6f611eb7a1121be23d6748ecceb61533041e:research/odd-e8-whole-k-native/B-PROGRAM.json.gz", + "sha256": "fd30f46e210e4f46302fbeb4055a0e61aa5dce1268a864b53db58406be5a2ed9", + "usage": "provenance" + }, + { + "git_blob": "bb208229abc25b768bf91f838faca7eb9c995de8", + "path": "research/odd-e8-whole-k-native/K-TEMPLATE.json", + "pin": "head:fc5e6f611eb7a1121be23d6748ecceb61533041e:research/odd-e8-whole-k-native/K-TEMPLATE.json", + "sha256": "7477f45dc0036a1e2da980964a2775696c259be56bc0d4e70ba62788dd853cdf", + "usage": "provenance" + } + ], + "local_author_inventory": "AUTHOR-FILES.json", + "local_author_sources": "AUTHOR-SOURCES.json", + "peer_review": { + "author": "Separate AI worker who also authored the two-cube fixture; inherited whole-K science authenticated, not independently reconstructed.", + "author_seal": "2253b65bc0dbccb7c232b555bcf59987082c1babc84b815998f4680de0453496", + "original_receipt_sha256": "40e3d0b457ca367d2ede9a908363744bd16b7db988fe4fa286fd3be58e213b64", + "original_script_sha256": "6d6bbded2fbb86e4cb9d16267fe9c478b01539b56891e0a59e58d26d8b380a83", + "portable_adapter": "Only default directory, author-metadata path mapping and receipt filename differ. Mathematical controls and resulting review receipt are unchanged.", + "scope": "Local algebra/source/lifecycle and structured modes; not human/kernel acceptance, full negative decoder or complete machine admission." + }, + "runtime_vendor_policy": "All runtime files are within this package. Exact input/code pins and canonical scientific program comparisons are enforced by run.py. No sibling package or network access is used at replay.", + "schema_version": 1, + "scope": "Both local E orientations and typedN3 only. Negative E Gaussian admission, full outer machine costs and new kappa remain unknown." +} diff --git a/research/odd-e8-lowrank-e-native/TASK.json b/research/odd-e8-lowrank-e-native/TASK.json new file mode 100644 index 0000000000..c11fec76e5 --- /dev/null +++ b/research/odd-e8-lowrank-e-native/TASK.json @@ -0,0 +1,76 @@ +{ + "actual_scope": "Construct both physical E=K(I-F_C)^-1 native orientations using the whole K word and20480 full-R spectral queries, actual original-source acquisition, owned inverse contacts/transpose, and an exact typed N3 caller. The negative E-coded half is not an independent Gaussian job.", + "ai_assistance": "Substantial OpenAI Codex assistance by a lead and separate geometry, physical-compiler and independent-review agents. This is not independent human or formal-kernel review.", + "author": "THU New Media Research Center (@thu-nmrc)", + "base_commit": "32890bc5de034ab8fc93ac88ead7279a6a416d04", + "bottleneck_link": "The odd-E8 side producer was unpriced in the former K-only component. Both E orientations now have an explicit paid profile and ordinary source/storage bill, leaving a concrete final Gaussian-terminal gate.", + "evidence": "PROOF.md; PRECISION-SCOPE.md; ROOT-CHECKPOINT-PROGRAM.json.gz; OWNED-E-PROGRAM.json; MODES-PROGRAM.json; N3-PROGRAM.json; TWO-CUBE-NATIVE-PROGRAM.json.gz; RESULT.json.", + "open_questions": [ + { + "blocked_by": "No profitable negative E Gaussian decoder or changed inventory has been constructed.", + "first_step": "Bind a decoder to actual paid/native contacts and original independent inputs with all-width coefficients and phases, or construct a different exact caller/target inventory.", + "question": "Can the negative N3 endpoint Q^-1 E3 E2^-1 E1 D123 yield enough independent full-rank Gaussian jobs for a favorable invoice?", + "why_it_matters": "Only the positive half is decoded. A fullH73 grant for the other half is unknown; H71 targets already fail before the new queries." + }, + { + "blocked_by": "The terminal profile is unresolved; the full outer conversion is not supplied.", + "first_step": "Specify the error ABI, derive coordinatewise precision with address dimension, and charge ordinary recodings, ownership, routing and storage for the actual admitted terminal profile.", + "question": "Can this complete construction satisfy the outer machine, precision and storage admission?", + "why_it_matters": "The finite field-l2 error-amplification factor does not settle coordinatewise fixedpoint rounding or full machine costs." + } + ], + "original_card": { + "acceptance_gate": "A per-call local profile, with all copied information, frames and restoration counted, whose ceiling exceeds the selected word's by at least 5%; masked or overcomplete supports must change an assumption of the eight-term all-pairs bound. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "allowed_variations": [ + "One masked, overcomplete or block decoder family with exact labels and supports.", + "A scoped lower bound on effective rank for one alphabet.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "bottleneck_link": "Rank-1 children are about half of recursive cost; the selected word's effective child rank is about 3.9. Larger-rank delivery lowers recursive cost per unit of paid mass.", + "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin. Ideal budget: rank-16 delivery is 2.31x (levers.py).", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "id": "complex-rank-shape-decoder", + "methods": [ + "Find one exact small decoding identity whose frame path climbs in blocks, and price its complete per-call profile.", + "Bound the best effective child rank achievable for one fixed support alphabet, including copies, frames and restoration." + ], + "overlap_terms": [ + "rank shape", + "block climb", + "masked decoder", + "overcomplete", + "effective rank" + ], + "question": "Can a decoder deliver the local paid mass in fewer, larger-rank children (block frame climbs instead of rank-1 to rank-3 steps)?", + "scope_change_triggers": [ + "Repacking idle remainders of an unchanged word (covered by the packing ceiling).", + "Repeating the eight-term all-pairs search inside its proved scope.", + "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.", + "Searching below C=40 in the #2017 Eisenstein binary scalar-rectangle or fixed-support block-linear additive pairing model; specify a changed premise instead. This bound does not cover every complex decoder.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/complex-decoder-field-extension-seed44/README.md", + "research/complex-frame-pair-decoders/README.md", + "research/selected-k8-unrestricted-ends/README.md", + "research/eisenstein-reduction-copy-floor/README.md" + ] + }, + "outcome": "partial", + "schema_version": 1, + "scope_change_reason": "The actual low-rank F_C modal correction and source-contact inverse-transpose replace the separated H module and the unavailable forward prequery. This is a positive local component with a priced structured global algorithm, not a completed supplier.", + "scope_status": "changed", + "stop_rule": "Retain the scoped local construction. Do not count the negative E terminal as H73, promote the conditional moment, or expand an unchanged terminal-only guess into a frontier claim. Further admission needs an actual all-width terminal decoder or changed output/caller inventory and complete outer costs.", + "task_id": "complex-rank-shape-decoder" +} diff --git a/research/odd-e8-lowrank-e-native/TWO-CUBE-NATIVE-PROGRAM.json.gz b/research/odd-e8-lowrank-e-native/TWO-CUBE-NATIVE-PROGRAM.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..8aaf8d87c9d867526992314be8846cc3e90d4a14 GIT binary patch literal 26536 zcmV(^K-Iq=iwFP!000026YRZhZ>&d>9r#y-`)LNC1{s+dk(n~)L+=R28Z)-1v1`DC zhE~Yew$>V{trzbY1ON9u=cyuDWL5E26?r)lq*jynUXsPiCo*2niHwZ+*AM^x>%aSY z%=B7!?W+PQM=5Wad zz9~8_x?(Ff^`TpjmbF)3b1(Qs-+cF%pMU!Lk6&XwKmX`Ie0BHyZPNR^jen>2(RX^E zWbgAnS>EY=-brr7zt8);li1!#3w(Yj>v^a5N%~G&{Z87J-$@Tjc%Sz{?8)YOh~B%I zLQAWzRAct8maZaMSCTSH_r0~z;|#%?%;d{*C6{7hY;W^F=MO*5uYdZXe)r>FzQ^DG z=Qlt6^mF|dZ~f!cAVVb(E!IK7NraFnJ_hKsJd z6pAaOO+O{3=$6e{k^~59O;@dQTVm1GSCBGi?WqQPogAxmy}gAT7`?~R5wRz6C3UWNsj;LyS}8HcX&Ev~6AvG; zR87mT)dK`Jn-vfJi?0*JwgQ_S`kj+&ExTEBn!d{{RvXs_4HPJUFmYi*QG#2;RafVX 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diff --git a/research/odd-e8-lowrank-e-native/TWO-CUBE-NATIVE.json b/research/odd-e8-lowrank-e-native/TWO-CUBE-NATIVE.json new file mode 100644 index 0000000000..a8174eb965 --- /dev/null +++ b/research/odd-e8-lowrank-e-native/TWO-CUBE-NATIVE.json @@ -0,0 +1,79 @@ +{ + "CLEAR": 0, + "COPY": 0, + "absolute_phase_operator_checks": 264, + "all_independent_main_operator_entries": 192, + "axis_dimension": 9, + "helpers": 0, + "low_rank_sparse_peak": 512, + "mode_eigenvalue_multiplicities": { + "2": 4, + "4": 2 + }, + "mode_rank": 6, + "mutation_controls": { + "actual_K_coefficient_mutation_rejected": true, + "actual_missing_source_full_exit_rejected": true, + "actual_wrong_ADD_chart_rejected": true, + "same_tableau_ordinary_phase_i_rejected": true + }, + "ordinary_backward": { + "ADD": 64, + "D": 240, + "P": 240, + "X": 208, + "phase": 96 + }, + "ordinary_forward": { + "ADD": 64, + "D": 240, + "P": 240, + "X": 96, + "phase": 96 + }, + "original_main_fields": 32, + "owned_fields": 0, + "paid_profile_backward": { + "2": 16, + "3": 16, + "5": 16, + "6": 16 + }, + "paid_profile_forward": { + "2": 16, + "3": 16, + "5": 16, + "6": 16 + }, + "port_order": [ + 0, + 7, + 27, + 57, + 76, + 81, + 87, + 92, + 1, + 6, + 28, + 58, + 75, + 82, + 86, + 93 + ], + "schema": "two-real-E8-cubes-native-phase-receipt/v1", + "scientific_payload_sha256": "10c924efdfd6ae37717f29db9abfd97c46a4e2446590cca78248c252def791d7", + "scope": "Actual native geometry/phase fixture for two real base8 cubes. Does not by itself implement E, lowrank owned acquisition, a whole caller or a terminal decoder.", + "source_cube_indices": [ + 0, + 1 + ], + "source_pins": { + "inputs/NORMALIZERS.json": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da", + "inputs/clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "two_cube_frame_tools.py": "e5b2ea1f60d554b3a285569602360c663ee8b387350424678b3bd0b0b5432bf4" + }, + "status": "PASS_EXACT_ORIGINAL_MAIN_OPERATOR_COLUMNS_AND_PHASES" +} diff --git a/research/odd-e8-lowrank-e-native/VERIFY.json b/research/odd-e8-lowrank-e-native/VERIFY.json new file mode 100644 index 0000000000..88a2b89913 --- /dev/null +++ b/research/odd-e8-lowrank-e-native/VERIFY.json @@ -0,0 +1,59 @@ +{ + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/run.py" + ], + "checks": "All six self-contained local E, root512 source-contact inverse/transpose, literal owned E, global20480-mode recoding, typedN3 and two actual cube phase engines; exact frozen receipts/programs and unchanged package bytes.", + "timeout_seconds": 300 + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-W", + "error", + "-B", + "{package}/run.py" + ], + "checks": "All six self-contained local E, root512 source-contact inverse/transpose, literal owned E, global20480-mode recoding, typedN3 and two actual cube phase engines; exact frozen receipts/programs and unchanged package bytes.", + "timeout_seconds": 300 + }, + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/peer_review.py" + ], + "checks": "Separate AI worker independent exact Q(i) controls and structural512contact/38912read/5632literal inverse/transpose/global20480mode checks, authenticated original author seal through explicit metadata mapping. No author Python code imported.", + "timeout_seconds": 150 + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-W", + "error", + "-B", + "{package}/peer_review.py" + ], + "checks": "Separate AI worker independent exact Q(i) controls and structural512contact/38912read/5632literal inverse/transpose/global20480mode checks, authenticated original author seal through explicit metadata mapping. No author Python code imported.", + "timeout_seconds": 150 + } + ], + "inputs": [], + "python": "3.12", + "requirements": [], + "schema_version": 1, + "status": "ready" +} diff --git a/research/odd-e8-lowrank-e-native/checkpoint.py b/research/odd-e8-lowrank-e-native/checkpoint.py new file mode 100644 index 0000000000..be1fb7b0ac --- /dev/null +++ b/research/odd-e8-lowrank-e-native/checkpoint.py @@ -0,0 +1,163 @@ +"""Actual root512 source-contact inverse and exact transposed owned word. + +Native unary operations are arbitrary invertible free operator letters in the +all-input replay. Their inverse/transpose physical words are also emitted. +Default is read-only; no sealed source package is modified. +""" +import argparse,gzip,hashlib,json,sys +from collections import Counter +from fractions import Fraction as F +from pathlib import Path +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent +SOURCE=HERE/'inputs' +PIN='f6b26f28f2a8f2dcfbf81f98c7ca18f967384b7b61518766494f8e821d5bf56f' +def need(q,s): + if not q:raise ValueError(s) +def canonical(x):return (json.dumps(x,sort_keys=True,separators=(',',':'))+'\n').encode() +def gf_inv(rows): + n=len(rows);r=[v|(1<<(n+j))for j,v in enumerate(rows)] + for j in range(n): + p=next(i for i in range(j,n)if r[i]>>j&1);r[p],r[j]=r[j],r[p] + for i in range(n): + if i!=j and r[i]>>j&1:r[i]^=r[j] + need([v&((1<>n for v in r] +def mono_transform(word,transpose=False): + out=[] + for e in reversed(word): + if e[0]=='P':out.append(['P',gf_inv(e[1])]) + elif e[0]=='D':out.append(['D',e[1],e[2]if transpose else[(-v)%4 for v in e[2]]]) + elif e[0]=='X':out.append(list(e)) + else:need(e[0]=='phase','actual monomial opcode');out.append(['phase',e[1]if transpose else(-e[1])%4]) + return out +# Free invertible event letters with a transpose involution, all noncommuting. +def reduce_prepend(letter,w): + return w[1:]if w and w[0]==-letter else(letter,)+w +def opword(w,letter):return reduce_prepend(letter,w) +def transformed_word(w): + # Transpose maps each event letter k to k+N with the same inverse sign. + return tuple((1 if x>0 else-1)*(abs(x)+1000000)for x in reversed(w)) +def add(dst,src,c): + for key,v in src.items(): + x=dst.get(key,F())+c*v + if x:dst[key]=x + else:dst.pop(key,None) +def run(program,main,initial=None,strict=True): + states={x:{(x,()):F(1)}for x in main}if initial is None else{k:dict(v)for k,v in initial.items()} + live=set(main) + for e in program: + k=e[0] + if k=='UNARY': + f=tuple(e[1]);letter=e[2] + need(f in live,'unary reads initialized field') + states[f]={(src,opword(w,letter)):c for(src,w),c in states[f].items()} + elif k=='ADD': + a,b=tuple(e[1]),tuple(e[2]);need(a in live and b in live,'ADD reads initialized owned/main field');add(states[a],states[b],F(e[3],e[4])) + elif k=='COPY': + a,b=tuple(e[1]),tuple(e[2]);need(a not in live and b in live,'COPY requires fresh owned destination and initialized source');states[a]=dict(states[b]);live.add(a) + else: + need(k=='CLEAR','known emitted opcode');a=tuple(e[1]);need(a in live,'CLEAR requires live owned field');need(a not in main,'no main CLEAR');states[a]={};live.remove(a) + need(all(f in main for f in live),'all owned fields cleared after final read') + return {f:states[f]for f in main} +def transpose_program(program): + out=[] + for e in reversed(program): + if e[0]=='UNARY':out.append(['UNARY',e[1],(1 if e[2]>0 else-1)*(abs(e[2])+1000000)]) + elif e[0]=='ADD':out.append(['ADD',e[2],e[1],e[3],e[4]]) + elif e[0]=='CLEAR': + # A reverse adjoint for a discarded owned variable starts at zero. + out.append(['ZERO_OWNED',e[1]]) + else: + need(e[0]=='COPY','transpose supported opcode');out.extend([['ADD',e[2],e[1],1,1],['CLEAR',e[1]]]) + # ZERO_OWNED does not read an ordinary variable; normalize it to a fresh + # initialized zero field, kept separate from COPY's overwrite prohibition. + return out +def run_transpose(program,main): + states={f:{(f,()):F(1)}for f in main};live=set(main) + for e in program: + k=e[0] + if k=='ZERO_OWNED': + f=tuple(e[1]);need(f not in live and f not in main,'adjoint owned zero is fresh');states[f]={};live.add(f) + elif k=='UNARY': + f=tuple(e[1]);need(f in live,'adjoint unary initialized');states[f]={(src,opword(w,e[2])):c for(src,w),c in states[f].items()} + elif k=='ADD': + a,b=tuple(e[1]),tuple(e[2]);need(a in live and b in live,'adjoint ADD initialized');add(states[a],states[b],F(e[3],e[4])) + else: + need(k=='CLEAR','known adjoint opcode');f=tuple(e[1]);need(f in live and f not in main,'owned adjoint CLEAR');states[f]={};live.remove(f) + need(live==set(main),'all adjoint owned fields cleaned') + return {f:states[f]for f in main} +def compile_program(source): + payload=json.loads(gzip.decompress((source/'B-PROGRAM.json.gz').read_bytes()));need(hashlib.sha256(canonical(payload)).hexdigest()==PIN,'actual B canonical science pin') + original=payload['program'];ports=payload['port_order'];main=[(r,p)for r in ['X','Y']for p in ports] + program=[];events={};versions=Counter();contacts={};usecounts=Counter();paid=Counter();defs={} + def wordid(w): + k=hashlib.sha256(canonical(w)).hexdigest();defs[k]=w;return k + for index,e in enumerate(original): + if e[0]=='ADD': + need(e[1]=='X'and e[3]=='Y','actual literal B has source-only Y') + p=e[4];contact=(versions[p],e[7]);need(p not in contacts or contacts[p]==contact,'every actual Y has one unchanged physical ADD contact') + contacts[p]=contact;usecounts[p]+=1;program.append(['ADD',[e[1],e[2]],[e[3],e[4]],e[5],e[6]]) + else: + need(e[0]in['MONOMIAL','BOUNDARY_MONOMIAL','PAID_PATH'],'known actual B instruction') + f=[e[1],e[2]];eid=index+1 + if e[1]=='Y':versions[e[2]]+=1 + if e[0]=='PAID_PATH': + rec=e[5];before=payload['definitions'][rec['before_monomial']];after=payload['definitions'][rec['after_monomial']];axes=rec['child_axes'];paid[len(axes)]+=1 + inverse={'kind':'PAID_PATH','before':wordid(mono_transform(after)),'positive_child_axes':axes,'after':wordid([['X',sum(1<>1)&1)][x]=C(1) + def gate(q,s): + O=scale(C(F(1,2),F(s,2)),I) + for x in range(N):O[x^q][x]+=C(F(1,2),F(-s,2)) + return O + Q0=gate(1,1);Qi0=gate(1,-1);D0=gate(2,1);Di0=gate(2,-1) + Q=diag(Q0,Q0);Qi=diag(Qi0,Qi0);D=diag(D0,D0);Di=diag(Di0,Di0);I=ident(8);Z=zeros(8) + K=block(zeros(4),P,P,zeros(4));R=mul(D,Q) + need(mul(K,K),I,'actual K involution');need(mul(K,R),mul(R,K),'actual fullGaussian centralization') + if mul(K,Q)==mul(Q,K):raise ValueError('noncommuting-Q control lost') + # FC=lambda*Pminus; active B=I-K=2Pminus, BC=2C. + Pminus=scale(F(1,2),add(I,scale(-1,K)));out=[] + FK=mul(diag(D,D),lower(mul(K,Qi)));BK=mul(diag(D,D),upper(scale(-1,mul(Q,K)))) + F0=mul(diag(D,D),lower(Qi));B0=mul(diag(D,D),upper(scale(-1,Q))) + for lam in [14,98,-1078]: + FC=scale(lam,Pminus);A=add(I,scale(-1,FC));Ai=add(I,scale(F(lam,1-lam),Pminus)) + need(mul(A,Ai),I,'inverse A exact') + for name,X,Xinv,residual in [('KA',A,Ai,Ai),('K_Ainverse',Ai,A,A)]: + E=mul(K,X);Ei=mul(K,Xinv);H=diag(E,prod(Qi,E,Q));Hi=diag(Ei,prod(Qi,Ei,Q));Delta=add(I,scale(-1,residual)) + leftF=prod(diag(E,I),FK,diag(I,E));leftB=prod(diag(Ei,I),BK,diag(I,Ei)) + rightF=prod(H,diag(D,D),lower(mul(residual,Qi)));rightB=prod(Hi,diag(D,D),upper(scale(-1,mul(Q,residual)))) + need(leftF,rightF,'forward E exact adapter');need(leftB,rightB,'backward E inverse exact adapter') + need(mul(leftF,lower(mul(Delta,Qi))),mul(H,F0),'forward lowrank defect correction') + need(mul(leftB,upper(scale(-1,mul(Q,Delta)))),mul(Hi,B0),'backward lowrank defect correction') + # Physical post-native backward correction uses original ground Y only: + # add -R Delta Y to native X before postX(E^-1). + scatter=block(Z,scale(-1,mul(Ei,mul(R,Delta))),Z,Z) + WB=add(leftB,scatter) + need(WB,mul(Hi,B0),'physical original-ground backward correction') + if name=='K_Ainverse': + # Inverse scheduling: source Y native inverse first, with its contact + # checkpoint retained, then undo correction and finish native X inverse. + # At matrix level y=E D^-1 Yout is acquired before X's native inverse. + # The literal K schedule must retain its Y common-frame contact via COPY. + BKi=mul(upper(mul(Q,K)),diag(Di,Di)) + y_acquire=mul(E,Di) + undo=block(I,mul(R,mul(FC,y_acquire)),Z,I) + WBi=prod(diag(I,E),BKi,undo,diag(E,I)) + need(mul(WBi,WB),ident(16),'checkpoint-scheduled physical inverse left') + need(mul(WB,WBi),ident(16),'checkpoint-scheduled physical inverse right') + # Transpose the obtained inverse linear algorithm; C^T=C, its inverse + # is positive C then ordinary X. The boundary is entirely monomial. + transpose=lambda M:list(map(list,zip(*M))) + Q2=mul(Q,Q);D2=mul(D,D);J=diag(Q2,I);Jinv=J + WF=prod(diag(D2,D2),J,transpose(WBi),Jinv) + need(WF,mul(H,F0),'actual symmetric E duality produces forward code') + # Omission produces an actual nonzero physical defect, not just syntax. + if leftF==mul(H,F0)or leftB==mul(Hi,B0):raise ValueError('omitted correction mutation accepted') + # Q must be in the displayed order: it cannot commute through Delta. + if mul(Delta,Q)==mul(Q,Delta):raise ValueError('noncommutative defect control lost') + out.append({'lambda':lam,'E':name,'forward_backward_adapters':True,'corrected_forward_backward':True,'omitted_correction_rejected':True,'Delta_Q_noncommuting':True,'physical_ground_backward_correction':True,'inverse_and_transpose_boundary_checked':name=='K_Ainverse'}) + return {'schema':'source-consuming-E-exact-small-model/v1','status':'PASS_EXACT_LOCAL_IDENTITIES_ONLY','address_axes':2,'owners':2,'complex_rational_main_matrix_dimension':16,'cases':out,'generic_identity':'For X commuting K with E=KX, [E,DQ]=0: postX(E) F_K preY(E)=H(E) diag(D,D) L(X^-1 Q^-1); postX(E^-1) B_K preY(E^-1)=H(E^-1) diag(D,D) U(-Q X^-1).','correction':'Delta=I-X^-1; right-prepend L(Delta Q^-1) or U(-Q Delta) to recover scalar core with codes E/E^-1. For X=A^-1, Delta=F_C exactly, with rank rank(F_C).','remaining':'Literal all-port owned checkpoint/reverse-transpose emitter and ordinary tariff; actual IDLE/boundary endpoints; full negative terminal E-word decoding; complete precision and moment. The inverse source-Y checkpoint schedule is verified here as exact block algebra, not yet a literal owned program.'} +if __name__=='__main__': + p=argparse.ArgumentParser();p.add_argument('--write',action='store_true');a=p.parse_args();r=calc();f=Path(__file__).with_name('E-ADAPTER.json') + if a.write:f.write_text(json.dumps(r,sort_keys=True,indent=2)+'\n') + else:need(r,json.loads(f.read_bytes()),'readonly receipt') + print(json.dumps(r,sort_keys=True)) diff --git a/research/odd-e8-lowrank-e-native/inputs/B-PROGRAM.json.gz b/research/odd-e8-lowrank-e-native/inputs/B-PROGRAM.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..6651986b9f8d1e4fe4162bdba62b645edcd46518 GIT binary patch literal 910130 zcmV(%K;pk2iwFP!000026YRZPuQW$?CH7YcKH0#L9QTU`@Qd~0r?KAz2t7hvEy5C8 zXi_s4=FfYrotMh0%BoZ6JBQ@ggK4svak8?qG9z~E`(FFM|5*OzU;gR8{nUT`=U;yO zyC47a&*N{}pa1PYeki^FW&HBX5C2;J?Ux^Z9Y6o_=fC{Tzx*_R{ZBvq+dr3I#t*;# z^Z2#=@HhYa4?q2v|79+J{jY!f!+-v7Kaaos@JlQIQvUKo`}3Idr}oqM`B&WHFXiW7 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>p&1]for p in range(120)];ALL=(1<<120)-1;nodes=[0] + def search(used,chosen): + nodes[0]+=1 + if used==ALL:return chosen + best=None + missing=ALL^used + while missing: + b=missing&-missing;missing-=b;p=b.bit_length()-1 + options=[i for i in byport[p]if not masks[i]&used] + if not options:return None + if best is None or len(options)-bZ*#k>Wo~Zv-@p5xe)u;(to^$m|K&Ho z>woz1r|*89zW=WOx8MB!hxMC(*}wb!Z+`sUcfYppzZ-r2m;a~#w0`*4pML!3pZdRi z_v`=kpT7Hd|Nejd_y6wS{=@(B-S^-9$M3#(-+y=JFyG2v*;X!Y7hhW`t9G~ca5KI3MS4(Q z1QP3u{6Tw_w|*5TaW7+8FMH67=)#NMC%+0_zX%_+S4ALumA?5`J?KS*&c8_G!izK^ zzUVpWRk7|xn%!RXKJ7)Z&R&&BdeQ#GS7i`hv_J7h5h%SXk@PCY{UUuUuR4`^RR-=w zatklggYqh*_$qGyBD`ZSVVJ-UqpuMtFj2M%8I-!2EFRk{#9wX7rjq>k)fs+$t}N%oV-Y}?L`j3UUlH~BE5cD zP1389iZ8-eZAD{)Hq!P1^m;e1?;gLk8me>8@yxiwYbz>KEhntjplMJXXM>$$mZC99qrVdQtn7O zB&$6nS8eab8p3WftunKVE|16Lzyfyg-G(3T#N4*eZLAaL2*dT+^z-Uli<4b1eeA@# zSWZ8y$HU&o{R}za=|(R3q&Qt_69J?=T#Pe@64{`cavW=;6}|Y`*POGtHHP)($Jv8j 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z{ry>E!C-`38t`(Y*qMP#XIHMd{M{rKvVQmeRWVE6gv;5fi^VPw_NB?axJ1;Ve3o*r zQz|0(45P1fb4b02h3))QVyssAY%qn**u*;2Cj`STHYfD6%5E{&$W5iT+ricPEYY^N z*IU0qRz1k!jX`}#P+i+-VB_V%fPO-7ePz&2YTt#MzA17(_*^o3wfAax7ZddfTV463 zh4K1Y9^=d|h7E*}Vb&#EF_=9&T)p4DDZ1%W<9AKBxi?<8q-C+HP4mpN)!z=M7C$jn ztLsxPKF!)<*p}PwjL23@*_@`rOQoIdw^EgeKqQ}OiBGNXr`oE@U;CdG-Zaf#%%x=p z`+ae)&p4C+P{^VlpkQ_7_jvfqhj#f}0w~X_c#o^-%1fcvMdqRVVy%|`!NL5F-Q&s5 z?~KRW$u=+b&$pA0r%XKZ7pGXNhBrQEw^|$yd~d~c&SfjSLwC-7YQsvwnnNpP_mXD< z^9(A>car5=RelJ-$U{KzvpoMP7N42y`sdBF9$qixUrMc!CkM(mFfHscK>J|#Vtnwm;=8rTtO|-< zXK>cS%bdU%%sKb-4=uq<@ao^XC zujWsm97thWS?NNuosaPP(KHsLbbZo>wZbN1Z?HF@;2V(ETlvMBn~zt=U)R4a-hH5s ziT9QTMT~uSkrH()6|K+Cbbi#wY)O5+ZuV)@z3s+YBxUF7BGK(?6_bZc5Kpr9^7Grz zM)jr~VHdwK6mZgXwl`M-<%JqzMfX=$X50nmr90qtUqnP<=!3f7GKjSIjdqgKeVzps zO-o@yI}#J-B^S3 by H2, source +S3->R9 by H6, reader ground->S3 by H3, reader S3->q_r-perp by H5. Every +transition is emitted with literal ordinary wrappers and positive coordinate +C children. The compiler's generic Phi_S Lagrangian identity gives the exact +Gaussian ranks even for these degenerate3-spaces. No orthonormal basis of S3 +is assumed. Each K ADD happens at the identical physical Phi_S3 word. + +The original physical x_i,y_i are independently arbitrary. The actual +ordinary entrance words identify geometric u_i=L_i Q^-1 x_i, v_i=L_i y_i: + + Phi_[qi] L_i Q^-1 on X_i; L_i on Y_i. + +They are compiled as ordinary monomials, so no query is supplied for free. +At the common chart Y_r=Phi_S(v_r+sum_s K_rs u_s), while X_s=Phi_S u_s +is never modified by an ADD. The source and reader exits, followed by their +emitted L_i^-1 and D L_i^-1 Phi_(qi-perp)^-1 wrappers, give + + X_i=D x_i, + Y_i=D(y_i+sum_j K_ij L_i^-1 L_j Q^-1 x_j). + +This is F_K. The stream is replayed on every independent original column, +retaining both actual Clifford operators and scalar coefficients. The exact +signed tableau plus absolute zero column determines each Clifford operator, +including its global scalar. Thus no projective phase has been discarded. + +The raw inverse-transpose of the forward triangular field word swaps each +ADD direction and negates its coefficient, and conjugates its physical +unitaries. Positive C children implement inverse children by C^-1=C X; +each such X is emitted. The actual central framing is X-only Q^2 on input +and output, together with the D^2 output powers. These ordinary translations +are included in the backward bill, giving + + B_K=diag(D,D) U(-Q C_K). + +The actual B stream, rather than an inferred scalar code, is separately +replayed on every original column and absolute phase. + +All120 sources occur in exactly one block and one parity direction, so the +word has120 copies of each of H2,H3,H5,H6. All240 main fields are original +arbitrary data, and all helpers/owned/COPY/CLEAR counts are zero. Actual +ordinary operations and opcode identity records are counted; they are not +zero-work instructions. + +Every literal one-column P/D/X/phase/C identity tensors over f positive +address columns. P and X lift columnwise, D sums its phase over columns, +and phase theta lifts as i^(f theta). The owner coefficient K_ij is applied +once at field width f, outside any tensor power. This proves the physical +word endpoint for all positive widths without tensoring an owner sum. +The retained finite/all-size compiler, tape, precision and outer assumptions +remain future caller obligations, not consequences of this finite replay. diff --git a/research/full120-e8-native/components/full-e8-native120-20261025-structural/README.md b/research/full120-e8-native/components/full-e8-native120-20261025-structural/README.md new file mode 100644 index 0000000000..c08154c291 --- /dev/null +++ b/research/full120-e8-native/components/full-e8-native120-20261025-structural/README.md @@ -0,0 +1,59 @@ +# Phase-complete full120 E8 n9 native F/B word + +This emits the actual new15-cube full120 native on240 arbitrary independent +original main fields. The explicit Weyl cube partition replaces the old +four-coordinate-support grouping. No old root input is identified with a +new one, and no supplied query, owned helper, COPY or CLEAR is assumed. + +Both orientations pass all1,440 nonzero/diagonal original operator blocks +and1,980 absolute-phase operator checks. Their paid profiles are exactly + + 120 H2 +120 H3 +120 H5 +120 H6. + +The actual forward ordinary bill is480 ADD,1800 D,1816 P,720 X,720 phase. +The backward bill has1560 X and otherwise the same counts. Extra P records +from the new Weyl-lift normalizers are included. Four actual mutants reject: +changed K coefficient, wrong ADD chart, omitted source exit child, and a +phase-i mutation invisible to the signed tableau alone. + +NATIVE120-NATIVE-PROGRAM.json.gz retains literal ordinary definitions, +forward/backward streams, every paid child axis list and wrapper, actual +normalizers, actual roots, and all240 original field IDs. Equality concerns +the decompressed canonical scientific payload, not gzip container bytes. + +Read-only reproduction (Python3.11+ standard library): + +``` +python3.11 native120.py +python3.11 -O native120.py +``` + +Both pass. `--write` is explicit author mode. Default intermediate dimension +is3; `--middle 6` is a separate paid-split authoring experiment and is not +part of this default receipt. + +The normalized endpoints are + + F_K=diag(D,D) L(C_K Q^-1), + B_K=diag(D,D) U(-Q C_K), + C_K=diag(L_i^-1) K diag(L_i), Q=C0, D=C_[1,9). + +The eight-mode R correction, E terminal decoder, full caller, precision and +outer supplier admission are not implemented here. No new kappa or scientific +adoption is claimed. Geometry and new normalizer phases are sourced from +`/tmp/full-e8-cube-cover-20261025-structural`; the new full odd3 physical +family is separate in `/tmp/full-e8-odd3-native120-20261025-structural`. + +Credit P112/E8 source authors, Dugongue's PR4929 coded producer, the retained +coded-native-caller Clifford/normalizer/compiler lineage, Ali Romman's odd +geometry, and the earlier balanced-native/whole-K phase constructors. This +work changes the inventory/partition and verifies an actual full120 word; +it does not claim a new Clifford compiler. Substantial OpenAI Codex assistance. +Apache-2.0; no independent human or proof-kernel verification claimed. + +## Open next questions + +- Reuse this actual native interface in a paid or changed-target decoder; + the second H(E) bank is not ordinary merely because E is owner-recodable. +- Compile a complete caller using the exact full120 modes and denominator14, + retaining its input acquisition, copies, restoration and precision costs. diff --git a/research/full120-e8-native/components/full-e8-native120-20261025-structural/frame_tools.py b/research/full120-e8-native/components/full-e8-native120-20261025-structural/frame_tools.py new file mode 100644 index 0000000000..7ec1c59b7d --- /dev/null +++ b/research/full120-e8-native/components/full-e8-native120-20261025-structural/frame_tools.py @@ -0,0 +1,56 @@ +"""Exact low-rank phases and analytic full-Gaussian native conjugation. + +Source Clifford compiler credit retained. No dense 2^n state is allocated. +""" +def install(ce,need,peak): + def sparse_zero(op,basis_state=0): + vec={basis_state:(1,0)};den=0 + for e in op.circuit: + k=e[0] + if k=='P':vec={ce.mv(e[1],x):a for x,a in vec.items()} + elif k=='X':vec={x^e[1]:a for x,a in vec.items()} + elif k=='D':vec={x:ce.mul_i(a,ce.qvalue(e[1],e[2],x,op.n))for x,a in vec.items()} + elif k=='phase':vec={x:ce.mul_i(a,e[1])for x,a in vec.items()} + else: + need(k=='C','literal sparse phase primitive');q,s=e[1:];out={} + for x in set(vec)|{x^q for x in vec}: + a,b=vec.get(x,(0,0));c,d=vec.get(x^q,(0,0));v=(a-s*b+c+s*d,b+s*a+d-s*c) + if v!=(0,0):out[x]=v + vec=out;den+=1 + peak[0]=max(peak[0],len(vec));need(len(vec)<=(1<<18),'bounded low-rank phase support') + while den and all(not(a&1)and not(b&1)for a,b in vec.values()):vec={x:(a//2,b//2)for x,(a,b)in vec.items()};den-=1 + return vec,den + ce.Op.zero_state=sparse_zero + def monomial(op,known_zero=None): + n=op.n;T=op.tab;need(all(x==0 and p%2==0 for x,z,p in T[n:]),'physical map is actually monomial') + G=ce.transpose([x for x,z,p in T[:n]],n);b=ce.mv(G,sum((p//2)<=((1-i)/2)^n sum_x i^wt(x)|x>. Thus R K_G R^-1|0>=(-i)^wt(d)|d>. Signed tableau fixes the remaining monomial.', + 'native_G_columns':cols} diff --git a/research/full120-e8-native/components/full-e8-native120-20261025-structural/inputs/COVER.json b/research/full120-e8-native/components/full-e8-native120-20261025-structural/inputs/COVER.json new file mode 100644 index 0000000000..44f977305d --- /dev/null +++ b/research/full120-e8-native/components/full-e8-native120-20261025-structural/inputs/COVER.json @@ -0,0 +1 @@ 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,94,95,109,111,115],[49,50,52,53,59,60,62,63],[49,50,52,53,70,71,73,74],[49,50,52,53,105,106,108,109],[49,50,54,55,59,60,64,65],[49,50,54,55,68,69,73,74],[49,50,54,55,105,106,110,111],[49,50,59,60,96,97,101,102],[49,50,68,69,96,97,108,109],[49,50,70,71,96,97,110,111],[49,51,54,57,59,61,64,115],[49,51,54,69,72,74,76,115],[49,51,54,103,105,107,110,115],[49,52,59,62,93,94,98,99],[49,52,70,73,93,94,104,107],[49,52,72,75,93,94,106,109],[49,53,56,57,59,63,66,115],[49,53,56,67,70,74,76,115],[49,53,56,103,105,109,115,119],[49,54,59,64,93,95,98,100],[49,54,68,73,93,95,103,107],[49,54,72,76,93,95,106,111],[49,56,59,66,93,97,98,102],[49,56,68,75,93,97,103,109],[49,56,70,76,93,97,104,111],[49,57,59,94,96,99,101,115],[49,67,70,94,96,107,110,115],[49,69,72,94,96,109,115,119],[50,51,55,57,60,61,65,115],[50,51,55,68,72,73,76,115],[50,51,55,103,106,107,111,115],[50,52,56,57,60,62,66,115],[50,52,56,67,71,73,76,115],[50,52,56,103,106,108,115,119],[50,53,60,63,93,94,98,99],[50,53,71,74,93,94,104,107],[50,53,72,75,93,94,105,108],[50,55,60,65,93,95,98,100],[50,55,69,74,93,95,103,107],[50,55,72,76,93,95,105,110],[50,56,60,66,93,96,98,101],[50,56,69,75,93,96,103,108],[50,56,71,76,93,96,104,110],[50,57,60,94,97,99,102,115],[50,67,71,94,97,107,111,115],[50,68,72,94,97,108,115,119],[51,52,55,56,61,62,65,66],[51,52,55,56,67,68,71,72],[51,52,55,56,107,108,111,119],[51,52,61,62,95,96,100,101],[51,52,67,68,95,96,104,105],[51,52,74,75,95,96,111,119],[51,53,54,56,61,63,64,66],[51,53,54,56,67,69,70,72],[51,53,54,56,107,109,110,119],[51,53,61,63,95,97,100,102],[51,53,67,69,95,97,104,106],[51,53,73,75,95,97,110,119],[51,54,61,64,94,96,99,101],[51,54,67,70,94,96,103,105],[51,54,74,76,94,96,109,119],[51,55,61,65,94,97,99,102],[51,55,67,71,94,97,103,106],[51,55,73,76,94,97,108,119],[51,57,61,93,95,98,100,115],[51,58,67,92,94,98,103,116],[51,64,73,92,94,101,108,116],[51,65,74,92,94,102,109,116],[51,68,73,93,95,105,110,115],[51,69,74,93,95,106,111,115],[52,53,54,55,62,63,64,65],[52,53,54,55,68,69,70,71],[52,53,54,55,108,109,110,111],[52,53,62,63,96,97,101,102],[52,53,68,69,96,97,105,106],[52,53,73,74,96,97,110,111],[52,54,62,64,94,95,99,100],[52,54,68,70,94,95,103,104],[52,54,75,76,94,95,109,111],[52,56,62,66,94,97,99,102],[52,56,68,72,94,97,103,106],[52,56,73,76,94,97,107,111],[52,57,62,93,96,98,101,115],[52,67,73,93,96,104,110,115],[52,69,75,93,96,106,115,119],[53,55,63,65,94,95,99,100],[53,55,69,71,94,95,103,104],[53,55,75,76,94,95,108,110],[53,56,63,66,94,96,99,101],[53,56,69,72,94,96,103,105],[53,56,74,76,94,96,107,110],[53,57,63,93,97,98,102,115],[53,67,74,93,97,104,111,115],[53,68,75,93,97,105,115,119],[54,55,64,65,96,97,101,102],[54,55,70,71,96,97,105,106],[54,55,73,74,96,97,108,109],[54,56,64,66,95,97,100,102],[54,56,70,72,95,97,104,106],[54,56,73,75,95,97,107,109],[54,58,70,92,96,98,105,116],[54,61,73,92,96,99,108,116],[54,65,76,92,96,102,116,119],[55,56,65,66,95,96,100,101],[55,56,71,72,95,96,104,105],[55,56,74,75,95,96,107,108],[55,58,71,92,97,98,106,116],[55,61,74,92,97,99,109,116],[55,64,76,92,97,101,116,119],[56,77,100,103,113,114,117,118],[57,58,62,64,69,71,75,76],[57,58,62,64,103,104,108,110],[57,58,63,65,68,70,75,76],[57,58,63,65,103,104,109,111],[57,58,68,70,99,100,108,110],[57,58,69,71,99,100,109,111],[57,59,61,64,69,72,74,76],[57,59,61,64,103,105,107,110],[57,59,63,66,67,70,74,76],[57,59,63,66,103,105,109,119],[57,59,67,70,99,101,107,110],[57,59,69,72,99,101,109,119],[57,60,61,65,68,72,73,76],[57,60,61,65,103,106,107,111],[57,60,62,66,67,71,73,76],[57,60,62,66,103,106,108,119],[57,60,67,71,99,102,107,111],[57,60,68,72,99,102,108,119],[57,61,68,73,98,100,105,110],[57,61,69,74,98,100,106,111],[57,62,67,73,98,101,104,110],[57,62,69,75,98,101,106,119],[57,63,67,74,98,102,104,111],[57,63,68,75,98,102,105,119],[57,64,71,75,102,105,107,112],[57,64,72,74,102,104,108,112],[57,65,70,75,101,106,107,112],[57,65,72,73,101,104,109,112],[57,66,70,74,100,106,108,112],[57,66,71,73,100,105,109,112],[58,59,61,62,71,72,74,75],[58,59,61,62,104,105,107,108],[58,59,65,66,67,68,74,75],[58,59,65,66,104,105,111,119],[58,59,67,68,100,101,107,108],[58,59,71,72,100,101,111,119],[58,60,61,63,70,72,73,75],[58,60,61,63,104,106,107,109],[58,60,64,66,67,69,73,75],[58,60,64,66,104,106,110,119],[58,60,67,69,100,102,107,109],[58,60,70,72,100,102,110,119],[58,61,70,73,98,99,105,108],[58,61,71,74,98,99,106,109],[58,62,69,76,102,105,107,112],[58,62,72,74,102,103,110,112],[58,63,68,76,101,106,107,112],[58,63,72,73,101,103,111,112],[58,64,67,73,98,101,103,108],[58,64,71,76,98,101,106,119],[58,65,67,74,98,102,103,109],[58,65,70,76,98,102,105,119],[58,66,68,74,99,106,110,112],[58,66,69,73,99,105,111,112],[59,60,62,63,70,71,73,74],[59,60,62,63,105,106,108,109],[59,60,64,65,68,69,73,74],[59,60,64,65,105,106,110,111],[59,60,68,69,101,102,108,109],[59,60,70,71,101,102,110,111],[59,61,69,76,102,104,108,112],[59,61,71,75,102,103,110,112],[59,62,70,73,98,99,104,107],[59,62,72,75,98,99,106,109],[59,63,67,76,100,106,108,112],[59,63,71,73,100,103,112,119],[59,64,68,73,98,100,103,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This does not claim a full native phase word, terminal E decoder, productive caller, new kappa or scientific adoption.","source_pins":{"COVER_semantic":"151c03c9f527e1bc242e0e6d50bee51f7db3163e4a7ae6a9e54e129328f09f89","NORMALIZERS112":"ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da","clifford":"2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962"},"status":"PASS_FULL120_WEYL_PHASE_LIFTS_AND_NEW8_NORMALIZERS","weyl_permutation_rows":[[1,2,496,8,484,468,436,372,244],[1,2,488,484,16,460,428,364,236],[1,2,472,468,460,32,412,348,220],[1,2,440,436,428,412,64,316,188],[1,2,376,372,364,348,316,128,124],[1,2,248,244,236,220,188,124,256],[1,496,4,8,482,466,434,370,242],[1,488,4,482,16,458,426,362,234],[1,472,4,466,458,32,410,346,218],[1,440,4,434,426,410,64,314,186],[1,376,4,370,362,346,314,128,122],[1,248,4,242,234,218,186,122,256],[1,468,466,8,454,32,406,342,214],[1,436,434,8,422,406,64,310,182],[1,372,370,8,358,342,310,128,118],[1,244,242,8,230,214,182,118,256],[1,460,458,454,16,32,398,334,206],[1,428,426,422,16,398,64,302,174],[1,364,362,358,16,334,302,128,110],[1,236,234,230,16,206,174,110,256],[1,348,346,342,334,32,286,128,94],[1,220,218,214,206,32,158,94,256],[1,316,314,310,302,286,64,128,62],[1,188,186,182,174,158,64,62,256],[1,124,122,118,110,94,62,128,256],[496,2,4,8,481,465,433,369,241],[488,2,4,481,16,457,425,361,233],[472,2,4,465,457,32,409,345,217],[440,2,4,433,425,409,64,313,185],[376,2,4,369,361,345,313,128,121],[248,2,4,241,233,217,185,121,256],[484,2,481,8,16,453,421,357,229],[436,2,433,8,421,405,64,309,181],[372,2,369,8,357,341,309,128,117],[244,2,241,8,229,213,181,117,256],[460,2,457,453,16,32,397,333,205],[364,2,361,357,16,333,301,128,109],[236,2,233,229,16,205,173,109,256],[412,2,409,405,397,32,64,285,157],[348,2,345,341,333,32,285,128,93],[220,2,217,213,205,32,157,93,256],[316,2,313,309,301,285,64,128,61],[188,2,185,181,173,157,64,61,256],[124,2,121,117,109,93,61,128,256],[482,481,4,8,16,451,419,355,227],[466,465,4,8,451,32,403,339,211],[370,369,4,8,355,339,307,128,115],[242,241,4,8,227,211,179,115,256],[426,425,4,419,16,395,64,299,171],[362,361,4,355,16,331,299,128,107],[234,233,4,227,16,203,171,107,256],[410,409,4,403,395,32,64,283,155],[346,345,4,339,331,32,283,128,91],[218,217,4,211,203,32,155,91,256],[314,313,4,307,299,283,64,128,59],[186,185,4,179,171,155,64,59,256],[122,121,4,115,107,91,59,128,256],[454,453,451,8,16,32,391,327,199],[422,421,419,8,16,391,64,295,167],[358,357,355,8,16,327,295,128,103],[230,229,227,8,16,199,167,103,256],[406,405,403,8,391,32,64,279,151],[342,341,339,8,327,32,279,128,87],[214,213,211,8,199,32,151,87,256],[310,309,307,8,295,279,64,128,55],[182,181,179,8,167,151,64,55,256],[118,117,115,8,103,87,55,128,256],[398,397,395,391,16,32,64,271,143],[334,333,331,327,16,32,271,128,79],[206,205,203,199,16,32,143,79,256],[302,301,299,295,16,271,64,128,47],[174,173,171,167,16,143,64,47,256],[110,109,107,103,16,79,47,128,256],[286,285,283,279,271,32,64,128,31],[158,157,155,151,143,32,64,31,256],[94,93,91,87,79,32,31,128,256],[62,61,59,55,47,31,64,128,256],[2,1,4,8,16,32,64,128,256],[4,2,1,8,16,32,64,128,256],[8,2,4,1,16,32,64,128,256],[16,2,4,8,1,32,64,128,256],[32,2,4,8,16,1,64,128,256],[64,2,4,8,16,32,1,128,256],[128,2,4,8,16,32,64,1,256],[256,2,4,8,16,32,64,128,1],[1,4,2,8,16,32,64,128,256],[1,8,4,2,16,32,64,128,256],[1,16,4,8,2,32,64,128,256],[1,32,4,8,16,2,64,128,256],[1,64,4,8,16,32,2,128,256],[1,128,4,8,16,32,64,2,256],[1,256,4,8,16,32,64,128,2],[1,2,8,4,16,32,64,128,256],[1,2,16,8,4,32,64,128,256],[1,2,32,8,16,4,64,128,256],[1,2,64,8,16,32,4,128,256],[1,2,128,8,16,32,64,4,256],[1,2,256,8,16,32,64,128,4],[1,2,4,16,8,32,64,128,256],[1,2,4,32,16,8,64,128,256],[1,2,4,64,16,32,8,128,256],[1,2,4,128,16,32,64,8,256],[1,2,4,256,16,32,64,128,8],[1,2,4,8,32,16,64,128,256],[1,2,4,8,64,32,16,128,256],[1,2,4,8,128,32,64,16,256],[1,2,4,8,256,32,64,128,16],[1,2,4,8,16,64,32,128,256],[1,2,4,8,16,128,64,32,256],[1,2,4,8,16,256,64,128,32],[1,2,4,8,16,32,128,64,256],[1,2,4,8,16,32,256,128,64],[1,2,4,496,488,472,440,376,248],[1,484,482,8,16,454,422,358,230],[468,2,465,8,453,32,405,341,213],[458,457,4,451,16,32,395,331,203],[434,433,4,8,419,403,64,307,179],[428,2,425,421,16,397,64,301,173],[1,412,410,406,398,32,64,286,158],[1,2,4,8,16,32,64,256,128]]} diff --git a/research/full120-e8-native/components/full-e8-native120-20261025-structural/inputs/clifford_exact.py b/research/full120-e8-native/components/full-e8-native120-20261025-structural/inputs/clifford_exact.py new file mode 100644 index 0000000000..166841a037 --- /dev/null +++ b/research/full120-e8-native/components/full-e8-native120-20261025-structural/inputs/clifford_exact.py @@ -0,0 +1,149 @@ +"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals. +Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d. +The tableau is supplemented by a literal circuit, so global phases are kept. +""" +from dataclasses import dataclass + +def parity(x):return x.bit_count()&1 +def rank(rows): + p={} + for x in rows: + while x: + b=x.bit_length()-1 + if b not in p:p[b]=x;break + x^=p[b] + return len(p) +def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<>j&1);a[j],a[k]=a[k],a[j] + for i in range(n): + if i!=j and a[i]>>j&1:a[i]^=a[j] + assert [r&((1<>n for r in a) +def basis_extend(cols,n): + out=[] + for x in list(cols)+[1<len(out):out.append(x) + assert len(out)==n + return tuple(out) +def nullspace(rows,n): + a=list(rows);p=[];k=0 + for j in range(n): + t=next((i for i in range(k,len(a)) if a[i]>>j&1),None) + if t is None:continue + a[t],a[k]=a[k],a[t] + for i in range(len(a)): + if i!=k and a[i]>>j&1:a[i]^=a[k] + p.append(j);k+=1 + return tuple((1<>j)&1)<>i&1:out=pmul(out,T[i]) + for i in range(n): + if z>>i&1:out=pmul(out,T[n+i]) + return out +def compose(A,B):return tuple(apply(A,p) for p in B) +def inverse(T): + n=len(T)//2;cols=[x|(z<>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4)) + return tuple(out) +def qvalue(Q,alpha,x,n): + return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4 +def mul_i(a,p): + x,y=a;p%=4 + return [(x,y),(-y,x),(-x,-y),(y,-x)][p] +@dataclass +class Op: + n:int + tab:tuple + circuit:list + def then(self,b): + assert self.n==b.n + return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit) + def adjoint(self): + circ=[] + for e in reversed(self.circuit): + if e[0]=='P':circ.append(('P',inv(e[1],self.n))) + elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2]))) + elif e[0]=='C':circ.append(('C',e[1],-e[2])) + elif e[0]=='phase':circ.append(('phase',(-e[1])%4)) + else:circ.append(e) + return Op(self.n,inverse(self.tab),circ) + def zero_state(self,basis=0): + N=1<>i)&1 for i in range(n)) + assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n)) + return Op(n,tuple([(1<>i&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>i)&1)) for i in range(n)]),[('X',b)]) +def fourier(n,axes=None): + out=ident(n) + for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<len(selected):picks.append(j);selected.append(x) + assert len(picks)==r and all(x>>r==0 for x in Bcols) + Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<>j&1:x^=p[j] + if x:p[x.bit_length()-1]=x + return tuple(p[j]for j in sorted(p,reverse=True)) +def calculate(mid=3): + need(mid in [3,6],'declared intermediate dimensions') + pins={'inputs/NORMALIZERS120.json':'0a27b5be30a78c0f418860c65eea2dd4221fc026cf9f2c86b7a8e865ab4d42df','inputs/clifford_exact.py':'2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962','frame_tools.py':'e5b2ea1f60d554b3a285569602360c663ee8b387350424678b3bd0b0b5432bf4','inputs/COVER.json':'151c03c9f527e1bc242e0e6d50bee51f7db3163e4a7ae6a9e54e129328f09f89'} + for f,p in pins.items():need(sha256((HERE/f).read_bytes()).hexdigest()==p,'source pin '+f) + ce=load('two_cube_clifford',HERE/'inputs/clifford_exact.py');frames=load('two_cube_frames',HERE/'frame_tools.py');peak=[1];sparse,monomial=frames.install(ce,need,peak) + normal=json.loads((HERE/'inputs/NORMALIZERS120.json').read_bytes());cover=json.loads((HERE/'inputs/COVER.json').read_bytes());roots=list(zip(*normal['mode_columns']));chosen=[(i,r['ports'])for i,r in enumerate(cover['cover15'])];ports=sum([ps for _,ps in chosen],[]);NPORT=len(ports);need(NPORT==120 and sorted(ports)==list(range(120)),'actual15cube full120 partition');n=9;R=ce.fourier(n);Q=ce.fourier(n,[0]);D=ce.fourier(n,range(1,n));defs={};anchors=[] + def define(word): + word=json.loads(json.dumps(word));key=sha256(canonical(word)).hexdigest();defs[key]=word;return key + def literal(word): + op=ce.ident(n) + for e in word: + if e[0]=='P':a=ce.perm(n,e[1]) + elif e[0]=='D':a=ce.diag(n,e[1],e[2]) + elif e[0]=='X':a=ce.xgate(n,e[1]) + elif e[0]=='phase':a=ce.Op(n,ce.identity(n),[tuple(e)]) + else:need(e[0]=='C','known literal');a=ce.cgate(n,e[1],e[2]) + op=op.then(a) + return op + phase_checks=[0] + def equal(A,B,label): + need(A.tab==B.tab,label+' signed tableau');need(sparse(A)==sparse(B),label+' absolute zero column');phase_checks[0]+=1 + def path(before,axes,after,expected): + need(all(e[0]in('P','D','X','phase')for e in before+after),'ordinary-only path wrappers') + actual=literal(before).then(ce.fourier(n,axes)).then(literal(after));equal(actual,expected,'actual paid path') + need(ce.rank([x for x,z,p in actual.tab[n:]])==len(axes),'paid rank') + return {'before_monomial':define(before),'child_axes':list(axes),'after_monomial':define(after),'rank':len(axes)} + normalizers={p:literal(normal['ports'][p]['K_word'])for p in ports};qs={p:normal['ports'][p]['q']for p in ports} + for p,L in normalizers.items():equal(L.then(R),R.then(L),'actual old normalizer centralizes full R') + Krows={};group_records=[];program=[] + def mono(role,p,word,label):program.append(['MONOMIAL',role,p,define(word),label]) + def paid(role,p,old,new,rec):program.append(['PAID_PATH',role,p,old,new,rec]) + for p in ports: + own=ce.canonical_frame(n,[qs[p]]) + mono('X',p,monomial(Q.adjoint().then(normalizers[p]).then(own)).circuit,'virtual_Q_source_entry') + mono('Y',p,normalizers[p].circuit,'original_ground_reader_entry') + for g,(support,ps)in enumerate(chosen): + parity={p:side for side,cls in enumerate(cover['cover15'][g]['source_parity_classes'])for p in cls};need(set(parity)==set(ps),'actual graph-derived cover bipartition') + for r in ps:Krows[r]={s:F(int(r==s))-F(sum(a*b for a,b in zip(roots[r],roots[s])),4)for s in ps};Krows[r]={s:v for s,v in Krows[r].items()if v} + need(all(len(Krows[r])==4 and all(abs(v)==F(1,2)for v in Krows[r].values())for r in ps),'actual four signed half K rows') + for parity_bit in [0,1]: + sources=[p for p in ps if parity[p]==parity_bit];readers=[p for p in ps if parity[p]!=parity_bit];S=list(basis(qs[p]for p in sources));other=basis(qs[p]for p in readers) + need(len(S)==len(other)==3 and all(not((a&b).bit_count()&1)for a in S for b in other),'actual orthogonal S3 classes') + original_S3=list(S) + for v in ce.nullspace(other,n): + if len(S)==mid:break + if len(basis(S+[v]))>len(S):S.append(v) + need(len(S)==mid and all(not((a&b).bit_count()&1)for a in S for b in other),'actual S'+str(mid)+' extension inside all reader q-perps') + Phi=ce.canonical_frame(n,S);cols=ce.basis_extend(S,n);K=frames.native_K(ce,cols);T,anchor=frames.native_full_conjugate(ce,need,monomial,cols);anchors.append(anchor);chart='cube%d:S%d:%d'%(g,mid,parity_bit) + entry=path(K.adjoint().circuit,range(mid),K.circuit,Phi);exit=path(K.adjoint().circuit,range(mid,n),T.circuit,Phi.adjoint().then(R)) + for p in sources: + own=ce.canonical_frame(n,[qs[p]]);flag=[qs[p]] + for v in S: + if len(basis(flag+[v]))>len(flag):flag.append(v) + flags=ce.basis_extend(flag,n);Ks=frames.native_K(ce,flags);small=frames.flag_frame(ce,flags,1);wide=frames.flag_frame(ce,flags,mid) + before=monomial(own.adjoint().then(small));after=monomial(wide.adjoint().then(Phi));rec=path(before.circuit+Ks.adjoint().circuit,range(1,mid),Ks.circuit+after.circuit,own.adjoint().then(Phi));paid('X',p,'line:'+str(p),chart,rec) + for p in readers:paid('Y',p,'ground',chart,entry) + for r in readers: + for s,v in sorted(Krows[r].items()):need(s in sources,'actual K cross-parity');program.append(['ADD','Y',r,'X',s,v.numerator,v.denominator,chart]) + for p in sources:paid('X',p,chart,'full9',exit) + for p in readers: + V=S[:] + for v in ce.nullspace((qs[p],),n): + if len(basis(V+[v]))>len(V):V.append(v) + need(len(V)==8,'qperp8');vc=ce.basis_extend(V,n);Kv=frames.native_K(ce,vc);low=frames.flag_frame(ce,vc,mid);target=frames.flag_frame(ce,vc,8) + before=monomial(Phi.adjoint().then(low));rec=path(before.circuit+Kv.adjoint().circuit,range(mid,8),Kv.circuit,Phi.adjoint().then(target));paid('Y',p,chart,'qperp8:'+str(p),rec) + Tv,anchor=frames.native_full_conjugate(ce,need,monomial,vc);anchors.append(anchor) + wrapper=monomial(Kv.adjoint().then(ce.fourier(n,[8])).then(Tv).then(normalizers[p].adjoint()).then(Q.adjoint()));equal(wrapper,target.adjoint().then(normalizers[p].adjoint()).then(D),'reader output wrapper') + mono('Y',p,wrapper.circuit,'reader_D_output') + group_records.append({'cube':g,'source_parity':parity_bit,'sources':sources,'readers':readers,'original_S3':original_S3,'S'+str(mid):S}) + for p in ports:mono('X',p,normalizers[p].adjoint().circuit,'source_D_output') + def conjugate(word): + out=[] + for e in word: + if e[0]=='D':out.append(['D',e[1],[(-v)%4 for v in e[2]]]) + elif e[0]=='phase':out.append(['phase',(-e[1])%4]) + else:need(e[0]in('P','X'),'conjugated monomial');out.append(e) + return out + backward=[] + for p in ports:backward.append(['MONOMIAL','X',p,define([['X',1]]),'input_Q_minus2']) + for e in program: + if e[0]=='MONOMIAL':backward.append(['MONOMIAL',e[1],e[2],define(conjugate(defs[e[3]])),'inverse_transpose_'+e[4]]) + elif e[0]=='ADD':backward.append(['ADD',e[3],e[4],e[1],e[2],-e[5],e[6],'conjugate:'+e[7]]) + else: + rec=e[5];new={'before_monomial':define(conjugate(defs[rec['before_monomial']])),'child_axes':rec['child_axes'],'after_monomial':define([['X',sum(1<X`4`%i!V-#-cd^WVc?Q~dkSe^=(GKmSFO5MGEEDZNrkzF6Y| 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No tensor power of the owner matrix or packing discount.", + "orthonormal_basis_raw27": [ + 262657, + 262658, + 262660, + 262664, + 262672, + 262688, + 262720, + 262784, + 262912, + 263679, + 264703, + 266751, + 270847, + 279039, + 295423, + 328191, + 393727, + 786431, + 1310719, + 2359295, + 4456447, + 8650751, + 17039359, + 33816575, + 67371007 + ], + "owned_fields": 0, + "phase_uniformity": "Every generated paid path uses only exact low-rank monomial gauges and the proved analytic native full-conjugation anchor; generic Lagrangian and phase proofs cover every family member. Default finite replay fully compiles cube000, not all3375 phase instances.", + "physical_ambient": 25, + "scalar_operator": "K_odd=(K1+K2+K3-K1 K2 K3)/2; factor operators act on distinct owner selector coordinates", + "schema": "full120-odd3-E8-whole-K-native-family-template/v1", + "whole_ordinary_profile": { + "ADD": 131328000, + "D": 25920000, + "P": 25920000, + "X": 10368000, + "phase": 10368000 + }, + "whole_original_inputs": 3456000, + "whole_paid_profile": { + "15": 1728000, + "16": 1728000, + "8": 1728000, + "9": 1728000 + } +} diff --git a/research/full120-e8-native/components/full-e8-odd3-native120-20261025-structural/PROOF.md b/research/full120-e8-native/components/full-e8-odd3-native120-20261025-structural/PROOF.md new file mode 100644 index 0000000000..7261392700 --- /dev/null +++ b/research/full120-e8-native/components/full-e8-odd3-native120-20261025-structural/PROOF.md @@ -0,0 +1,105 @@ +# Actual full120 odd3 geometry and retained generic native phase construction + +The source is the new exact15-cube partition, not the former14 support +cubes. For every cube its actual root Gram defines symmetric K_i with +K_i^2=I, four signed-half entries per row, and an actual4+4 binary parity +split of orthogonal3-spaces. The source cube certificate and normalizers +are pinned byte-for-byte in inputs. + +On a512-owner product cube put + + K_odd=(K1+K2+K3-K1 K2 K3)/2. + +The factors act on different owner selectors. Substituting the eight choices +Ki=+/-1 proves K_odd^2=I in their quotient algebra; symmetry is preserved. +Its support has twelve one-factor terms of magnitude1/4 and64 triple-factor +terms of magnitude1/16. They are disjoint because each base Ki has zero +diagonal. Every nonzero coefficient reverses total parity, giving76 entries +and scalar row absolute sum7. The native word applies each coefficient once. + +All actual labels q=(q1,q2,q3) lie in the same nondegenerate25-space U inside +F2^27, consisting of equal three-block parities. A single explicit orthonormal +basis of U is used for every one of3375 cubes. Physical coordinates are +pairings with that basis, rather than a new cube-local chart. The exhaustive +family checker verifies every1,728,000 actual physical label is norm one +and noncharacteristic. In every product cube, each total-parity class has +256 actual labels spanning S9, with restricted pairing rank1 and radical +rank8; the opposite S9 is orthogonal and the joint span has dimension10. +All actual reader q are tested against all nine opposite-source basis +vectors. Thus the native incidence is established for the new full120 +partition itself and is not inferred from the old112-root family. + +For a full binary basis G and its inverse A=G^-1, let + + K_G=D_(I+A^T A) P_G, + Phi_(G,r)=K_G C_[0,r) K_G^-1. + +This retained canonical-frame compiler works for degenerate S. Its Z-image +is Lambda_S={(x,z):x in S,z+x in S-perp}. For S subset T, the intersection +of the two Lagrangians has dimension25-dim(T)+dim(S), giving Gaussian rank +dim(T)-dim(S). Bases of one S differ by ordinary monomial gauges. + +The actual common S9 therefore supports source line->S9 (H8), reader +ground->S9 (H9), source S9->full R25 (H16) and reader S9->q-perp24 (H15). +Every ADD is executed at the identical literal Phi_S9 chart. Sources retain +their independent geometric original u_s, and readers retain arbitrary v_r. +After exits they are respectively R25 u_s and +Phi_(q_r-perp)(v_r+sum_s K_rs u_s). + +For a physical q, the retained real normalizer chooses an orthogonal binary +G_q taking e0 to q, by one even transvection if q0=0 and two if q0=1. +The noncharacteristic condition ensures the needed spare coordinate exists. +For row j of G_q let z_j=(wt(row_j)-1)/2 mod2 and set L_q=Z_z P_Gq. +Orthogonality cancels the quadratic terms in the weight expansion, leaving +wt(G_q^-1 x)-wt(x)=2z.x mod4. Hence L_q commutes with full R25 including +its exact phase. This argument holds for every actual label, and core.py +emits/checks the complete literal normalizer data for all512 root-case ports. + +The ordinary normalized entrance/exit maps are + + X entry: Phi_[q_i] L_i Q^-1; Y entry: L_i; + X exit: L_i^-1; Y exit: D L_i^-1 Phi_(q_i-perp)^-1. + +They produce the actual independent-input endpoint + + X_i=D x_i, + Y_i=D(y_i+sum_j K_ij L_i^-1 L_j Q^-1 x_j). + +Every wrapper is emitted ordinary; Q^-1 is virtual only inside the proved +ordinary entrance identity, not a supplied query. C_K is a real symmetric +involution commuting full R25 because it is the actual per-owner ordinary +normalizer similarity of scalar K_odd. This does not commute C_K past Q. + +The retained generic compiler includes an analytic full-Gaussian conjugate +anchor. If a_j=G^-1 e_j and d_j=floor(wt(a_j)/2) mod2, then + + R25 K_G R25^-1 |0> = (-i)^wt(d) |d>. + +It follows by expanding the actual diagonal Z4 polynomial together with +wt(G^-1 x) mod4; quadratic terms cancel. Its signed tableau and this absolute +column determine the emitted ordinary conjugate without allocating2^25 +amplitudes. All other monomial gauges have bounded sparse phase evaluations. +The reader output wrapper is reduced algebraically to two one-axis Gaussian +factors and these ordinary maps. Core.py checks the retained analytic anchor +against actual root-case signed tableaux and compiles all512 reader outputs. + +These generic frame/phase formulas apply to every actual cube whose geometry +was exhaustively checked. The default finite replay additionally emits a +complete new512-port cube, including added axis roots; it does not claim to +have run every phase instance of all3375 cubes. All original scalar columns, +actual fields, chart reads, normalizers, paid children and ordinary primitives +of that representative are present in its payload. The generic proof supplies +the all-family template rather than an unsupported sample extrapolation. + +Each one-column address identity tensors across any positive field width f. +Scalar phase theta becomes i^(f theta); owner coefficients remain outside +tensor powers and occur once. Original independent inputs are retained, and +no owned/helper/COPY/CLEAR credit is introduced. The complete native profile +is therefore H8+H9+H15+H16 per owner under the retained all-column native and +finite-template contracts. Their physical/tape/precision/outer supplier +admission remains distinct from this local identity. + +The fitting C=I-A has rank22,016 and modal eigenvalues225/2 (multiplicity +21,504) and-1350 (multiplicity512). The native K alone does not implement +that modal service or restore the negative terminal E bank. No new exponent +follows from the better43/3375 modal ratio. diff --git a/research/full120-e8-native/components/full-e8-odd3-native120-20261025-structural/README.md b/research/full120-e8-native/components/full-e8-odd3-native120-20261025-structural/README.md new file mode 100644 index 0000000000..8e7ddc4453 --- /dev/null +++ b/research/full120-e8-native/components/full-e8-odd3-native120-20261025-structural/README.md @@ -0,0 +1,60 @@ +# Full120 odd3: all3375 actual physical cubes and one phase-complete native word + +The new full120 cube partition gives15^3=3375 product cubes and1,728,000 +source owners in one declared global I25 address geometry. Every actual q +is checked in that same chart: all1,728,000 labels are norm one and +noncharacteristic; each of6750 source parity classes has256 ports spanning +S9, restricted pairing rank1/radical dimension8. Opposite S9 classes are +orthogonal and jointly span10 dimensions. The checker performs15,552,000 +actual reader-q versus source-basis dot checks. No cube-local coordinate +adapter is granted free. + +`core.py` actually emits the full512-owner cube(0,0,0), which includes roots +introduced by the full120 cover. It includes1024 arbitrary original main +inputs, all38,912 scalar ADDs, all actual ordinary frame/normalizer words, +and512 positive children of each H8,H9,H15,H16. The root-case ordinary bill +is7680 P,7680 D,3072 X,3072 phase and38,912 ADD. No helper, owned field, +COPY or CLEAR is used. The new native scalar matrix remains + + K_odd=(K1+K2+K3-K1 K2 K3)/2. + +This is the actual K service, with normalized endpoint +`diag(D,D)L(C_K Q^-1)`. It is not the full uncoded A service. The complete +family paid profile is1,728,000 children of each H8,H9,H15,H16 under the +retained generic frame/phase proof. The default phase replay emits one +complete cube, not every ordinary word for all3375 cubes. + +The full fitting C=I-A has rank22,016 and ratio43/3375 per owner, improving +the old5/343 modal ratio. This reduces a future modal bill; it is not an +implemented terminal decoder or a complete caller improvement. The second +H(E) bank remains nonordinary in general. No new kappa, supplier admission, +scientific adoption or selected-frontier update is claimed. + +Read-only reproduction (Python3.11+ standard library): + +``` +python3.11 family_geometry120.py +python3.11 -O family_geometry120.py +python3.11 core.py +python3.11 -O core.py +``` + +All pass. `--write` authors receipts; defaults compare canonical payloads, +excluding gzip container bytes and environment metadata from scientific +identity. `--cube a,b,c --write` emits another actual product instance. + +Credit the retained E8/P112 data, Dugongue's PR4929 code, physical normalizer +and Clifford/compiler lineage, Ali Romman's odd direct-sum construction, +and the earlier whole-K generic phase tools. This work changes the actual +base inventory and verifies the new geometry and representative word; the +generic native compiler is retained source material. Substantial OpenAI +Codex assistance. Apache-2.0; no independent human/kernel acceptance claimed. + +## Open next questions + +- A paid terminal decoder or changed target caller must supply the remaining + E/H/F3 services while charging all source acquisition and restoration. +- The better modal ratio changes the available price allowance. Replay an + actual complete paid/target invoice before asserting an exponent gain. +- Uniform precision, tape/storage and compiler closure remain separate + supplier obligations even after the new finite native identities pass. diff --git a/research/full120-e8-native/components/full-e8-odd3-native120-20261025-structural/core.py b/research/full120-e8-native/components/full-e8-odd3-native120-20261025-structural/core.py new file mode 100644 index 0000000000..f0d8051504 --- /dev/null +++ b/research/full120-e8-native/components/full-e8-odd3-native120-20261025-structural/core.py @@ -0,0 +1,226 @@ +"""Whole odd-E8 K native template; phase-complete emitted root cube. + +All 15^3 product cubes use this same constructor with literal cube indices. +The default replay emits/checks cube(0,0,0); --cube a,b,c checks another +instance. Global geometry and the generic proof justify the structured +forall-family word without expanding131328000 ordinary ADD instructions. + +Credits: Ali Romman's #5439 geometry; PR5464 polarized physical phase tools; +the retained original native/Clifford and coded-normalizer source lineage. +Apache-2.0; substantial OpenAI Codex assistance. No kappa/caller claim. +""" +from pathlib import Path +from fractions import Fraction as F +from collections import Counter +from itertools import product +from hashlib import sha256 +import argparse,gzip,importlib.util,json,sys,time +HERE=Path(__file__).resolve().parent +sys.dont_write_bytecode=True +PINS={'NORMALIZERS.json':'0a27b5be30a78c0f418860c65eea2dd4221fc026cf9f2c86b7a8e865ab4d42df','COVER.json':'151c03c9f527e1bc242e0e6d50bee51f7db3163e4a7ae6a9e54e129328f09f89', + 'clifford_exact.py':'2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962'} +def need(ok,msg): + if not ok:raise ValueError(msg) +def load(name,path): + spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);sys.modules[name]=m;spec.loader.exec_module(m);return m +def canonical(rows): + p={} + for x in rows: + for j in sorted(p,reverse=True): + if x>>j&1:x^=p[j] + if x:p[x.bit_length()-1]=x + for j in sorted(p): + for k in p: + if k!=j and p[k]>>j&1:p[k]^=p[j] + return tuple(p[j]for j in sorted(p,reverse=True)) +def add(dst,src,q): + for k,v in src.items(): + value=dst.get(k,F(0))+q*v + if value:dst[k]=value + else:dst.pop(k,None) +def calculate(cube_tuple=(0,0,0)): + for name,pin in PINS.items():need(sha256((HERE/'inputs'/name).read_bytes()).hexdigest()==pin,'pin '+name) + geometry=load('wholeK_geometry',HERE/'geometry_tools.py');frames=load('wholeK_frames',HERE/'frame_tools.py');ce=load('wholeK_clifford',HERE/'inputs/clifford_exact.py') + normal=json.loads((HERE/'inputs/NORMALIZERS.json').read_bytes());roots=list(zip(*normal['mode_columns']));labels=[p['q']for p in normal['ports']] + cover=json.loads((HERE/'inputs/COVER.json').read_bytes());cubes=[] + for ci,record in enumerate(cover['cover15']): + ports=record['ports'];colors={p:j for j,side in enumerate(record['source_parity_classes'])for p in side};parity=[colors[p]for p in ports] + K=[[F(int(i==j))-F(sum(a*b for a,b in zip(roots[ports[i]],roots[ports[j]])),4)for j in range(8)]for i in range(8)] + need(all(sum(K[i][j]*K[j][k]for j in range(8))==int(i==k)for i,k in product(range(8),repeat=2)),'actual Weyl cube involution') + need(all(sum(bool(v)for v in row)==4 and all(v in (0,F(1,2),F(-1,2))for v in row)for row in K),'actual full120 four signed half entries') + need(all(not K[i][j]or parity[i]!=parity[j]for i,j in product(range(8),repeat=2)),'actual graph-derived cross parity') + cubes.append({'root_support':ci,'ports':ports,'parity':parity,'K':K}) + need(len(cubes)==15 and len(cube_tuple)==3 and all(0<=i<15 for i in cube_tuple),'valid15^3 actual cube tuple') + selected=[cubes[i]for i in cube_tuple];n=25 + U=[1|(1<<9)|(1<<18)]+[(1<<(9*b))^(1<<(9*b+j))for b in range(3)for j in range(1,9)] + orth=geometry.ortho_basis(U) + def qlabel(triple): + raw=sum(labels[p]<<(9*j)for j,p in enumerate(triple)) + need(geometry.span_contains(U,raw),'actual port in U25') + q=sum(geometry.dot(raw,b)<NW}v^;CT*yzu_TeA)rLm5pj;^T3Xns^V&3=G&pLHs4B3; 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"actual_source_ADD_reads_checked": 38912, + "actual_source_ports": 512, + "all_independent_main_operator_rows_checked": 1024, + "arbitrary_main_fields": 1024, + "controls": { + "missing_actual_owned_snapshot_rejected": true, + "owned_early_CLEAR_rejected": true, + "wrong_actual_inverse_orientation_rejected": true, + "wrong_transpose_actual_ADD_sign_rejected": true + }, + "emitted_literal_inverse_and_inverse_transpose_definitions": true, + "exact_inverse_nonzero_operator_terms": 39936, + "inverse_and_transpose_same_paid_profile": true, + "inverse_monomial_or_paid_events": 5632, + "left_and_right_generic_inverse": true, + "native_paid_profile": { + "15": 512, + "16": 512, + "8": 512, + "9": 512 + }, + "owned_CLEAR": 512, + "owned_COPY": 512, + "owned_snapshot_fields": 512, + "schema": "actual-full120-root512-owned-inverse-transpose-review/v1", + "scientific_payload_sha256": "0878720144c6c2a34eb424fd01af3460c2b69362ee457765a489be93be9d644f", + "scope": "Actual new full120 base or root512 native B source-checkpoint compiler, over arbitrary independent noncommuting invertible event operators. Exact inverse and transpose owned lifecycles. Native physical phase science inherited through actual literal monomial inverse/transpose and C^-1=C X_mask identities. E/global lowrank query not included in this native-only replay; separate exact fixture binds those adapters.", + "source_B_science": "4af0f3b0649792387295e37d8a9cf239d47bc8146b07060f886f5ac6a6d2b66e", + "source_contact_reads_each": 76, + "source_contacts_checked": 512, + "status": "PASS_ACTUAL_NATIVE_SOURCE_CHECKPOINT_AND_FREE_OPERATOR_TRANSPOSE", + "transpose_all_operator_entries": true +} diff --git a/research/full120-e8-lowrank-e-native/author/backward512.py b/research/full120-e8-lowrank-e-native/author/backward512.py new file mode 100644 index 0000000000..c8b4a9bf16 --- /dev/null +++ b/research/full120-e8-lowrank-e-native/author/backward512.py @@ -0,0 +1,144 @@ +"""Literal inverse-transpose native K companion; default is read-only. + +--write authors B-PROGRAM/B-MODULE, never the frozen forward science. +""" +from pathlib import Path +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +import argparse,gzip,importlib.util,json,sys +HERE=Path(__file__).resolve().parent +sys.dont_write_bytecode=True +def need(ok,why): + if not ok:raise ValueError(why) +def load(name,path): + spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);sys.modules[name]=m;spec.loader.exec_module(m);return m +def calculate(root): + original=json.loads(gzip.decompress((root/'K-PROGRAM.json.gz').read_bytes())) + original_digest=sha256((json.dumps(original,sort_keys=True,separators=(',',':'))+'\n').encode()).hexdigest() + need(original_digest=='1aeba5ae2276ff58e24ed9ca84f08830c0bb7321432bc74e42472f0029bfb1c2','actual new full120 forward phase science pin') + ce=load('wholeK_backward_primitive',root/'clifford_exact.py');frames=load('new120_backward_frames',root/'frame_tools.py');sparse,monomial=frames.install(ce,need,[1]) + n=original['axis_dimension'];ports=original['port_order'];olddefs=original['definitions'];definitions={} + def define(word): + word=json.loads(json.dumps(word));key=sha256(json.dumps(word,separators=(',',':')).encode()).hexdigest();definitions.setdefault(key,word);return key + def conjugate(word): + out=[] + for e in word: + if e[0]=='D':out.append(['D',e[1],[(-a)%4 for a in e[2]]]) + elif e[0]=='phase':out.append(['phase',(-e[1])%4]) + else:need(e[0]in('P','X'),'no Gaussian hidden in monomial');out.append(e) + return out + def literal(word): + value=ce.ident(n) + for e in word: + if e[0]=='P':part=ce.perm(n,e[1]) + elif e[0]=='D':part=ce.diag(n,e[1],e[2]) + elif e[0]=='X':part=ce.xgate(n,e[1]) + elif e[0]=='phase':part=ce.Op(n,ce.identity(n),[tuple(e)]) + else:need(e[0]=='C','known primitive');part=ce.cgate(n,e[1],e[2]) + value=value.then(part) + return value + translated={};checks=0 + def translate_path(path): + nonlocal checks + key=json.dumps(path,sort_keys=True,separators=(',',':')) + if key not in translated: + pre=conjugate(olddefs[path['before_monomial']]);post=conjugate(olddefs[path['after_monomial']]);axes=path['child_axes'];mask=sum(1<>a&1];positive=ce.fourier(sn,axes);inverse=positive.adjoint();compiled=positive.then(ce.xgate(sn,mask)) + need(inverse.tab==compiled.tab,'positive-child inverse signed tableau') + for x in range(1< E^-T. Real scalar ADD swaps roles and negates coefficient. Monomial becomes complex conjugate. C_minus child is emitted as positive C_plus followed by X_axis_mask.', + 'boundary':'Input X Q^-2; output both banks D^2 then output X Q^2. Consecutive X-bank output masks are literally composed into X_all25.', + 'normalized_endpoint':'B_K=diag(D,D) U(-Q C_K), without requiring [C_K,Q]=0', + 'all_widths':'One-copy address maps tensor-lift; phase theta -> i^(f theta). Owner scalar coefficients transposed/negated once, never raised to width f.'} + canonical=(json.dumps(payload,sort_keys=True,separators=(',',':'))+'\n').encode();encoded=gzip.compress(canonical,mtime=0) + summary={'schema':'full120-odd3-E8-whole-K-backward-native/v1','status':'PASS','forward_scientific_payload_sha256':original_digest, + 'backward_scientific_payload_sha256':sha256(canonical).hexdigest(),'paid_profile':dict(sorted(paid.items())), + 'ordinary_literal_profile':dict(sorted(ordinary.items())),'distinct_conjugated_paid_paths':checks, + 'all_independent_scalar_columns':1024,'small_dense_child_inversion_cases':primitive_checks, + 'actual_rank8_word_absolute_phase_checked':True,'normalized_endpoint':payload['normalized_endpoint'], + 'helpers':0,'owned_fields':0,'COPY':0,'CLEAR':0,'new_kappa':False, + 'scope':'Literal backward native K companion, including ordinary boundaries. It does not supply H or close/admit an outer caller.'} + return summary,payload,encoded +def main(): + ap=argparse.ArgumentParser();ap.add_argument('--package',type=Path,default=HERE/'inputs');ap.add_argument('--write',action='store_true');args=ap.parse_args();root=args.package.resolve() + summary,payload,encoded=calculate(root) + if args.write: + (root/'B-MODULE.json').write_text(json.dumps(summary,sort_keys=True,indent=2)+'\n');(root/'B-PROGRAM.json.gz').write_bytes(encoded) + else: + need(json.loads((root/'B-MODULE.json').read_bytes())==json.loads(json.dumps(summary)),'frozen backward semantic receipt') + need(json.loads(gzip.decompress((root/'B-PROGRAM.json.gz').read_bytes()))==json.loads(json.dumps(payload)),'frozen backward actual word') + print('PASS whole-K literal backward native; columns1024; '+summary['backward_scientific_payload_sha256']) +if __name__=='__main__':main() diff --git a/research/full120-e8-lowrank-e-native/author/checkpoint120.py b/research/full120-e8-lowrank-e-native/author/checkpoint120.py new file mode 100644 index 0000000000..142e55ec51 --- /dev/null +++ b/research/full120-e8-lowrank-e-native/author/checkpoint120.py @@ -0,0 +1,163 @@ +"""Actual root512 source-contact inverse and exact transposed owned word. + +Native unary operations are arbitrary invertible free operator letters in the +all-input replay. Their inverse/transpose physical words are also emitted. +Default is read-only; no sealed source package is modified. +""" +import argparse,gzip,hashlib,json,sys +from collections import Counter +from fractions import Fraction as F +from pathlib import Path +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent +SOURCE=HERE/'inputs' +PINS={'base120':'87d7cad7133ed0a2950b1d4fa2397e20e3c7bcedb90db95a15130aa03da543ae','root512':'4af0f3b0649792387295e37d8a9cf239d47bc8146b07060f886f5ac6a6d2b66e'} +def need(q,s): + if not q:raise ValueError(s) +def canonical(x):return (json.dumps(x,sort_keys=True,separators=(',',':'))+'\n').encode() +def gf_inv(rows): + n=len(rows);r=[v|(1<<(n+j))for j,v in enumerate(rows)] + for j in range(n): + p=next(i for i in range(j,n)if r[i]>>j&1);r[p],r[j]=r[j],r[p] + for i in range(n): + if i!=j and r[i]>>j&1:r[i]^=r[j] + need([v&((1<>n for v in r] +def mono_transform(word,transpose=False): + out=[] + for e in reversed(word): + if e[0]=='P':out.append(['P',gf_inv(e[1])]) + elif e[0]=='D':out.append(['D',e[1],e[2]if transpose else[(-v)%4 for v in e[2]]]) + elif e[0]=='X':out.append(list(e)) + else:need(e[0]=='phase','actual monomial opcode');out.append(['phase',e[1]if transpose else(-e[1])%4]) + return out +# Free invertible event letters with a transpose involution, all noncommuting. +def reduce_prepend(letter,w): + return w[1:]if w and w[0]==-letter else(letter,)+w +def opword(w,letter):return reduce_prepend(letter,w) +def transformed_word(w): + # Transpose maps each event letter k to k+N with the same inverse sign. + return tuple((1 if x>0 else-1)*(abs(x)+1000000)for x in reversed(w)) +def add(dst,src,c): + for key,v in src.items(): + x=dst.get(key,F())+c*v + if x:dst[key]=x + else:dst.pop(key,None) +def run(program,main,initial=None,strict=True): + states={x:{(x,()):F(1)}for x in main}if initial is None else{k:dict(v)for k,v in initial.items()} + live=set(main) + for e in program: + k=e[0] + if k=='UNARY': + f=tuple(e[1]);letter=e[2] + need(f in live,'unary reads initialized field') + states[f]={(src,opword(w,letter)):c for(src,w),c in states[f].items()} + elif k=='ADD': + a,b=tuple(e[1]),tuple(e[2]);need(a in live and b in live,'ADD reads initialized owned/main field');add(states[a],states[b],F(e[3],e[4])) + elif k=='COPY': + a,b=tuple(e[1]),tuple(e[2]);need(a not in live and b in live,'COPY requires fresh owned destination and initialized source');states[a]=dict(states[b]);live.add(a) + else: + need(k=='CLEAR','known emitted opcode');a=tuple(e[1]);need(a in live,'CLEAR requires live owned field');need(a not in main,'no main CLEAR');states[a]={};live.remove(a) + need(all(f in main for f in live),'all owned fields cleared after final read') + return {f:states[f]for f in main} +def transpose_program(program): + out=[] + for e in reversed(program): + if e[0]=='UNARY':out.append(['UNARY',e[1],(1 if e[2]>0 else-1)*(abs(e[2])+1000000)]) + elif e[0]=='ADD':out.append(['ADD',e[2],e[1],e[3],e[4]]) + elif e[0]=='CLEAR': + # A reverse adjoint for a discarded owned variable starts at zero. + out.append(['ZERO_OWNED',e[1]]) + else: + need(e[0]=='COPY','transpose supported opcode');out.extend([['ADD',e[2],e[1],1,1],['CLEAR',e[1]]]) + # ZERO_OWNED does not read an ordinary variable; normalize it to a fresh + # initialized zero field, kept separate from COPY's overwrite prohibition. + return out +def run_transpose(program,main): + states={f:{(f,()):F(1)}for f in main};live=set(main) + for e in program: + k=e[0] + if k=='ZERO_OWNED': + f=tuple(e[1]);need(f not in live and f not in main,'adjoint owned zero is fresh');states[f]={};live.add(f) + elif k=='UNARY': + f=tuple(e[1]);need(f in live,'adjoint unary initialized');states[f]={(src,opword(w,e[2])):c for(src,w),c in states[f].items()} + elif k=='ADD': + a,b=tuple(e[1]),tuple(e[2]);need(a in live and b in live,'adjoint ADD initialized');add(states[a],states[b],F(e[3],e[4])) + else: + need(k=='CLEAR','known adjoint opcode');f=tuple(e[1]);need(f in live and f not in main,'owned adjoint CLEAR');states[f]={};live.remove(f) + need(live==set(main),'all adjoint owned fields cleaned') + return {f:states[f]for f in main} +def compile_program(source,mode): + PIN=PINS[mode];filename='NATIVE120-NATIVE-PROGRAM.json.gz'if mode=='base120'else'B-PROGRAM.json.gz';payload=json.loads(gzip.decompress((source/filename).read_bytes()));need(hashlib.sha256(canonical(payload)).hexdigest()==PIN,'actual new full120 B canonical science pin') + original=payload['backward_program']if mode=='base120'else payload['program'];ports=payload['port_order'];main=[(r,p)for r in ['X','Y']for p in ports] + program=[];events={};versions=Counter();contacts={};usecounts=Counter();paid=Counter();defs={} + def wordid(w): + k=hashlib.sha256(canonical(w)).hexdigest();defs[k]=w;return k + for index,e in enumerate(original): + if e[0]=='ADD': + need(e[1]=='X'and e[3]=='Y','actual literal B has source-only Y') + p=e[4];contact=(versions[p],e[7]);need(p not in contacts or contacts[p]==contact,'every actual Y has one unchanged physical ADD contact') + contacts[p]=contact;usecounts[p]+=1;program.append(['ADD',[e[1],e[2]],[e[3],e[4]],e[5],e[6]]) + else: + need(e[0]in['MONOMIAL','BOUNDARY_MONOMIAL','PAID_PATH'],'known actual B instruction') + f=[e[1],e[2]];eid=index+1 + if e[1]=='Y':versions[e[2]]+=1 + if e[0]=='PAID_PATH': + rec=e[5];before=payload['definitions'][rec['before_monomial']];after=payload['definitions'][rec['after_monomial']];axes=rec['child_axes'];paid[len(axes)]+=1 + inverse={'kind':'PAID_PATH','before':wordid(mono_transform(after)),'positive_child_axes':axes,'after':wordid([['X',sum(1<>1)&1)][x]=C(1) + def gate(q,s): + O=scale(C(F(1,2),F(s,2)),I) + for x in range(N):O[x^q][x]+=C(F(1,2),F(-s,2)) + return O + Q0=gate(1,1);Qi0=gate(1,-1);D0=gate(2,1);Di0=gate(2,-1) + Q=diag(Q0,Q0);Qi=diag(Qi0,Qi0);D=diag(D0,D0);Di=diag(Di0,Di0);I=ident(8);Z=zeros(8) + K=block(zeros(4),P,P,zeros(4));R=mul(D,Q) + need(mul(K,K),I,'actual K involution');need(mul(K,R),mul(R,K),'actual fullGaussian centralization') + if mul(K,Q)==mul(Q,K):raise ValueError('noncommuting-Q control lost') + # FC=lambda*Pminus; active B=I-K=2Pminus, BC=2C. + Pminus=scale(F(1,2),add(I,scale(-1,K)));out=[] + FK=mul(diag(D,D),lower(mul(K,Qi)));BK=mul(diag(D,D),upper(scale(-1,mul(Q,K)))) + F0=mul(diag(D,D),lower(Qi));B0=mul(diag(D,D),upper(scale(-1,Q))) + for lam in [15,F(225,2),-1350]: + FC=scale(lam,Pminus);A=add(I,scale(-1,FC));Ai=add(I,scale(F(lam,1-lam),Pminus)) + need(mul(A,Ai),I,'inverse A exact') + for name,X,Xinv,residual in [('KA',A,Ai,Ai),('K_Ainverse',Ai,A,A)]: + E=mul(K,X);Ei=mul(K,Xinv);H=diag(E,prod(Qi,E,Q));Hi=diag(Ei,prod(Qi,Ei,Q));Delta=add(I,scale(-1,residual)) + leftF=prod(diag(E,I),FK,diag(I,E));leftB=prod(diag(Ei,I),BK,diag(I,Ei)) + rightF=prod(H,diag(D,D),lower(mul(residual,Qi)));rightB=prod(Hi,diag(D,D),upper(scale(-1,mul(Q,residual)))) + need(leftF,rightF,'forward E exact adapter');need(leftB,rightB,'backward E inverse exact adapter') + need(mul(leftF,lower(mul(Delta,Qi))),mul(H,F0),'forward lowrank defect correction') + need(mul(leftB,upper(scale(-1,mul(Q,Delta)))),mul(Hi,B0),'backward lowrank defect correction') + # Physical post-native backward correction uses original ground Y only: + # add -R Delta Y to native X before postX(E^-1). + scatter=block(Z,scale(-1,mul(Ei,mul(R,Delta))),Z,Z) + WB=add(leftB,scatter) + need(WB,mul(Hi,B0),'physical original-ground backward correction') + if name=='K_Ainverse': + # Inverse scheduling: source Y native inverse first, with its contact + # checkpoint retained, then undo correction and finish native X inverse. + # At matrix level y=E D^-1 Yout is acquired before X's native inverse. + # The literal K schedule must retain its Y common-frame contact via COPY. + BKi=mul(upper(mul(Q,K)),diag(Di,Di)) + y_acquire=mul(E,Di) + undo=block(I,mul(R,mul(FC,y_acquire)),Z,I) + WBi=prod(diag(I,E),BKi,undo,diag(E,I)) + need(mul(WBi,WB),ident(16),'checkpoint-scheduled physical inverse left') + need(mul(WB,WBi),ident(16),'checkpoint-scheduled physical inverse right') + # Transpose the obtained inverse linear algorithm; C^T=C, its inverse + # is positive C then ordinary X. The boundary is entirely monomial. + transpose=lambda M:list(map(list,zip(*M))) + Q2=mul(Q,Q);D2=mul(D,D);J=diag(Q2,I);Jinv=J + WF=prod(diag(D2,D2),J,transpose(WBi),Jinv) + need(WF,mul(H,F0),'actual symmetric E duality produces forward code') + # Omission produces an actual nonzero physical defect, not just syntax. + if leftF==mul(H,F0)or leftB==mul(Hi,B0):raise ValueError('omitted correction mutation accepted') + # Q must be in the displayed order: it cannot commute through Delta. + if mul(Delta,Q)==mul(Q,Delta):raise ValueError('noncommutative defect control lost') + out.append({'lambda':str(lam),'E':name,'forward_backward_adapters':True,'corrected_forward_backward':True,'omitted_correction_rejected':True,'Delta_Q_noncommuting':True,'physical_ground_backward_correction':True,'inverse_and_transpose_boundary_checked':name=='K_Ainverse'}) + return {'schema':'source-consuming-E-exact-small-model/v1','status':'PASS_EXACT_LOCAL_IDENTITIES_ONLY','address_axes':2,'owners':2,'complex_rational_main_matrix_dimension':16,'cases':out,'generic_identity':'For X commuting K with E=KX, [E,DQ]=0: postX(E) F_K preY(E)=H(E) diag(D,D) L(X^-1 Q^-1); postX(E^-1) B_K preY(E^-1)=H(E^-1) diag(D,D) U(-Q X^-1).','correction':'Delta=I-X^-1; right-prepend L(Delta Q^-1) or U(-Q Delta) to recover scalar core with codes E/E^-1. For X=A^-1, Delta=F_C exactly, with rank rank(F_C).','scope':'This small fixture proves local noncommuting-Q identities. Separate MACROS120 and MODES120 objects bind actual owned base120 words and the structured odd3 constructor. Negative terminal E-word decoding and full outer precision/TM/storage admission remain UNKNOWN.'} +if __name__=='__main__': + p=argparse.ArgumentParser();p.add_argument('--write',action='store_true');a=p.parse_args();r=calc();f=Path(__file__).with_name('E-ADAPTER.json') + if a.write:f.write_text(json.dumps(r,sort_keys=True,indent=2)+'\n') + else:need(r,json.loads(f.read_bytes()),'readonly receipt') + print(json.dumps(r,sort_keys=True)) diff --git a/research/full120-e8-lowrank-e-native/author/inputs/B-MODULE.json b/research/full120-e8-lowrank-e-native/author/inputs/B-MODULE.json new file mode 100644 index 0000000000..f6bf4137a0 --- /dev/null +++ b/research/full120-e8-lowrank-e-native/author/inputs/B-MODULE.json @@ -0,0 +1,30 @@ +{ + "CLEAR": 0, + "COPY": 0, + "actual_rank8_word_absolute_phase_checked": true, + "all_independent_scalar_columns": 1024, + "backward_scientific_payload_sha256": "4af0f3b0649792387295e37d8a9cf239d47bc8146b07060f886f5ac6a6d2b66e", + "distinct_conjugated_paid_paths": 1028, + "forward_scientific_payload_sha256": "1aeba5ae2276ff58e24ed9ca84f08830c0bb7321432bc74e42472f0029bfb1c2", + "helpers": 0, + "new_kappa": false, + "normalized_endpoint": "B_K=diag(D,D) U(-Q C_K), without requiring [C_K,Q]=0", + "ordinary_literal_profile": { + "ADD": 38912, + "D": 7680, + "P": 7680, + "X": 6656, + "phase": 3072 + }, + "owned_fields": 0, + "paid_profile": { + "8": 512, + "9": 512, + "15": 512, + "16": 512 + }, + "schema": "full120-odd3-E8-whole-K-backward-native/v1", + "scope": "Literal backward native K companion, including ordinary boundaries. It does not supply H or close/admit an outer caller.", + "small_dense_child_inversion_cases": 26, + "status": "PASS" +} diff --git a/research/full120-e8-lowrank-e-native/author/inputs/B-PROGRAM.json.gz b/research/full120-e8-lowrank-e-native/author/inputs/B-PROGRAM.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..ff8968585bc0ebf9e00b874db20bf6219603a0db GIT binary patch literal 836583 zcmV(&K;ge1iwFP!000026YRaot}Mxx9ri1U97(__%KD}VXd+HDqBJX@z$#cPCiE&_ z;bj&nfJy{`tTDR{#9ZfBgFQzy8PH z+uxPH{_B7HCDr=3_QxN;{7d@RKYsbM{r<;a|Mqu(`K|x??|=E%|D674zx?^1+n?!| zzx&^R`R$+nmp;$_*MIlRfBdh%x4-@JM@fH4fBU8Uwe|j6`K|r_C%)ou>GwbW^{;=l z`oI0&{-5+`tH1p9_tIW|`Mv!YeB^KGH{AN=&%gdMy7Ei^cfY>;n*P7v{`lwm+rQw~ zfBWn2zy7_lFTdu${@d?0{q4V@um9)o|N3u#{_+pM{NMldck18&^4EX+lc)Kw_;gOc z|G$6y@*n<5v17llxA>&`cfb4}fBpTBR{rhJ-~LPc{N=Yl z+utxS{|ztkFQeDL{PsIK_YeP!i^{Td<==Aq=Rg1LU;om6{ri6uFZl02z5H5R|LynR z{zPvvnE(A(Awf!nF-+y}fM}<}%{)y4GN346Xa$K`oMYc{`{bEFPFGdMvqJNQ2qi;qjFFbB38!;X) 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,94,95,109,111,115],[49,50,52,53,59,60,62,63],[49,50,52,53,70,71,73,74],[49,50,52,53,105,106,108,109],[49,50,54,55,59,60,64,65],[49,50,54,55,68,69,73,74],[49,50,54,55,105,106,110,111],[49,50,59,60,96,97,101,102],[49,50,68,69,96,97,108,109],[49,50,70,71,96,97,110,111],[49,51,54,57,59,61,64,115],[49,51,54,69,72,74,76,115],[49,51,54,103,105,107,110,115],[49,52,59,62,93,94,98,99],[49,52,70,73,93,94,104,107],[49,52,72,75,93,94,106,109],[49,53,56,57,59,63,66,115],[49,53,56,67,70,74,76,115],[49,53,56,103,105,109,115,119],[49,54,59,64,93,95,98,100],[49,54,68,73,93,95,103,107],[49,54,72,76,93,95,106,111],[49,56,59,66,93,97,98,102],[49,56,68,75,93,97,103,109],[49,56,70,76,93,97,104,111],[49,57,59,94,96,99,101,115],[49,67,70,94,96,107,110,115],[49,69,72,94,96,109,115,119],[50,51,55,57,60,61,65,115],[50,51,55,68,72,73,76,115],[50,51,55,103,106,107,111,115],[50,52,56,57,60,62,66,115],[50,52,56,67,71,73,76,115],[50,52,56,103,106,108,115,119],[50,53,60,63,93,94,98,99],[50,53,71,74,93,94,104,107],[50,53,72,75,93,94,105,108],[50,55,60,65,93,95,98,100],[50,55,69,74,93,95,103,107],[50,55,72,76,93,95,105,110],[50,56,60,66,93,96,98,101],[50,56,69,75,93,96,103,108],[50,56,71,76,93,96,104,110],[50,57,60,94,97,99,102,115],[50,67,71,94,97,107,111,115],[50,68,72,94,97,108,115,119],[51,52,55,56,61,62,65,66],[51,52,55,56,67,68,71,72],[51,52,55,56,107,108,111,119],[51,52,61,62,95,96,100,101],[51,52,67,68,95,96,104,105],[51,52,74,75,95,96,111,119],[51,53,54,56,61,63,64,66],[51,53,54,56,67,69,70,72],[51,53,54,56,107,109,110,119],[51,53,61,63,95,97,100,102],[51,53,67,69,95,97,104,106],[51,53,73,75,95,97,110,119],[51,54,61,64,94,96,99,101],[51,54,67,70,94,96,103,105],[51,54,74,76,94,96,109,119],[51,55,61,65,94,97,99,102],[51,55,67,71,94,97,103,106],[51,55,73,76,94,97,108,119],[51,57,61,93,95,98,100,115],[51,58,67,92,94,98,103,116],[51,64,73,92,94,101,108,116],[51,65,74,92,94,102,109,116],[51,68,73,93,95,105,110,115],[51,69,74,93,95,106,111,115],[52,53,54,55,62,63,64,65],[52,53,54,55,68,69,70,71],[52,53,54,55,108,109,110,111],[52,53,62,63,96,97,101,102],[52,53,68,69,96,97,105,106],[52,53,73,74,96,97,110,111],[52,54,62,64,94,95,99,100],[52,54,68,70,94,95,103,104],[52,54,75,76,94,95,109,111],[52,56,62,66,94,97,99,102],[52,56,68,72,94,97,103,106],[52,56,73,76,94,97,107,111],[52,57,62,93,96,98,101,115],[52,67,73,93,96,104,110,115],[52,69,75,93,96,106,115,119],[53,55,63,65,94,95,99,100],[53,55,69,71,94,95,103,104],[53,55,75,76,94,95,108,110],[53,56,63,66,94,96,99,101],[53,56,69,72,94,96,103,105],[53,56,74,76,94,96,107,110],[53,57,63,93,97,98,102,115],[53,67,74,93,97,104,111,115],[53,68,75,93,97,105,115,119],[54,55,64,65,96,97,101,102],[54,55,70,71,96,97,105,106],[54,55,73,74,96,97,108,109],[54,56,64,66,95,97,100,102],[54,56,70,72,95,97,104,106],[54,56,73,75,95,97,107,109],[54,58,70,92,96,98,105,116],[54,61,73,92,96,99,108,116],[54,65,76,92,96,102,116,119],[55,56,65,66,95,96,100,101],[55,56,71,72,95,96,104,105],[55,56,74,75,95,96,107,108],[55,58,71,92,97,98,106,116],[55,61,74,92,97,99,109,116],[55,64,76,92,97,101,116,119],[56,77,100,103,113,114,117,118],[57,58,62,64,69,71,75,76],[57,58,62,64,103,104,108,110],[57,58,63,65,68,70,75,76],[57,58,63,65,103,104,109,111],[57,58,68,70,99,100,108,110],[57,58,69,71,99,100,109,111],[57,59,61,64,69,72,74,76],[57,59,61,64,103,105,107,110],[57,59,63,66,67,70,74,76],[57,59,63,66,103,105,109,119],[57,59,67,70,99,101,107,110],[57,59,69,72,99,101,109,119],[57,60,61,65,68,72,73,76],[57,60,61,65,103,106,107,111],[57,60,62,66,67,71,73,76],[57,60,62,66,103,106,108,119],[57,60,67,71,99,102,107,111],[57,60,68,72,99,102,108,119],[57,61,68,73,98,100,105,110],[57,61,69,74,98,100,106,111],[57,62,67,73,98,101,104,110],[57,62,69,75,98,101,106,119],[57,63,67,74,98,102,104,111],[57,63,68,75,98,102,105,119],[57,64,71,75,102,105,107,112],[57,64,72,74,102,104,108,112],[57,65,70,75,101,106,107,112],[57,65,72,73,101,104,109,112],[57,66,70,74,100,106,108,112],[57,66,71,73,100,105,109,112],[58,59,61,62,71,72,74,75],[58,59,61,62,104,105,107,108],[58,59,65,66,67,68,74,75],[58,59,65,66,104,105,111,119],[58,59,67,68,100,101,107,108],[58,59,71,72,100,101,111,119],[58,60,61,63,70,72,73,75],[58,60,61,63,104,106,107,109],[58,60,64,66,67,69,73,75],[58,60,64,66,104,106,110,119],[58,60,67,69,100,102,107,109],[58,60,70,72,100,102,110,119],[58,61,70,73,98,99,105,108],[58,61,71,74,98,99,106,109],[58,62,69,76,102,105,107,112],[58,62,72,74,102,103,110,112],[58,63,68,76,101,106,107,112],[58,63,72,73,101,103,111,112],[58,64,67,73,98,101,103,108],[58,64,71,76,98,101,106,119],[58,65,67,74,98,102,103,109],[58,65,70,76,98,102,105,119],[58,66,68,74,99,106,110,112],[58,66,69,73,99,105,111,112],[59,60,62,63,70,71,73,74],[59,60,62,63,105,106,108,109],[59,60,64,65,68,69,73,74],[59,60,64,65,105,106,110,111],[59,60,68,69,101,102,108,109],[59,60,70,71,101,102,110,111],[59,61,69,76,102,104,108,112],[59,61,71,75,102,103,110,112],[59,62,70,73,98,99,104,107],[59,62,72,75,98,99,106,109],[59,63,67,76,100,106,108,112],[59,63,71,73,100,103,112,119],[59,64,68,73,98,100,103,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full120 E8 roots, all Weyl-reflection closure and cube orbit, exact15-cube partition, actual q parity-class rank3/orthogonality. Native paid ranks follow the retained generic source/read canonical-frame construction; phase-complete full120 normalized words, terminal decoder and whole caller admission remain separate.","source_pin":"ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da","status":"PASS_FULL120_CLOSED_E8_15_NATIVE_CUBE_EXACT_COVER"} diff --git a/research/full120-e8-lowrank-e-native/author/inputs/K-MODULE.json b/research/full120-e8-lowrank-e-native/author/inputs/K-MODULE.json new file mode 100644 index 0000000000..e384beac04 --- /dev/null +++ b/research/full120-e8-lowrank-e-native/author/inputs/K-MODULE.json @@ -0,0 +1,73 @@ +{ + "CLEAR": 0, + "COPY": 0, + "all_original_scalar_columns_checked": 1024, + "axis_dimension": 25, + "code_contract": { + "C_K_commutes_full_R": true, + "C_K_squared_identity": true, + "C_K_symmetric": true, + "proof": "K_odd symmetric involution and real orthogonal direct-owner normalizer similarity; each L_i commutes R exactly" + }, + "cube_tuple": [ + 0, + 0, + 0 + ], + "environment_metadata": { + "program_container_bytes": 1328463, + "program_container_sha256": "696c02bc2aefa0cd0dd0c92d40e0e821d9ae7c4e7798182a2c53861098d70fec" + }, + "helpers": 0, + "logical_growth": { + "max_scalar_denominator_exponent": 4, + "proof": "Each reader retains its own v plus76 distinct independent u terms:12 magnitudes1/4 and64 magnitudes1/16. Sources unchanged; all physical charts/wrappers unitary.", + "reader_max_row_l1": "8", + "source_max_row_l1": "1" + }, + "mutation_controls": { + "missing_actual_ADD_changes_independent_endpoint": true, + "same_tableau_phase_i_rejected": true, + "wrong_parity_common_chart_transport_rank": 2 + }, + "new_kappa": false, + "normalized_endpoint": "F_K=diag(D,D) L(C_K Q^-1), C_K=diag(L_i^-1) K_odd diag(L_i), D=C_[1,25), Q=C_0", + "normalized_entry": "All original x_i,y_i arbitrary independent at physical ground; all virtual-Q source-line entry wrappers are emitted ordinary monomials.", + "ordinary_literal_profile": { + "ADD": 38912, + "D": 7680, + "P": 7680, + "X": 3072, + "phase": 3072 + }, + "original_main_inputs": 1024, + "owned_fields": 0, + "paid_path_applications": 2048, + "paid_profile": { + "15": 512, + "16": 512, + "8": 512, + "9": 512 + }, + "phase_compilation": { + "all_positive_widths": "literal one-copy phases tensor lift; phase opcode theta becomes i^(f theta); owner scalar coefficients applied once", + "all_wrappers_monomial": true, + "low_rank_sparse_peak_support": 512, + "native_full_conjugate_analytic_anchors": 514, + "reader_output_wrappers": 512, + "source_input_wrappers": 512 + }, + "reader_endpoint": "D(y_i+sum_j K_odd[i,j] L_i^-1 L_j Q^-1 x_j)", + "reader_fields": 512, + "schema": "full120-odd3-E8-K-normalized-native-rootcase/v1", + "scientific_program_payload_sha256": "1aeba5ae2276ff58e24ed9ca84f08830c0bb7321432bc74e42472f0029bfb1c2", + "scope": "Whole local block-diagonal K native constructor, with phase-complete emitted cube instance and generic forall3375 proof plus independent all-family geometry. It does not implement H, install F3, close any outer caller, admit precision/work/storage, or improve kappa.", + "source_endpoint": "D x_i on every independent original source x_i", + "source_fields": 512, + "source_pins": { + "COVER.json": "151c03c9f527e1bc242e0e6d50bee51f7db3163e4a7ae6a9e54e129328f09f89", + "NORMALIZERS.json": "0a27b5be30a78c0f418860c65eea2dd4221fc026cf9f2c86b7a8e865ab4d42df", + "clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + }, + "status": "PASS_PHASE_COMPLETE_K_NATIVE_ROOTCASE_AND_GENERIC_FAMILY_TEMPLATE" +} diff --git a/research/full120-e8-lowrank-e-native/author/inputs/K-PROGRAM.json.gz b/research/full120-e8-lowrank-e-native/author/inputs/K-PROGRAM.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..10f7c1a513ec0de91821b51585623e086874919d GIT binary patch literal 1328463 zcmV(?K-a$?iwFP!000026YRa&jxD*BCHN~sJbM8oH%HZD_XiYEFAWF@fn#QLhawUo 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len(out)==n + return tuple(out) +def nullspace(rows,n): + a=list(rows);p=[];k=0 + for j in range(n): + t=next((i for i in range(k,len(a)) if a[i]>>j&1),None) + if t is None:continue + a[t],a[k]=a[k],a[t] + for i in range(len(a)): + if i!=k and a[i]>>j&1:a[i]^=a[k] + p.append(j);k+=1 + return tuple((1<>j)&1)<>i&1:out=pmul(out,T[i]) + for i in range(n): + if z>>i&1:out=pmul(out,T[n+i]) + return out +def compose(A,B):return tuple(apply(A,p) for p in B) +def inverse(T): + n=len(T)//2;cols=[x|(z<>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4)) + return tuple(out) +def qvalue(Q,alpha,x,n): + return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4 +def mul_i(a,p): + x,y=a;p%=4 + return [(x,y),(-y,x),(-x,-y),(y,-x)][p] +@dataclass +class Op: + n:int + tab:tuple + circuit:list + def then(self,b): + assert self.n==b.n + return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit) + def adjoint(self): + circ=[] + for e in reversed(self.circuit): + if e[0]=='P':circ.append(('P',inv(e[1],self.n))) + elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2]))) + elif e[0]=='C':circ.append(('C',e[1],-e[2])) + elif e[0]=='phase':circ.append(('phase',(-e[1])%4)) + else:circ.append(e) + return Op(self.n,inverse(self.tab),circ) + def zero_state(self,basis=0): + N=1<>i)&1 for i in range(n)) + assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n)) + return Op(n,tuple([(1<>i&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>i)&1)) for i in range(n)]),[('X',b)]) +def fourier(n,axes=None): + out=ident(n) + for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<len(selected):picks.append(j);selected.append(x) + assert len(picks)==r and all(x>>r==0 for x in Bcols) + Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<=((1-i)/2)^n sum_x i^wt(x)|x>. Thus R K_G R^-1|0>=(-i)^wt(d)|d>. 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A transpose word reverses chronological order and exchanges ADD source and destination. SCALE and SWAP are self-transpose. The checker applies each word to all120 independent input roles using exact rational arithmetic, then compares the complete matrix with the supplied target. + +At every prefix P it records the maximum absolute row sum r and maximum absolute column sum c. The induced Euclidean norm satisfies ||P||2²≤rc. Receipt values are exact rational numbers. This is an error-amplification bound for the complete120-field l2 norm, independent of each field's address dimension. It is stronger than multiplying a per-field coefficient bound by the number of fields. + +For a three-owner-axis recoder, blocks within a fixed axis have disjoint120-field supports. Completing one block does not multiply the norm of another block. Consequently an axis prefix is bounded by max(1,maximum-prefix-norm,endpoint-norm). Preceding completed axes multiply at most twice. The receipt therefore gives squared whole-three-axis bound max(1,maxprefixproduct,endpointproduct)*max(1,endpointproduct)^2. No factor exponential in120² is introduced. + +The package does not claim coordinate rounding allocation, a Turing-machine runtime bound, source acquisition, a Gaussian decoder or an exponent improvement. Owner coefficients occur once. Common-chart field availability remains an input interface requirement. + +Run `python3 -I -B check.py` and `python3 -I -B -O check.py`. Default execution is read-only; `--write` is author mode. Python3.10+ and the standard library suffice. The source program was copied byte for byte from `/tmp/full-e8-modal-source-span-20261025-joint-native-review/KERNEL-PROGRAM.json.gz`, whose canonical payload SHA256 is0b526f1a38a73a82ae66e1b0182ed2fa8c14e16d703cd38fff4dc491d3b7c15b. Runtime uses only the same-folder copy. The same AI worker authored the kernel basis and this norm replay; this is neither independent authorship nor a human audit. diff --git a/research/full120-e8-lowrank-e-native/author/inputs/prefix/RECEIPT.json b/research/full120-e8-lowrank-e-native/author/inputs/prefix/RECEIPT.json new file mode 100644 index 0000000000..dab9f510a1 --- /dev/null +++ b/research/full120-e8-lowrank-e-native/author/inputs/prefix/RECEIPT.json @@ -0,0 +1,56 @@ +{ + "schema": "full120-owner-prefix-norm-peer/v1", + "program_canonical_sha256": "0b526f1a38a73a82ae66e1b0182ed2fa8c14e16d703cd38fff4dc491d3b7c15b", + "status": "PASS_FOUR_EXACT_PREFIX_ORIENTATIONS", + "orientations": { + "to_modal": { + "operations": 7217, + "max_prefix_row_l1": "545", + "max_prefix_column_l1": "82091/90", + "max_prefix_row_times_column": "4244678/9", + "max_product_step_zero_based": 6751, + "endpoint_row_l1": "30", + "endpoint_column_l1": "58/5", + "endpoint_row_times_column": "348", + "max_denominator_bitlength": 10, + "whole_three_axis_l2_amplification_squared_upper": "57116387168" + }, + "from_modal": { + "operations": 7217, + "max_prefix_row_l1": "368", + "max_prefix_column_l1": "11483/10", + "max_prefix_row_times_column": "4157281/15", + "max_product_step_zero_based": 3029, + "endpoint_row_l1": "32", + "endpoint_column_l1": "58", + "endpoint_row_times_column": "1856", + "max_denominator_bitlength": 10, + "whole_three_axis_l2_amplification_squared_upper": "14320735522816/15" + }, + "to_modal_transpose": { + "operations": 7217, + "max_prefix_row_l1": "4433/15", + "max_prefix_column_l1": "229/5", + "max_prefix_row_times_column": "2974543/225", + "max_product_step_zero_based": 6794, + "endpoint_row_l1": "58/5", + "endpoint_column_l1": "30", + "endpoint_row_times_column": "348", + "max_denominator_bitlength": 11, + "whole_three_axis_l2_amplification_squared_upper": "40025450608/25" + }, + "from_modal_transpose": { + "operations": 7217, + "max_prefix_row_l1": "239", + "max_prefix_column_l1": "62", + "max_prefix_row_times_column": "12896", + "max_product_step_zero_based": 6197, + "endpoint_row_l1": "58", + "endpoint_column_l1": "32", + "endpoint_row_times_column": "1856", + "max_denominator_bitlength": 9, + "whole_three_axis_l2_amplification_squared_upper": "44423315456" + } + }, + "scope": "Coefficient matrices on120 independent common-chart fields. Bounds are for field-l2 additive errors, independent of address width. Three-axis batches act on disjoint120-field blocks within each owner axis. No coordinate rounding allocation, source acquisition, Gaussian decoder, runtime theorem or exponent claim." +} diff --git a/research/full120-e8-lowrank-e-native/author/inputs/prefix/check.py b/research/full120-e8-lowrank-e-native/author/inputs/prefix/check.py new file mode 100644 index 0000000000..653a7f7dae --- /dev/null +++ b/research/full120-e8-lowrank-e-native/author/inputs/prefix/check.py @@ -0,0 +1,37 @@ +"""Exact coefficient-norm certificates for four chronological owner recoders.""" +from pathlib import Path +from fractions import Fraction as F +from hashlib import sha256 +import argparse,gzip,json +HERE=Path(__file__).resolve().parent +def need(q,s): + if not q:raise ValueError(s) +def canon(x):return(json.dumps(x,sort_keys=True,separators=(',',':'))+'\n').encode() +def transpose(word): + return [['ADD',e[2],e[1],e[3],e[4]]if e[0]=='ADD'else e[:]for e in reversed(word)] +def measure(word,target): + n=120;A=[[F(i==j)for j in range(n)]for i in range(n)];rows=[F(1)]*n;cols=[F(1)]*n;rowpeak=colpeak=productpeak=F(1);denbit=1;worst=-1 + for step,e in enumerate(word): + if e[0]=='SWAP': + i,j=e[1:];A[i],A[j]=A[j],A[i];rows[i],rows[j]=rows[j],rows[i];changed=[] + else: + i=e[1];old=A[i] + if e[0]=='SCALE':v=F(e[2],e[3]);new=[v*x for x in old] + else:j=e[2];v=F(e[3],e[4]);new=[x+v*y for x,y in zip(old,A[j])] + A[i]=new;rows[i]=sum(map(abs,new));cols=[a+abs(y)-abs(x)for a,x,y in zip(cols,old,new)];changed=[i] + r=max(rows);c=max(cols);p=r*c + rowpeak=max(rowpeak,r);colpeak=max(colpeak,c) + if p>productpeak:productpeak=p;worst=step + for i in changed:denbit=max(denbit,max(x.denominator.bit_length()for x in A[i])) + need(A==target,'full chronological elementary word equals target') + endproduct=max(rows)*max(cols);axisbound=max(F(1),productpeak,endproduct) + return {'operations':len(word),'max_prefix_row_l1':str(rowpeak),'max_prefix_column_l1':str(colpeak),'max_prefix_row_times_column':str(productpeak),'max_product_step_zero_based':worst,'endpoint_row_l1':str(max(rows)),'endpoint_column_l1':str(max(cols)),'endpoint_row_times_column':str(endproduct),'max_denominator_bitlength':denbit,'whole_three_axis_l2_amplification_squared_upper':str(axisbound*max(F(1),endproduct)**2)} +def calculate(): + raw=gzip.decompress((HERE/'KERNEL-PROGRAM.json.gz').read_bytes());p=json.loads(raw);T=[[F(x)for x in row]for row in p['T120']];Ti=[[F(x)for x in row]for row in p['T_inverse120']] + cases=[('to_modal',p['to_modal_kernel_word'],Ti),('from_modal',p['from_modal_kernel_word'],T),('to_modal_transpose',transpose(p['to_modal_kernel_word']),[list(x)for x in zip(*Ti)]),('from_modal_transpose',transpose(p['from_modal_kernel_word']),[list(x)for x in zip(*T)])] + return {'schema':'full120-owner-prefix-norm-peer/v1','program_canonical_sha256':sha256(canon(p)).hexdigest(),'status':'PASS_FOUR_EXACT_PREFIX_ORIENTATIONS','orientations':{name:measure(word,target)for name,word,target in cases},'scope':'Coefficient matrices on120 independent common-chart fields. Bounds are for field-l2 additive errors, independent of address width. Three-axis batches act on disjoint120-field blocks within each owner axis. No coordinate rounding allocation, source acquisition, Gaussian decoder, runtime theorem or exponent claim.'} +if __name__=='__main__': + a=argparse.ArgumentParser();a.add_argument('--write',action='store_true');args=a.parse_args();r=calculate() + if args.write:(HERE/'RECEIPT.json').write_text(json.dumps(r,indent=2)+'\n') + else:need(json.loads((HERE/'RECEIPT.json').read_bytes())==r,'readonly exact prefix receipt') + print(r['status']);print(json.dumps(r['orientations'],sort_keys=True)) diff --git a/research/full120-e8-lowrank-e-native/author/macros120.py b/research/full120-e8-lowrank-e-native/author/macros120.py new file mode 100644 index 0000000000..f7ce5e3dba --- /dev/null +++ b/research/full120-e8-lowrank-e-native/author/macros120.py @@ -0,0 +1,169 @@ +"""Executable phase-complete base120 E macros with owned inverse transpose. + +This emits literal finite primitive lists for all240 base main fields. Its +proof is compositional: actual native phase object, exact owner recoder, +actual source-contact compiler, and the displayed noncommuting block algebra. +The1,728,000-owner extension is the separately specified structured loop. +""" +import argparse,gzip,hashlib,importlib.util,json,sys +from collections import Counter +from fractions import Fraction as F +from pathlib import Path +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent +spec=importlib.util.spec_from_file_location('macros120_modes',HERE/'modes120.py');m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m) +spec=importlib.util.spec_from_file_location('macros120_checkpoint',HERE/'checkpoint120.py');c=importlib.util.module_from_spec(spec);spec.loader.exec_module(c) +need=m.need;canonical=m.canonical +def build(): + native=m.loadgz('NATIVE120-NATIVE-PROGRAM.json.gz',m.NATIVE_PIN) + kernel=m.loadgz('KERNEL-PROGRAM.json.gz',m.KERNEL_PIN) + cache=json.loads(gzip.decompress((HERE/'BASE120-CHECKPOINT-PROGRAM.json.gz').read_bytes())) + receipt=json.loads((HERE/'BASE120-CHECKPOINT.json').read_bytes()) + need(hashlib.sha256(canonical(cache)).hexdigest()==receipt['scientific_payload_sha256'],'actual base source-contact payload pin') + need(cache['source_B_canonical_sha256']==m.NATIVE_PIN,'same actual native source-contact object') + ports=list(range(120));main=[(b,p)for b in['X','Y']for p in ports];defs={} + def wordid(w): + key=hashlib.sha256(canonical(w)).hexdigest();defs[key]=w;return key + def unary(field,word,label): + paid=[len(e[1])for e in word if e[0]=='C'];need(len(paid)<=1,'one positive child per unary event') + return ['U',field,wordid(word),paid[0]if paid else 0,label] + def mono(bank,p,inverse=False): + w=native['definitions'][native['normalizer_words'][str(p)]] + need(all(q[0]in['P','X']or(q[0]=='D'and all(v%2==0 for v in q[2]))or(q[0]=='phase'and q[1]%2==0)for q in w),'actual physical normalizers are real signed permutations') + return unary([bank,p],c.mono_transform(w)if inverse else w,'physical_L_inverse'if inverse else'physical_L') + def recoder(bank,direction): + out=[] + for e in kernel['to_modal_kernel_word'if direction=='to'else'from_modal_kernel_word']: + if e[0]=='ADD':out.append(['ADD',[bank,e[1]],[bank,e[2]],e[3],e[4]]) + elif e[0]=='SWAP':out.append(['SWAP',[bank,e[1]],[bank,e[2]]]) + else:out.append(['SCALE',[bank,e[1]],e[2],e[3]]) + return out + def chart(bank,direction):return [mono(bank,p,direction=='out')for p in ports] + def code(bank,inverse=False): + # E=K A^-1; Ei=K A. The active scale is negative in both base cases. + scale=F(-14)if inverse else F(-1,14) + out=chart(bank,'in')+recoder(bank,'to')+[['SCALE',[bank,i],scale.numerator,scale.denominator]for i in range(8)]+recoder(bank,'from') + cubes={group['cube']:sorted(group['sources']+group['readers'])for group in native['groups']} + need(len(cubes)==15,'all15 actual native cubes') + for g in cubes.values(): + need(len(g)==8,'explicit native eight-root cube partition') + out.extend([['OWN_ZERO',['kscratch',j]]for j in range(8)]) + for j,p in enumerate(g): + out.extend([['ADD',['kscratch',j],[bank,s],num,den]for s,num,den in native['literal_scalar_K_rows'][str(p)]]) + out.extend([['SWAP',[bank,p],['kscratch',j]]for j,p in enumerate(g)]) + out.extend([['CLEAR',['kscratch',j]]for j in range(8)]) + return out+chart(bank,'out') + def gather(): + return chart('Y','in')+recoder('Y','to')+[['COPY',['mode',a],['Y',a]]for a in range(8)]+recoder('Y','from')+chart('Y','out')+[unary(['mode',a],[['C',list(range(9))]],'original_ground_full_R9_query')for a in range(8)] + def scatter(sign): + return chart('X','in')+recoder('X','to')+[['ADD',['X',a],['mode',a],15*sign,1]for a in range(8)]+recoder('X','from')+chart('X','out') + def original_native(): + out=[] + for e in native['backward_program']: + if e[0]=='ADD':out.append(['ADD',[e[1],e[2]],[e[3],e[4]],e[5],e[6]]) + elif e[0]=='PAID_PATH': + r=e[5];w=native['definitions'][r['before_monomial']]+[['C',r['child_axes']]]+native['definitions'][r['after_monomial']];out.append(unary([e[1],e[2]],w,'actual_native_'+e[0])) + else:out.append(unary([e[1],e[2]],native['definitions'][e[3]],'actual_native_'+e[0])) + return out + def checkpoint_pass(name): + out=[] + for e in cache[name]: + if e[0]!='UNARY':out.append(e);continue + r=cache['events'][str(abs(e[2]))]['inverse_literal'];need(e[2]<0,'inverse source-contact event orientation') + if r['kind']=='MONOMIAL':w=cache['monomial_definitions'][r['word']] + else:w=cache['monomial_definitions'][r['before']]+[['C',r['positive_child_axes']]]+cache['monomial_definitions'][r['after']] + out.append(unary(e[1],w,'actual_source_checkpoint_'+name)) + return out + clear_modes=[['CLEAR',['mode',a]]for a in range(8)] + code_ex=code('X');code_eix=code('X',True) + back=gather()+code('Y',True)+original_native()+scatter(-1)+code_eix+clear_modes + inverse=code_ex+checkpoint_pass('source_Y_only_pass')+code('Y')+gather()+scatter(1)+clear_modes+checkpoint_pass('target_X_only_pass')+[['CLEAR',['cache',p]]for p in cache['ports']] + def transpose(program): + out=[] + for e in reversed(program): + op=e[0] + if op=='ADD':out.append(['ADD',e[2],e[1],e[3],e[4]]) + elif op=='COPY':out.extend([['ADD',e[2],e[1],1,1],['CLEAR',e[1]]]) + elif op=='CLEAR':out.append(['OWN_ZERO',e[1]]) + elif op=='OWN_ZERO':out.append(['CLEAR',e[1]]) + elif op in['SWAP','SCALE']:out.append(e) + else: + need(op=='U','linear transpose primitive opcode') + # P^T=P^-1, D^T=D, X^T=X, C^T=C, scalar phase unchanged. + w=[] + for q in reversed(defs[e[2]]): + w.append(['P',c.gf_inv(q[1])]if q[0]=='P'else q) + out.append(unary(e[1],w,'linear_transpose:'+e[4])) + return out + tr=transpose(inverse) + # Boundary: diag(D²,D²) J inverse^T J^-1, J=diag(Q²,I). + forward=[unary(['X',p],[['X',1]],'input_Q_minus2')for p in ports]+tr+[unary(['X',p],[['X',511]],'output_Dsquare_Qsquare')for p in ports]+[unary(['Y',p],[['X',510]],'output_Dsquare')for p in ports] + payload={'schema':'literal-full120-base-positive-E-owned-macros/v1','native_science_sha256':m.NATIVE_PIN,'kernel_science_sha256':m.KERNEL_PIN,'actual_source_checkpoint_sha256':receipt['scientific_payload_sha256'],'axis_dimension':9,'main':main,'definitions':defs,'backward':back,'inverse':inverse,'linear_transpose_inverse':tr,'forward':forward,'ordinary_E_X':code_ex,'ordinary_E_inverse_X':code_eix,'operator_ABI':{'backward':'[[E_inverse D, -E_inverse R],[0,D E_inverse]]=H(E_inverse) B0','inverse':'[[D_inverse E,Q E D_inverse],[0,E D_inverse]]','forward':'[[E D,0],[D E Q_inverse,D E]]=H(E) F0','H':'H(T)=diag(T,Q_inverse T Q); R=D Q; E commutes R and is real symmetric. E generally does not commute Q or D.','mode_gather':'Actual original Y before backward precode. Inverse first finishes actual inverse source-Y pass with owned contact cache, then codes Y by E to acquire original ground.'},'width_contract':'Every literal address word tensor lifts; field ADD/SCALE coefficients act once. phase theta is i^(width*theta). Gaussian C_axes inverse is positive C_axes then X_axis_mask. No expanded address matrix is claimed.'} + return payload +def inspect(program,payload): + main={tuple(f)for f in payload['main']};live=set(main);peak=0;count=Counter();paid=Counter();coefficient=F(1) + for e in program: + op=e[0];count[op]+=1 + if op in['OWN_ZERO','COPY']: + f=tuple(e[1]);need(f not in live and f not in main,'owned allocation fresh') + if op=='COPY':need(tuple(e[2])in live,'owned COPY reads initialized field') + live.add(f);peak=max(peak,len(live)-len(main)) + elif op=='CLEAR':f=tuple(e[1]);need(f in live and f not in main,'owned only CLEAR after use');live.remove(f) + elif op in['ADD','SWAP']: + need(tuple(e[1])in live and tuple(e[2])in live,'binary op initialized');need(e[1]!=e[2],'distinct binary fields') + if op=='ADD':coefficient=max(coefficient,abs(F(e[3],e[4]))) + elif op=='SCALE':need(tuple(e[1])in live,'SCALE initialized');coefficient=max(coefficient,abs(F(e[2],e[3]))) + else: + need(op=='U'and tuple(e[1])in live,'known initialized unary') + word=payload['definitions'][e[2]];pc=Counter() + for q in word: + if q[0]=='C':paid[len(q[1])]+=1;pc[len(q[1])]+=1 + else:need(q[0]in['P','D','X','phase'],'literal unary opcode');count['physical_'+q[0]]+=1 + need(pc==({e[3]:1}if e[3]else{}),'declared actual child rank') + need(live==main,'all owned fields cleaned after final use') + return {'paid':dict(sorted(paid.items())),'ordinary_and_literal_counts':dict(sorted(count.items())),'peak_owned_fields':peak,'maximum_scalar_absolute_coefficient':str(coefficient)} +def scalar_code_replay(program,payload): + # Common-chart owner projection only; physical L_i normalization and its + # inverse supply the actual block L_i^-1 E_ij L_j by construction. + states={('X',p):{p:F(1)}for p in range(120)} + def add(a,b,q): + for j,v in states[b].items(): + z=states[a].get(j,F())+q*v + if z:states[a][j]=z + else:states[a].pop(j,None) + for e in program: + op=e[0];f=tuple(e[1]) + if op=='OWN_ZERO':states[f]={} + elif op=='CLEAR':del states[f] + elif op=='SWAP':g=tuple(e[2]);states[f],states[g]=states[g],states[f] + elif op=='ADD':add(f,tuple(e[2]),F(e[3],e[4])) + elif op=='SCALE':states[f]={j:F(e[2],e[3])*v for j,v in states[f].items()} + else:need(op=='U'and e[4]in['physical_L','physical_L_inverse'],'code has only actual physical normalization') + return [[states['X',p].get(j,F())for j in range(120)]for p in range(120)] +def calculate(): + p=build();receipts={k:inspect(p[k],p)for k in['ordinary_E_X','ordinary_E_inverse_X','backward','inverse','linear_transpose_inverse','forward']} + expected={2:120,3:120,5:120,6:120,9:8} + for k in['backward','inverse','linear_transpose_inverse','forward']:need(receipts[k]['paid']==expected,'actual E module paid profile '+k) + native=m.loadgz('NATIVE120-NATIVE-PROGRAM.json.gz',m.NATIVE_PIN);kernel=m.loadgz('KERNEL-PROGRAM.json.gz',m.KERNEL_PIN) + K=m.scalar_K(native);M=[[F(x)for x in r]for r in kernel['root_M120x8']];C=[[sum(x*y for x,y in zip(r,s))/4 for s in M]for r in M] + for name,s in[('ordinary_E_X',F(1,14)),('ordinary_E_inverse_X',F(1))]: + want=[[K[i][j]+s*C[i][j]for j in range(120)]for i in range(120)] + need(scalar_code_replay(p[name],p)==want,'actual emitted common-chart code all14400 entries '+name) + # Structural mutants are meaningful even before a numerical field replay. + bad=[e for e in p['inverse']if not(e[0]=='COPY'and e[1][0]=='cache')] + try:inspect(bad,p) + except ValueError:missing=True + else:missing=False + need(missing,'removed actual source caches rejected') + bad=[list(e)for e in p['backward']];j=next(i for i,e in enumerate(bad)if e[0]=='ADD'and e[2][0]=='mode');bad.insert(j,['CLEAR',bad[j][2]]) + try:inspect(bad,p) + except ValueError:early=True + else:early=False + need(early,'early original-ground mode CLEAR rejected') + r={'schema':'full120-literal-positive-E-owned-macro-review/v1','status':'PASS_ACTUAL_BASE120_E_MACRO_AND_STRUCTURED_COMPOSITION','main_fields':240,'main_address_axes':9,'all14400_common_chart_code_entries_each_direction':True,'all_literal_owned_lifecycles':True,'actual_native_paid_phase_object':m.NATIVE_PIN,'actual_contact_inverse_and_transpose_all240_independent_operator_rows':'BASE120-CHECKPOINT.json','noncommuting_physical_allcolumn_fixture':'OWNED-E.json:three lambdas15,225/2,-1350;16 independent maincolumns each','noncommuting_generic_operator_identity':p['operator_ABI'],'receipts':receipts,'controls':{'missing_actual_source_cache_rejected':missing,'early_ground_mode_clear_rejected':early},'scientific_payload_sha256':hashlib.sha256(canonical(p)).hexdigest(),'scope':'The emitted base120 primitive words are actual, including every paid child, ordinary address word and phase. Exact common-chart scalarcode replay plus sealed native phase science and actual native owned inverse/transpose prove composition. This checker does not propagate a122880-by122880 dense matrix. The odd3 family uses the explicit structured owner loop and its independently pinned512 native template. No negative E decoder, formal supplier or new kappa.'} + return json.loads(canonical(r)),json.loads(canonical(p)) +if __name__=='__main__': + ap=argparse.ArgumentParser();ap.add_argument('--write',action='store_true');a=ap.parse_args();r,p=calculate() + if a.write:(HERE/'MACROS120.json').write_text(json.dumps(r,sort_keys=True,indent=2)+'\n');(HERE/'MACROS120-PROGRAM.json.gz').write_bytes(gzip.compress(canonical(p),mtime=0)) + else:need(json.loads((HERE/'MACROS120.json').read_bytes())==r,'read-only macro receipt');need(json.loads(gzip.decompress((HERE/'MACROS120-PROGRAM.json.gz').read_bytes()))==p,'read-only actual primitive macro') + print(json.dumps(r,sort_keys=True)) diff --git a/research/full120-e8-lowrank-e-native/author/modes120.py b/research/full120-e8-lowrank-e-native/author/modes120.py new file mode 100644 index 0000000000..02c650a4bb --- /dev/null +++ b/research/full120-e8-lowrank-e-native/author/modes120.py @@ -0,0 +1,109 @@ +"""Exact full120 modal recoder, physical E code, and structured odd3 invoice. + +The ordinary owner matrices act once on fields. Address words alone tensor +lift with positive field width. No all-family dense matrix is materialized. +""" +import argparse,gzip,hashlib,json,sys +from collections import Counter +from fractions import Fraction as F +from itertools import product +from pathlib import Path +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent +SOURCE=HERE/'inputs' +KERNEL_PIN='0b526f1a38a73a82ae66e1b0182ed2fa8c14e16d703cd38fff4dc491d3b7c15b' +NATIVE_PIN='87d7cad7133ed0a2950b1d4fa2397e20e3c7bcedb90db95a15130aa03da543ae' +ROOT_PIN='1aeba5ae2276ff58e24ed9ca84f08830c0bb7321432bc74e42472f0029bfb1c2' +def need(q,s): + if not q:raise ValueError(s) +def canonical(x):return(json.dumps(x,sort_keys=True,separators=(',',':'))+'\n').encode() +def loadgz(name,pin): + p=json.loads(gzip.decompress((SOURCE/name).read_bytes()));need(hashlib.sha256(canonical(p)).hexdigest()==pin,'pinned '+name);return p +def eye(n):return [[F(i==j)for j in range(n)]for i in range(n)] +def mm(A,B): + out=[[F()for _ in B[0]]for _ in A] + for i,r in enumerate(A): + for k,a in enumerate(r): + if a: + for j,b in enumerate(B[k]): + if b:out[i][j]+=a*b + return out +def rowword(word,n=120): + A=eye(n) + for e in word: + if e[0]=='SWAP':A[e[1]],A[e[2]]=A[e[2]],A[e[1]] + elif e[0]=='SCALE':A[e[1]]=[F(e[2],e[3])*x for x in A[e[1]]] + else: + need(e[0]=='ADD','owner elementary opcode');i,j=e[1:3];q=F(e[3],e[4]);A[i]=[x+q*y for x,y in zip(A[i],A[j])] + return A +def transword(word): + return [[e[0],e[2],e[1],*e[3:]]if e[0]=='ADD'else e for e in reversed(word)] +def scalar_K(native): + K=[[F()for _ in range(120)]for _ in range(120)] + for i,r in native['literal_scalar_K_rows'].items(): + for j,num,den in r:K[int(i)][int(j)]=F(num,den) + return K +def countword(w):return dict(sorted(Counter(e[0]for e in w).items())) +def calculate(): + kernel=loadgz('KERNEL-PROGRAM.json.gz',KERNEL_PIN) + native=loadgz('NATIVE120-NATIVE-PROGRAM.json.gz',NATIVE_PIN) + root=loadgz('K-PROGRAM.json.gz',ROOT_PIN) + T=[[F(x)for x in r]for r in kernel['T120']];Ti=[[F(x)for x in r]for r in kernel['T_inverse120']] + to=kernel['to_modal_kernel_word'];fr=kernel['from_modal_kernel_word'] + need(rowword(to)==Ti and rowword(fr)==T,'both actual elementary words independently replayed') + need(mm(T,Ti)==eye(120)and mm(Ti,T)==eye(120),'both all14400 exact inverse entries') + M=[[F(x)for x in r]for r in kernel['root_M120x8']] + C=[[sum(x*y for x,y in zip(r,s))/4 for s in M]for r in M] + need(all(T[i][:8]==M[i]for i in range(120)),'first8 columns are actual M') + need(all(Ti[a][i]==M[i][a]/60 for a in range(8)for i in range(120)),'modal analysis is actual M^T/60') + need(all(sum(M[i][a]*T[i][b]for i in range(120))==0 for a in range(8)for b in range(8,120)),'remaining112 columns in actual kernel') + K=scalar_K(native);need(mm(K,K)==eye(120),'actual native K^2=I') + need(mm(K,M)==[[-x for x in r]for r in M],'actual native K M=-M') + need(mm(K,C)==[[-x for x in r]for r in C]and mm(C,K)==[[-x for x in r]for r in C],'both K C=-C') + E=[[K[i][j]+C[i][j]/14 for j in range(120)]for i in range(120)] + Ei=[[K[i][j]+C[i][j]for j in range(120)]for i in range(120)] + need(mm(E,Ei)==eye(120)and mm(Ei,E)==eye(120),'actual E and inverse all14400 entries') + # Code evaluation means T^-1, A scale, T, then K, with scalar coefficients + # once. The negative A-inverse modal scale must not be lost. + def code(sc): + U=[[T[i][j]*(sc if j<8 else 1)for j in range(120)]for i in range(120)] + return mm(K,mm(U,Ti)) + need(code(F(-1,14))==E and code(F(-14))==Ei,'literal modal scales implement E and E inverse') + wrong=code(F(1,14));need(wrong!=E,'wrong inverse modal sign rejected') + need(mm(K,Ei)==[[F(i==j)-C[i][j]for j in range(120)]for i in range(120)],'K Ei+C=I exact') + need(mm(C,Ei)==[[14*x for x in r]for r in C],'post-precode source is not original source') + need(mm(C,Ei)!=C,'late original-ground modal gather rejected') + # U25 is the one common physical chart used by the actual whole native. + template=json.loads((SOURCE/'K-TEMPLATE.json').read_bytes());orth=template['orthonormal_basis_raw27'] + dot=lambda x,y:(x&y).bit_count()&1 + need(len(orth)==25 and all(dot(x,y)==int(i==j)for i,x in enumerate(orth)for j,y in enumerate(orth)),'actual U25 orthonormal chart') + need(all(len({((x>>(9*j))&511).bit_count()%2 for j in range(3)})==1 for x in orth),'common equal-block-parity U25') + sectors=[];h=0 + for flags in product([0,1],repeat=3): + a=sum(flags);dim=8**a*112**(3-a);lam=F(225,2)if a==2 else F(-1350)if a==3 else F() + if lam:h+=dim + sectors.append({'modal_axis_flags':list(flags),'dimension':dim,'C_eigenvalue':str(lam),'A_scale':str(1-lam),'A_inverse_scale':str(1/(1-lam))}) + need(h==22016,'global actual rank22016') + # Scalar Kodd majority formula on eight sign sectors. On every active C + # sector at least two factors are modal, and hence have K sign minus. + for signs in product([-1,1],repeat=3): + majority=F(sum(signs)-signs[0]*signs[1]*signs[2],2) + need(majority in[-1,1],'Kodd involution on all eigenspaces') + if signs.count(-1)>=2:need(majority==-1,'Kodd=-I on C support') + counts=countword(to);need(counts==countword(fr)=={'ADD':7042,'SCALE':84,'SWAP':91},'actual kernel elementary tariff') + def invoice(k,v,rank,rowterms,scratch,n): + b=k*v//120 + code={'ADD':2*b*counts['ADD']+rowterms*v,'SCALE':2*b*counts['SCALE']+rank,'SWAP':2*b*counts['SWAP']+v,'physical_L_field_map':2*v,'OWN_ZERO':v,'CLEAR':v,'peak_scratch':scratch} + query={'ADD':4*b*counts['ADD']+rank,'SCALE':4*b*counts['SCALE'],'SWAP':4*b*counts['SWAP'],'physical_L_field_map':4*v,'COPY':rank,'CLEAR':rank,'paid':{str(n):rank}} + upper=dict(query);upper['ADD']+=rank;upper['OWN_ZERO']=rank;upper['CLEAR']=2*rank + return {'axis_word_batches_per_direction':b,'ordinary_code_E_or_inverse':code,'original_ground_query_plus_scatter':query,'query_or_transpose_upper':upper,'owned_inverse_peak_upper':v+rank+scratch} + invoices={'base120':invoice(1,120,8,4,8,9),'odd3':invoice(3,120**3,h,76,512,25)} + payload={'schema':'full120-positive-E-structured-constructor/v1','kernel_science_sha256':KERNEL_PIN,'native120_science_sha256':NATIVE_PIN,'native512_science_sha256':ROOT_PIN,'base_modal_scale':{'E':'-1/14','E_inverse':'-14'},'odd3_sectors':sectors,'base_owner_recoder':{'to':'inputs/KERNEL-PROGRAM.json.gz:to_modal_kernel_word','from':'inputs/KERNEL-PROGRAM.json.gz:from_modal_kernel_word'},'global_owner_recoder':{'ambient':25,'selector_shape':[120,120,120],'physical_normalizers':'Actual K-TEMPLATE U25 chart and q tuple; ordinary exact signed Clifford L_i from actual K native constructor. These address monomials commute with R25 with phase; no claim they commute Q or D separately.','orthonormal_basis_raw27':orth,'loop':'For axis a=0,1,2 and lexicographic other selector coordinates in0..119 apply the emitted120-field word on that axis. Restore in reverse axis order using the inverse word.','scalar_coefficients':'Each owner coefficient acts once; only address monomials tensor lift with field width.'},'code_recipe':['Apply each actual physical L_i to its field.','Apply to-modal word in place on each selector axis.','SCALE active sectors by A_inverse_scale for E or A_scale for E_inverse.','Restore from-modal words in reverse axis order.','Apply actual scalar K (base8cube/odd3 512cube) into owned zero output scratch, read all inputs, SWAP outputs into mains, CLEAR old mains from scratch; reuse8/512 fields.','Apply L_i inverse.'],'query_recipe':['On unchanged original ground Y apply L_i then to-modal selector words.','COPY every active coordinate into its owned mode; restore original Y exactly via inverse recoder and L_i inverse.','Apply one full positive R9 or R25 to each owned mode.','After native B but before postX(E_inverse), apply L_i and to-modal words to X, ADD -lambda times each retained mode at its active coordinate, then restore and L_i inverse.','CLEAR modes only after their final scatter. In inverse schedule original Y is first acquired using the actual source-contact inverse, before query.'],'physical_operator_claim':'C_phys=L^-1 Cscalar L commutes R. E=K(I-C)^-1, E_inverse=K+C. The emitted ordinary code uses no Q-conjugation assumption. Backward output is H(E_inverse)B0, forward obtained from owned inverse transpose is H(E)F0. H(T)=diag(T,Q^-1 T Q).','global_scalar_C':'(C1 C2+C1 C3+C2 C3-C1 C2 C3)/2; factors act on distinct owner selector axes.','global_scalar_K':'(K1+K2+K3-K1 K2 K3)/2; actual76-entry rows, row-l1=7.','invoices':invoices} + result={'schema':'full120-E-modal-structured-proof/v1','status':'PASS_EXPLICIT_POSITIVE_E_CONSTRUCTOR','base_E_and_inverse_all14400_entries':True,'base_recoder_replay_entries':28800,'base_K_C_compatibility':True,'original_ground_timing_control_rejected':True,'modal_inverse_sign_control_rejected':True,'global_dimension':120**3,'global_nonzero_modes':h,'global_C_eigenvalues':['225/2','-1350'],'global_E_eigenvalues_on_active':['2/223','-1/1351'],'query_paid_per_local_module':{'25':h},'native_paid_per_local_module':{str(r):120**3 for r in[8,9,15,16]},'base_local_module_paid':{str(r):120 for r in[2,3,5,6]}|{'9':8},'invoices':invoices,'kernel_science_sha256':KERNEL_PIN,'scientific_payload_sha256':hashlib.sha256(canonical(payload)).hexdigest(),'negative_terminal':'UNKNOWN','whole_caller_or_new_kappa':False,'scope':'Actual base native and512 native template pins, exact scalar recoder/mode proof, owned source checkpoint and small noncommuting-Q fulloperator fixture jointly compose this structured constructor. No1,728,000-by1,728,000 matrix or full3375 native phase stream is claimed expanded. Positive E code/query only; no ordinary negative decoder or formal supplier admission.'} + return result,payload +if __name__=='__main__': + ap=argparse.ArgumentParser();ap.add_argument('--write',action='store_true');a=ap.parse_args();r,p=calculate() + for name,obj in [('MODES120.json',r),('MODES120-PROGRAM.json',p)]: + if a.write:(HERE/name).write_text(json.dumps(obj,sort_keys=True,indent=2)+'\n') + else:need(json.loads((HERE/name).read_bytes())==obj,'read-only '+name) + print(json.dumps(r,sort_keys=True)) diff --git a/research/full120-e8-lowrank-e-native/author/n3.py b/research/full120-e8-lowrank-e-native/author/n3.py new file mode 100644 index 0000000000..a938019b84 --- /dev/null +++ b/research/full120-e8-lowrank-e-native/author/n3.py @@ -0,0 +1,97 @@ +"""Three distinct fresh stages: literal owned typed E caller and positive exit.""" +import argparse,hashlib,importlib.util,json,sys +from collections import Counter +from fractions import Fraction as F +from pathlib import Path +HERE=Path(__file__).resolve().parent +spec=importlib.util.spec_from_file_location('n3_owned',HERE/'owned_e.py');oe=importlib.util.module_from_spec(spec);sys.modules[spec.name]=oe;spec.loader.exec_module(oe) +C=oe.C;N=16;W=64;MAIN=oe.MAIN + +def need(q,s): + if not q:raise ValueError(s) +def eye(n):return [[C(i==j)for j in range(n)]for i in range(n)] +def zeros(n,m=None):return [[C()for j in range(n if m is None else m)]for i in range(n)] +def plus(A,B):return [[a+b for a,b in zip(r,s)]for r,s in zip(A,B)] +def times(c,A):return [[c*x for x in r]for r in A] +def left(A,B): + out=zeros(len(A),len(B[0])) + for i,r in enumerate(A): + for k,c in enumerate(r): + if c: + for j,x in enumerate(B[k]): + if x:out[i][j]+=c*x + return out +def prod(*As): + r=eye(len(As[0])) + for A in As:r=left(r,A) + return r +def block(A,B,D,E):return [a+b for a,b in zip(A,B)]+[a+b for a,b in zip(D,E)] +def diag(A,B):return block(A,zeros(len(A)),zeros(len(A)),B) +def perm(fun): + A=zeros(N) + for x in range(N):A[fun(x)][x]=C(1) + return A +def X(q):return perm(lambda x:x^q) +def gate(q,sgn=1):return plus(times(C(F(1,2),F(sgn,2)),eye(N)),times(C(F(1,2),F(-sgn,2)),X(q))) +def swap(x,s): + b0=x&1;bs=(x>>s)&1 + return x^((1|(1<>1)<>1)&1)][x]=C(1) +def translation(q): + O=zeros(4) + for x in range(4):O[x^q][x]=C(1) + return O +def gate(q,s=1):return add(scale(C(F(1,2),F(s,2)),I4),scale(C(F(1,2),F(-s,2)),translation(q))) +MAP={'I':I4,'P':P,**{'X'+str(q):translation(q)for q in [1,2,3]},'C0':gate(1),'C1':gate(2),'R':mul(gate(1),gate(2))} +def left(A,B):return [[sum((A[i][k]*B[k][j]for k in range(len(A))),C())for j in range(len(B[0]))]for i in range(len(A))] +def ownzero():return [[C()for j in range(16)]for i in range(4)] +def coded(bank,a,b,label): + f,g=bank;u,v=label+'a',label+'b' + return [['COPY',u,f],['COPY',v,g],['SCALE',f,a.numerator,a.denominator],['SCALE',g,a.numerator,a.denominator],['ADD',f,v,b.numerator,b.denominator,'P'],['ADD',g,u,b.numerator,b.denominator,'P'],['CLEAR',u],['CLEAR',v]] +def modes(lam,sign,label): + # FC=(lambda/2)[I;-P][I,-P]. Source Y is read before any overwrite. + g=label+'g' + return [['OWN_ZERO',g],['ADD',g,'Y0',1,1,'I'],['ADD',g,'Y1',-1,1,'P'],['PAID',g,'R',2],['ADD','X0',g,(sign*F(lam,2)).numerator,(sign*F(lam,2)).denominator,'I'],['ADD','X1',g,(-sign*F(lam,2)).numerator,(-sign*F(lam,2)).denominator,'P'],['CLEAR',g]] +def nativeB(): + # Exact inverse-transpose of F=[[D,0],[Pswap,D]], with ordinary X powers. + out=[['MONO',f,'X1']for f in ['X0','X1']] + for f in ['Y0','Y1']:out.extend([['PAID',f,'C1',1],['MONO',f,'X2']]) + out.extend([['ADD','X0','Y1',-1,1,'P'],['ADD','X1','Y0',-1,1,'P']]) + for f in ['X0','X1']:out.extend([['PAID',f,'C1',1],['MONO',f,'X2']]) + out.extend([['MONO',f,'X3']for f in ['X0','X1']]);out.extend([['MONO',f,'X2']for f in ['Y0','Y1']]) + return out +def programs(lam): + ei_a=F(lam,2);ei_b=1-ei_a;e_a=F(lam,2*(lam-1));e_b=F(lam-2,2*(lam-1)) + # Gather and transform the original Y mode first; retain it across nativeB. + q=modes(lam,-1,'back_mode_');split=4 + back=q[:split]+coded(['Y0','Y1'],ei_a,ei_b,'by')+nativeB()+q[split:-1]+coded(['X0','X1'],ei_a,ei_b,'bx')+q[-1:] + inv=coded(['X0','X1'],e_a,e_b,'ix') + inv.extend([['MONO',f,'X2']for f in ['Y0','Y1']]) + inv.extend([['COPY','cache0','Y0'],['COPY','cache1','Y1']]) + inv.extend([['PAID',f,'C1',1]for f in ['Y0','Y1']]) + inv+=coded(['Y0','Y1'],e_a,e_b,'iy')+modes(lam,1,'inverse_mode_') + inv.extend([['MONO',f,'X3']for f in ['X0','X1']]);inv.extend([['PAID',f,'C1',1]for f in ['X0','X1']]) + inv.extend([['ADD','X0','cache1',1,1,'P'],['ADD','X1','cache0',1,1,'P']]) + inv.extend([['MONO',f,'X1']for f in ['X0','X1']]);inv.extend([['CLEAR','cache0'],['CLEAR','cache1']]) + tr=[] + for e in reversed(inv): + if e[0]=='COPY':tr.extend([['ADD',e[2],e[1],1,1,'I'],['CLEAR',e[1]]]) + elif e[0]=='CLEAR':tr.append(['OWN_ZERO',e[1]]) + elif e[0]=='OWN_ZERO':tr.append(['CLEAR',e[1]]) + elif e[0]=='ADD':tr.append(['ADD',e[2],e[1],e[3],e[4],e[5]]) # I,P are symmetric. + elif e[0]=='SCALE':tr.append(list(e)) + else:need(e[0]in ['MONO','PAID'],True,'transpose known symmetric fixture primitive');tr.append(list(e)) + forward=[['MONO',f,'X1']for f in ['X0','X1']]+tr+[['MONO',f,'X3']for f in ['X0','X1']]+[['MONO',f,'X2']for f in ['Y0','Y1']] + return back,inv,tr,forward + +def run(program,initial=None): + vals={f:[[C(int(4*j+i==k))for k in range(16)]for i in range(4)]for j,f in enumerate(MAIN)}if initial is None else{f:[list(r)for r in initial[4*j:4*j+4]]for j,f in enumerate(MAIN)} + live=set(MAIN);peak=0;paid=Counter();ops=Counter() + for e in program: + op=e[0];ops[op]+=1 + if op in ['OWN_ZERO','COPY']: + f=e[1];need(f not in live and f not in MAIN,True,'owned destination must be fresh and zero') + if op=='COPY':need(e[2]in live,True,'COPY source initialized');vals[f]=[list(r)for r in vals[e[2]]] + else:vals[f]=ownzero() + live.add(f);peak=max(peak,len(live)-4) + elif op=='CLEAR':need(e[1]in live and e[1]not in MAIN,True,'owned only CLEAR after use');vals[e[1]]=ownzero();live.remove(e[1]) + elif op=='SCALE':need(e[1]in live,True,'SCALE initialized');vals[e[1]]=scale(F(e[2],e[3]),vals[e[1]]) + elif op=='ADD': + f,g=e[1:3];need(f in live and g in live,True,'ADD initialized owned/source');vals[f]=add(vals[f],scale(F(e[3],e[4]),left(MAP[e[5]],vals[g]))) + else: + need(op in ['MONO','PAID']and e[1]in live,True,'known initialized unary');vals[e[1]]=left(MAP[e[2]],vals[e[1]]) + if op=='PAID':paid[e[3]]+=1 + need(live,set(MAIN),'all owned temporaries cleaned') + return sum([vals[f]for f in MAIN],[]),{'paid':dict(sorted(paid.items())),'ordinary':dict(sorted((k,v)for k,v in ops.items()if k!='PAID')),'peak_owned_fields':peak} +def matrix_json(M):return [[[str(z.a),str(z.b)]for z in r]for r in M] +def targets(lam): + Q=diag(gate(1),gate(1));Qi=diag(gate(1,-1),gate(1,-1));D=diag(gate(2),gate(2));I=ident(8);Z=zeros(4) + K=block(Z,P,P,Z);Pm=scale(F(1,2),add(I,scale(-1,K)));FC=scale(lam,Pm);A=add(I,scale(-1,FC));Ai=add(I,scale(F(lam,1-lam),Pm));E=mul(K,Ai);Ei=mul(K,A) + HF=diag(E,prod(Qi,E,Q));HB=diag(Ei,prod(Qi,Ei,Q));WF=mul(HF,mul(diag(D,D),lower(Qi)));WB=mul(HB,mul(diag(D,D),upper(scale(-1,Q)))) + return WF,WB + +def calculate(): + cases=[];payload=[] + for lam in [15,F(225,2),-1350]: + back,inv,tr,forward=programs(lam);B,bi=run(back);Bi,ii=run(inv);T,ti=run(tr);FF,fi=run(forward);WF,WB=targets(lam) + need(B,WB,'literal owned backward E adapter all16 input columns and phases') + need(mul(Bi,B),ident(16),'literal owned inverse left all16columns') + need(mul(B,Bi),ident(16),'literal owned inverse right all16columns') + need(T,list(map(list,zip(*Bi))),'literal owned transpose all256 operatorentries') + need(FF,WF,'literal owned forward E adapter all16 inputcolumns absolutephase') + need(bi['paid'],{1:4,2:1},'back paid native4H1 +rH2') + need(ii['paid'],bi['paid'],'inverse same Gaussian paidprofile');need(fi['paid'],bi['paid'],'forward same Gaussian paidprofile') + controls={} + bad=[e for e in back if not(e[0]=='PAID'and e[2]=='R')];controls['missing_owned_R_query_rejected']=run(bad)[0]!=WB + bad=[list(e)for e in forward];bad[-4]=['MONO','X0','X1'];controls['wrong_forward_Dsquare_boundary_rejected']=run(bad)[0]!=WF + bad=[list(e)for e in inv];i=next(i for i,e in enumerate(bad)if e[0]=='COPY'and e[1]=='cache0');bad[i]=['OWN_ZERO','cache0'];controls['lost_actual_source_contact_rejected']=run(bad)[0]!=Bi + bad=[list(e)for e in tr];i=next(i for i,e in enumerate(bad)if e[0]=='ADD');bad[i]=list(bad[i]);bad[i][3]=-bad[i][3];controls['wrong_transpose_ADD_sign_rejected']=run(bad)[0]!=T + bad=[list(e)for e in inv];i=next(i for i,e in enumerate(bad)if e[0]=='ADD'and e[2]=='cache0');bad.insert(i,['CLEAR','cache0']) + try:run(bad) + except ValueError:controls['owned_source_early_CLEAR_rejected']=True + need(all(controls.values())and len(controls)==5,True,'all physical/phase/owned controls') + cases.append({'lambda':str(lam),'backward':bi,'inverse':ii,'transpose':ti,'forward':fi,'all16_arbitrary_main_columns_exact':True,'absolute_phases_exact':True,'all256_transpose_operator_entries_exact':True,'controls':controls,'backward_matrix_sha256':hashlib.sha256(json.dumps(matrix_json(B),separators=(',',':')).encode()).hexdigest(),'forward_matrix_sha256':hashlib.sha256(json.dumps(matrix_json(FF),separators=(',',':')).encode()).hexdigest()}) + payload.append({'lambda':str(lam),'backward':back,'inverse':inv,'transpose':tr,'forward':forward}) + result={'schema':'owned-E-adapter-fulloperator-fixture/v1','status':'PASS_LITERAL_BOTH_ORIENTATIONS_WITH_OWNED_SOURCE_CHECKPOINT','field_width':1,'address_axes':2,'arbitrary_independent_main_fields':4,'main_operator_dimension':16,'cases':cases,'scope':'Exact complete small noncommuting-Q full operators, with original source acquisition, same paid profiles, owned lifecycle and absolute phase. Global all-port implementation uses separate actual root512 native checkpoint proof and rational spectral mode theorem. No negative E terminal decoding or complete caller claimed.'} + return json.loads(json.dumps(result)),json.loads(json.dumps(payload)) +if __name__=='__main__': + ap=argparse.ArgumentParser();ap.add_argument('--write',action='store_true');a=ap.parse_args();r,p=calculate();rpath=HERE/'OWNED-E.json';ppath=HERE/'OWNED-E-PROGRAM.json' + if a.write:rpath.write_text(json.dumps(r,sort_keys=True,indent=2)+'\n');ppath.write_text(json.dumps(p,sort_keys=True,indent=2)+'\n') + else:need(r,json.loads(rpath.read_bytes()),'read-only owned E receipt');need(p,json.loads(ppath.read_bytes()),'read-only owned E program') + print(json.dumps(r,sort_keys=True)) diff --git a/research/full120-e8-lowrank-e-native/author/precision120.py b/research/full120-e8-lowrank-e-native/author/precision120.py new file mode 100644 index 0000000000..2c2c39a969 --- /dev/null +++ b/research/full120-e8-lowrank-e-native/author/precision120.py @@ -0,0 +1,56 @@ +"""Finite field-collection l2 constants and structured ordinary invoice. + +These bounds concern additive errors measured in l2 of entire fields, not a +coordinate rounding allocation or a Turing-machine supplier admission. +""" +import argparse,hashlib,importlib.util,json,math,sys +from fractions import Fraction as F +from pathlib import Path +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent +def need(q,s): + if not q:raise ValueError(s) +def canonical(x):return(json.dumps(x,sort_keys=True,separators=(',',':'))+'\n').encode() +def sqrtceil(x): + z=(x.numerator+x.denominator-1)//x.denominator;r=math.isqrt(z);return r if r*r>=z else r+1 +def add(*ds): + out={} + for d in ds: + for k,v in d.items():out[k]=out.get(k,0)+v + return out +def times(n,d):return{k:n*v for k,v in d.items()} +def calculate(): + spec=importlib.util.spec_from_file_location('precision120_prefix',HERE/'inputs/prefix/check.py');p=importlib.util.module_from_spec(spec);spec.loader.exec_module(p) + pr=p.calculate();need(pr==json.loads((HERE/'inputs/prefix/RECEIPT.json').read_bytes()),'four exact actual word prefix receipts') + need(pr['program_canonical_sha256']=='0b526f1a38a73a82ae66e1b0182ed2fa8c14e16d703cd38fff4dc491d3b7c15b','same exact modal kernel science') + bound=max(F(q['whole_three_axis_l2_amplification_squared_upper'])for q in pr['orientations'].values());S=sqrtceil(bound) + need(S*S>=bound,'integer whole three-axis prefix bound') + # A complete scalar K stage uses zero scratch, partial row accumulations, + # SWAP, CLEAR. All partial coefficient row/column sums are <=7. Thus its + # extended main+scratch prefix norm is <=sqrt(1+7²)<8, and so is its adjoint. + spec=importlib.util.spec_from_file_location('precision120_modes',HERE/'modes120.py');m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m) + root=m.loadgz('K-PROGRAM.json.gz',m.ROOT_PIN);rows=root['literal_scalar_K_rows'];col={};rmax=F() + for row in rows.values(): + rmax=max(rmax,sum(abs(F(num,den))for j,num,den in row)) + for j,num,den in row:col[j]=col.get(j,F())+abs(F(num,den)) + cmax=max(col.values());need(rmax==cmax==7,'actual512 scalar K row and column l1=7') + # Uniform bound covers E, Ei, and their primitive linear adjoints. Four + # recoder orientations are needed because transpose reverses the row word. + C=8*1351*S*S + Q=2*1351*S**4 + M=16*C*C*Q + whole=M**3*C**3 + V=120**3;h=22016;axis_batches=3*120**2 + code={'ADD':2*axis_batches*7042+76*V,'SCALE':2*axis_batches*84+h,'SWAP':2*axis_batches*91+V,'P':2*V,'D':2*V,'OWN_ZERO':V,'CLEAR':V} + query={'ADD':4*axis_batches*7042+2*h,'SCALE':4*axis_batches*84,'SWAP':4*axis_batches*91,'P':4*V,'D':4*V,'COPY':h,'OWN_ZERO':h,'CLEAR':2*h} + native={'ADD':77*V,'P':15*V,'D':15*V,'X':20*V,'phase':6*V,'COPY':V,'OWN_ZERO':V,'CLEAR':2*V} + module=add(times(2,code),query,native) + n3=add(times(3,module),times(3,code),{'SWAP':V,'SCALE':V}) + logs={name:value.bit_length()for name,value in [('three_axis_stack',S),('ordinary_code',C),('query_pair',Q),('local_module',M),('N3_with_three_positive_exit_codes',whole)]} + r={'schema':'full120-positive-E-field-l2-and-ordinary-tariff/v1','status':'PASS_FINITE_FIELD_L2_CONSTANTS_AND_STRUCTURED_INVOICE','actual_kernel_prefix_receipt_sha256':hashlib.sha256(canonical(pr)).hexdigest(),'three_axis_recoder_squared_bound':str(bound),'three_axis_recoder_integer_norm_bound':S,'K_partial_extended_stage_norm_bound':8,'actual_K_row_l1':str(rmax),'actual_K_column_l1':str(cmax),'max_A_or_Ainverse_sector_scale':1351,'code_prefix_suffix_norm_bound':str(C),'query_gather_scatter_prefix_suffix_norm_bound':str(Q),'local_module_prefix_suffix_norm_bound':str(M),'three_modules_plus_three_positive_exit_codes_norm_bound':str(whole),'strict_power_of_two_log2_upper':logs,'error_ABI':'For any fixed emitted primitive word with L additive error injections, each of whole-field-collection l2 norm <=epsilon, output l2 error <=L*M*epsilon for a local module (or L*whole*epsilon for the N3 prefix). Paid Gaussian and signed address monomial operations are unitary at every positive width. Prefix/suffix bounds include linear adjoint orientations and owned zero/COPY/CLEAR.','ordinary_E_or_inverse_code':code,'ordinary_query_or_adjoint_upper':query,'ordinary_native_inverse_transpose_boundaries_upper':native,'ordinary_local_module_upper':module,'ordinary_N3_plus_positive_exit_upper':n3,'paid_N3':{str(r):3*V for r in[8,9,15,16]}|{'25':3*h},'owned_local_and_N3_peak_upper':V+h+512,'ordinary_normalizer_contract':'The odd3 actual constructor uses one ordinary P and one real D for each L or L inverse; the base120 normalizers can have one extra P, counted literally in MACROS120.','scope':'Bounds are finite constants independent of positive address field width, measured in l2 of the collection of whole fields. Per-coordinate rounding can incur a square-root dimension factor and requires a separate precision allocation. No all-size TM/storage theorem, negative terminal decoding, target moment or exponent admission is claimed.'} + return r +if __name__=='__main__': + ap=argparse.ArgumentParser();ap.add_argument('--write',action='store_true');a=ap.parse_args();r=calculate() + if a.write:(HERE/'PRECISION120.json').write_text(json.dumps(r,sort_keys=True,indent=2)+'\n') + else:need(json.loads((HERE/'PRECISION120.json').read_bytes())==r,'read-only precision and tariff receipt') + print(json.dumps(r,sort_keys=True)) diff --git a/research/full120-e8-lowrank-e-native/author/replay.py b/research/full120-e8-lowrank-e-native/author/replay.py new file mode 100644 index 0000000000..a237eb804a --- /dev/null +++ b/research/full120-e8-lowrank-e-native/author/replay.py @@ -0,0 +1,21 @@ +"""Normal/optimized read-only science replay; transient logs outside packet.""" +import argparse,concurrent.futures,hashlib,json,subprocess,sys,tempfile +from pathlib import Path +HERE=Path(__file__).resolve().parent +CASES=[['e_adapter.py'],['owned_e.py'],['n3.py'],['backward512.py'],['checkpoint120.py','--mode','base120'],['checkpoint120.py','--mode','root512'],['modes120.py'],['macros120.py'],['precision120.py']] +def main(): + ap=argparse.ArgumentParser();ap.add_argument('--write',action='store_true');ap.add_argument('--jobs',type=int,default=1);a=ap.parse_args();logdir=Path(tempfile.mkdtemp(prefix='full-e8-E120-normal-O-')) + def run(item): + optimized,args=item;flags=['-O']if optimized else[];cmd=[sys.executable,*flags,'-I','-B',*args];r=subprocess.run(cmd,cwd=HERE,capture_output=True) + key=('-'.join(args)).replace('/','_')+('-O'if optimized else'-normal');(logdir/(key+'.stdout')).write_bytes(r.stdout);(logdir/(key+'.stderr')).write_bytes(r.stderr) + if r.returncode:raise RuntimeError(str(cmd)+' failed; logs '+str(logdir)+' '+r.stderr.decode(errors='replace')[-2000:]) + return {'command':['python3',*flags,'-I','-B',*args],'returncode':r.returncode,'stdout_sha256':hashlib.sha256(r.stdout).hexdigest(),'stderr_sha256':hashlib.sha256(r.stderr).hexdigest()} + items=[(o,args)for args in CASES for o in[False,True]] + with concurrent.futures.ThreadPoolExecutor(max_workers=a.jobs)as pool:results=list(pool.map(run,items)) + r={'schema':'full120-E-positive-science-normal-O-replay/v1','status':'PASS_ALL18_READONLY_SCIENCE_REPLAYS','cases':results,'no_scientific_assertions_required':True,'scope':'Read-only exact recomputation against retained receipts and primitive payloads; no negative terminal decoder or caller admission.'} + if a.write:(HERE/'REPLAY.json').write_text(json.dumps(r,sort_keys=True,indent=2)+'\n') + else: + old=json.loads((HERE/'REPLAY.json').read_bytes()) + if old!=r:raise ValueError('read-only replay report mismatch') + print(r['status']);print('transient_logs='+str(logdir)) +if __name__=='__main__':main() diff --git a/research/full120-e8-lowrank-e-native/author/seal.py b/research/full120-e8-lowrank-e-native/author/seal.py new file mode 100644 index 0000000000..264a147d85 --- /dev/null +++ b/research/full120-e8-lowrank-e-native/author/seal.py @@ -0,0 +1,14 @@ +"""Payload-only SHA256 seal; no external runtime dependency.""" +import argparse,hashlib +from pathlib import Path +HERE=Path(__file__).resolve().parent +def payload(): + return sorted(p for p in HERE.rglob('*')if p.is_file()and p.name!='FILES.sha256'and p.suffix!='.log'and'__pycache__'not in p.parts) +def main(): + ap=argparse.ArgumentParser();ap.add_argument('--write',action='store_true');a=ap.parse_args() + content=''.join(hashlib.sha256(p.read_bytes()).hexdigest()+' '+p.relative_to(HERE).as_posix()+'\n'for p in payload()) + target=HERE/'FILES.sha256' + if a.write:target.write_text(content) + elif target.read_text()!=content:raise ValueError('payload set or byte digest differs from locked seal') + print('PASS_PAYLOAD_SEAL '+hashlib.sha256(content.encode()).hexdigest()+' '+str(len(payload()))+' files') +if __name__=='__main__':main() diff --git a/research/full120-e8-lowrank-e-native/peer/FILES.json b/research/full120-e8-lowrank-e-native/peer/FILES.json new file mode 100644 index 0000000000..b6cbfcc1cd --- /dev/null +++ b/research/full120-e8-lowrank-e-native/peer/FILES.json @@ -0,0 +1,36 @@ +{ + "files": { + "NOTE.md": { + "bytes": 2371, + "sha256": "87f09243d467e6a499767932c46efbc39bfcc3c117a4405391d623eb3cc4d715" + }, + "RESULT.json": { + "bytes": 7282, + "sha256": "f430e7a36854eb7ee691ecec6546cb82c70cc170cc654191eb36372a794090a0" + }, + "check.py": { + "bytes": 7247, + "sha256": "4c40765cfff583fc96a9f5a1561f5d7ea0e74b64d60e63e1ce836ea3d5077cc0" + }, + "inputs/KERNEL-PROGRAM.json.gz": { + "bytes": 53970, + "sha256": "990f8cc1bcd7b258000ac07050bbccf3a6b036440d36784d5fe6346e5afdee2c" + }, + "inputs/MACROS120-PROGRAM.json.gz": { + "bytes": 1371124, + "sha256": "cad6b43f27b83c9c9fcb2a3114ddbf7875b07a77658861eec2812a845ed29bb6" + }, + "inputs/NATIVE120-NATIVE-PROGRAM.json.gz": { + "bytes": 236505, + "sha256": "594bd83ddfc834cc030acb2670ec3d6dd405e5e87edfda33156be40518fc7706" + }, + "inputs/affine_oracle.py": { + "bytes": 7768, + "sha256": "b481c5544dd1087d7938c8b3fd95f351b2385be42c365ac2a12d9d1116729aaa" + }, + "inputs/clifford_exact.py": { + "bytes": 6824, + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + } + } +} diff --git a/research/full120-e8-lowrank-e-native/peer/NOTE.md b/research/full120-e8-lowrank-e-native/peer/NOTE.md new file mode 100644 index 0000000000..fd6da3a4b5 --- /dev/null +++ b/research/full120-e8-lowrank-e-native/peer/NOTE.md @@ -0,0 +1,40 @@ +# Separate literal physical E macro replay + +This reviewer imports no geometry, E compiler or checkpoint author script. +It interprets the actual base120 backward and forward primitive words, +including every paid child, owned COPY/CLEAR, source contact and scalar +recoding operation. It tests six independent original inputs: X/Y at old +root0 and at new roots112 and119. Every one of the240 returned fields and +every zero block is checked for each selected input. This is not a replay +of all240 original input columns. + +Signed tableaux are composed with the retained exact Clifford primitive. +A separate polynomial affine-support phase oracle reconstructs the literal +tableau and absolute phase. Operators with identical signed tableau are +collected only after their absolute phase is folded into rational complex +coefficients. Phase is multiplied by width modulo4, whereas owner scalar +coefficients act once. All four positive width phase residues pass, with +3960 nonzero and7560 zero blocks in total. These are exact formal tensor +operator combinations; no floating-point or dense address matrix is used. +A phase-i change is detected even though its signed tableau is unchanged. + +The expected endpoints use physical E_ij=L_i^-1 e_ij L_j and +E_inverse_ij=L_i^-1 ei_ij L_j, where e=K+C/14, ei=K+C and C=MM^T/4. +Forward is [[E D,0],[D E Q^-1,D E]]. Backward is +[[E_inverse D,-E_inverse R],[0,D E_inverse]]. Only commutation with full R +is assumed. Each complete orientation pays H2/H3/H5/H6 each120 and H9 eight +times, including on original input columns whose data happen to be zero. +All owned lifetimes return to the original main set; backward peak16 and +forward peak128 are authenticated by literal execution. + +Macro canonical science is +bea35cef68dc0fc09b7c8fbb590a2f84e63929ca2fd3057d6df00867fa376560. +The actual native and modal/kernel science pins are separately checked. +This is another AI implementation with shared Clifford conventions, not +independent human, kernel or all-family scientific acceptance. The n25 +structured constructor, complete negative decoder, precision/outer machine +admission and any new kappa remain separate obligations. + +Credit the retained native/Clifford compiler and affine oracle lineage, +the full120 source author and triangle-kernel author. Substantial OpenAI +Codex assistance; Apache-2.0 and copied input notices remain applicable. diff --git a/research/full120-e8-lowrank-e-native/peer/RESULT.json b/research/full120-e8-lowrank-e-native/peer/RESULT.json new file mode 100644 index 0000000000..d494f63318 --- /dev/null +++ b/research/full120-e8-lowrank-e-native/peer/RESULT.json @@ -0,0 +1 @@ +{"author_scripts_imported":false,"independent_phase_backend":"polynomial affine support","macro_science_sha256":"bea35cef68dc0fc09b7c8fbb590a2f84e63929ca2fd3057d6df00867fa376560","nonzero_blocks":3960,"orientations":2,"original_columns":6,"phase_i_mutant_rejected":true,"scope":"Full literal forward/backward macro on six selected actual original inputs (old root0 and added roots112,119 in both banks). All240 returned fields and owned lifetimes checked for each, in all four tensor width phase residues; owner scalar coefficients apply once. Not all240 input columns, no dense address matrix, no independent n25 or whole-caller 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diff --git a/research/full120-e8-lowrank-e-native/peer/check.py b/research/full120-e8-lowrank-e-native/peer/check.py new file mode 100644 index 0000000000..5c257ee011 --- /dev/null +++ b/research/full120-e8-lowrank-e-native/peer/check.py @@ -0,0 +1,115 @@ +"""Separate exact physical base120 macro replay on six original columns. + +No author script is imported. A shared signed-tableau primitive and separate +polynomial affine phase oracle interpret actual literal address words. +""" +from pathlib import Path +from fractions import Fraction as F +from collections import Counter +from hashlib import sha256 +from itertools import product +import argparse,gzip,importlib.util,json,sys +D=Path(__file__).resolve().parent +def need(q,s): + if not q:raise ValueError(s) +def canon(x):return(json.dumps(x,sort_keys=True,separators=(',',':'))+'\n').encode() +def load(n,p): + s=importlib.util.spec_from_file_location(n,p);m=importlib.util.module_from_spec(s);sys.modules[n]=m;s.loader.exec_module(m);return m +def calculate(): + ce=load('physical120_macro_ce',D/'inputs/clifford_exact.py');ao=load('physical120_macro_affine',D/'inputs/affine_oracle.py');n=9 + def data(name):return json.loads(gzip.decompress((D/'inputs'/name).read_bytes())) + p=data('MACROS120-PROGRAM.json.gz');native=data('NATIVE120-NATIVE-PROGRAM.json.gz');kernel=data('KERNEL-PROGRAM.json.gz') + need(sha256(canon(p)).hexdigest()=='bea35cef68dc0fc09b7c8fbb590a2f84e63929ca2fd3057d6df00867fa376560','actual literal macro science pin') + need(sha256(canon(native)).hexdigest()=='87d7cad7133ed0a2950b1d4fa2397e20e3c7bcedb90db95a15130aa03da543ae','native science pin') + need(sha256(canon(kernel)).hexdigest()=='0b526f1a38a73a82ae66e1b0182ed2fa8c14e16d703cd38fff4dc491d3b7c15b','owner kernel science pin') + need(p['native_science_sha256']==sha256(canon(native)).hexdigest(),'macro binds actual native') + def literal(w): + U=ce.ident(n) + for e in w: + if e[0]=='P':V=ce.perm(n,e[1]) + elif e[0]=='D':V=ce.diag(n,e[1],e[2]) + elif e[0]=='X':V=ce.xgate(n,e[1]) + elif e[0]=='C':V=ce.fourier(n,e[1]) if isinstance(e[1],list) else ce.cgate(n,e[1],e[2]) + else:need(e[0]=='phase','literal primitive');V=ce.Op(n,ce.identity(n),[tuple(e)]) + U=U.then(V) + return U + ops={k:literal(w)for k,w in p['definitions'].items()} + L={int(i):literal(native['definitions'][k])for i,k in native['normalizer_words'].items()} + G=ce.fourier(n,list(range(1,n)));Q=ce.fourier(n,[0]);R=ce.fourier(n) + M=kernel['root_M120x8'];K={(int(i),j):F(a,b)for i,row in native['literal_scalar_K_rows'].items()for j,a,b in row} + C={(i,j):sum(F(a)*F(b)for a,b in zip(M[i],M[j]))/4 for i in range(120)for j in range(120)} + coefficients={False:{(i,j):K.get((i,j),F())+C[i,j]/14 for i in range(120)for j in range(120)},True:{(i,j):K.get((i,j),F())+C[i,j]for i in range(120)for j in range(120)}} + # Operators with equal signed tableau differ by a global mu4 phase. Fold + # that phase into exact rational complex coefficients to permit cancellation. + registry={};phasecache={};composition={} + def reg(U): + tab=tuple(tuple(r)for r in U.tab) + ck=canon(U.circuit) + if ck not in phasecache: + need(ao.tableau_from_word(U.circuit,n)==tab,'independent literal signed tableau') + phasecache[ck]=ao.anchor(U)['mu4_phase'] + phase=phasecache[ck] + if tab not in registry:registry[tab]=(U,phase) + return tab,(phase-registry[tab][1])%4 + def turn(z,k): + a,b=z;return [(a,b),(-b,a),(-a,-b),(b,-a)][k%4] + def plus(dst,src,q=F(1)): + for k,(a,b)in src.items(): + x,y=dst.get(k,(F(),F()));z=(x+q*a,y+q*b) + if z==(0,0):dst.pop(k,None) + else:dst[k]=z + def unary(src,U,uid): + out={} + for k,z in src.items(): + pair=(uid,k) + if pair not in composition:composition[pair]=reg(registry[k][0].then(U)) + t,phase=composition[pair];a,b=turn(z,phase*width);x,y=out.get(t,(F(),F()));out[t]=(a+x,b+y) + return{k:z for k,z in out.items()if z!=(0,0)} + iid,ip=reg(ce.ident(n));need(ip==0,'identity phase') + main=[tuple(f)for f in p['main']] + def replay(word,column): + vals={f:({iid:(F(1),F())}if f==column else{})for f in main};bill=Counter();peak=0 + for e in word: + op=e[0];f=tuple(e[1]);need(f in vals or op in['OWN_ZERO','COPY'],'initialized field') + if op in['OWN_ZERO','COPY']: + need(f not in vals and f not in main,'fresh owned allocation');vals[f]={}if op=='OWN_ZERO'else dict(vals[tuple(e[2])]);peak=max(peak,len(vals)-len(main)) + elif op=='CLEAR':need(f not in main,'owned-only clear');del vals[f] + elif op=='SWAP':g=tuple(e[2]);vals[f],vals[g]=vals[g],vals[f] + elif op=='SCALE':q=F(e[2],e[3]);vals[f]={k:(q*a,q*b)for k,(a,b)in vals[f].items()if q} + elif op=='ADD':plus(vals[f],vals[tuple(e[2])],F(e[3],e[4])) + else: + need(op=='U','known macro grammar');vals[f]=unary(vals[f],ops[e[2]],e[2]);bill.update([e[3]]if e[3]else[]) + need(set(vals)==set(main),'owned fields all discharged') + return vals,bill,peak + def term(q,U): + if not q:return{} + k,ph=reg(U);return{k:turn((q,F()),ph*width)} + tested=[];blocks=0;zero=0 + for width,orientation,role,j in product([1,2,3,4],['backward','forward'],['X','Y'],[0,112,119]): + column=(role,j);vals,bill,peak=replay(p[orientation],column);need(bill==Counter({2:120,3:120,5:120,6:120,9:8}),'actual complete paid invoice') + for outrole,i in main: + q=F();U=ce.ident(n) + if orientation=='backward': + q=coefficients[True][i,j] + if outrole=='X'and role=='X':U=G.then(L[j]).then(L[i].adjoint()) + elif outrole=='X'and role=='Y':q=-q;U=R.then(L[j]).then(L[i].adjoint()) + elif outrole=='Y'and role=='Y':U=L[j].then(L[i].adjoint()).then(G) + else:q=F() + else: + q=coefficients[False][i,j] + if outrole=='X'and role=='X':U=G.then(L[j]).then(L[i].adjoint()) + elif outrole=='Y'and role=='X':U=Q.adjoint().then(L[j]).then(L[i].adjoint()).then(G) + elif outrole=='Y'and role=='Y':U=L[j].then(L[i].adjoint()).then(G) + else:q=F() + need(vals[outrole,i]==term(q,U),'complete physical macro block '+str((width,orientation,column,(outrole,i)))) + blocks+=bool(q);zero+=not bool(q) + tested.append({'width_residue':width%4,'orientation':orientation,'original_column':list(column),'peak_owned':peak,'paid':dict(bill)}) + # A final phase-i change has exactly the same signed tableau, but fails the + # independent absolute phase comparison on an actual nonzero returned block. + k=next(iter(registry));U=registry[k][0];bad=U.then(ce.Op(n,ce.identity(n),[('phase',1)]));kb,ph=reg(bad);need(kb==k and ph==1,'same tableau absolute-phase mutant detected') + return {'status':'PASS_SEPARATE_PHYSICAL_BASE120_E_MACRO_COLUMNS','macro_science_sha256':sha256(canon(p)).hexdigest(),'tests':tested,'nonzero_blocks':blocks,'zero_blocks':zero,'original_columns':6,'orientations':2,'width_residues':[0,1,2,3],'phase_i_mutant_rejected':True,'author_scripts_imported':False,'shared_Clifford_primitive':True,'independent_phase_backend':'polynomial affine support','scope':'Full literal forward/backward macro on six selected actual original inputs (old root0 and added roots112,119 in both banks). All240 returned fields and owned lifetimes checked for each, in all four tensor width phase residues; owner scalar coefficients apply once. Not all240 input columns, no dense address matrix, no independent n25 or whole-caller proof.'} +if __name__=='__main__': + ap=argparse.ArgumentParser();ap.add_argument('--write',action='store_true');a=ap.parse_args();r=json.loads(canon(calculate()));path=D/'RESULT.json' + if a.write:path.write_bytes(canon(r)) + else:need(json.loads(path.read_bytes())==r,'read-only peer receipt') + print(json.dumps(r,sort_keys=True)) diff --git a/research/full120-e8-lowrank-e-native/peer/inputs/KERNEL-PROGRAM.json.gz b/research/full120-e8-lowrank-e-native/peer/inputs/KERNEL-PROGRAM.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..f6e51bdc489f30e81fbb4c6acf78b0e449c58692 GIT binary patch literal 53970 zcmZU)bx<6<7dHB~h2l`GxVsdJ%OWlAu7w3kad(QhxVsj2ch|)o7I!J`E(`3kd;9yo zxifd>=8xo=Nivg}VN+$Z}HE&Ct?{o6B!;kEy-ggdBnOckee+?QPtj& z8WNzt?LgvP*hEhL&pIzx_sKRav-;rjo+9DMOy;t$9eRi^+#bzKYAmydfQ$ru#0r4T zi^FfiU^fO2HLk_dtyVhe`SUVjvGV#o0NR+bY&dDIKVVA= 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mul_i(a,b,p):return[(a,b),(-b,a),(-a,-b),(b,-a)][p%4] +def qvalue(alpha,S,x): + value=0 + while x: + bit=x&-x;j=bit.bit_length()-1;x^=bit;value+=alpha[j]+2*parity(S[j]&x) + return value%4 +def support_map(B,x): + out=0 + while x: + bit=x&-x;out^=B[bit.bit_length()-1];x^=bit + return out +def echelon(B): + piv={} + for j,col in enumerate(B): + x=col;word=1<=0 and 0<=basis<1<>i)&1)==self.alpha[i]%2 for i in range(r)),'quadratic diagonal equals linear parity') + need(all(((self.S[i]>>j)&1)==((self.S[j]>>i)&1)for i in range(r)for j in range(i)),'symmetric binary quadratic form') + need((self.ar*self.ar+self.ai*self.ai)*(1<>j)&1)==((S[j]>>i)&1)for i in range(self.n)for j in range(i))and all(alpha[i]%2==((S[i]>>i)&1)for i in range(self.n)),'Clifford diagonal polynomial') + const,a,T=pullback(alpha,S,self.b,self.B);self.phase(const);self.alpha=[(x+y)%4 for x,y in zip(self.alpha,a)];self.S=[x^y for x,y in zip(self.S,T)] + else: + need(kind=='C'and isinstance(e[2],int)and e[2]in[-1,1]and isinstance(e[1],int)and 0<=e[1]<1<>j)&1))%4 for j,a in enumerate(self.alpha)];self.S=[row^(h if h>>j&1 else 0)for j,row in enumerate(self.S)];self.stats['C_same']+=1 + else: + need(h!=0,'odd derivative has nonzero support constraint');eta=((s-delta)//2)%2;p=(h&-h).bit_length()-1;y0=(1<>j&1 else 0)for j in range(r)if j!=p];const,a,T=pullback(self.alpha,self.S,y0,cols) + self.b^=support_map(self.B,y0);self.B=[support_map(self.B,c)for c in cols];self.alpha=a;self.S=T;self.phase(const);self.scalar(1,s);self.stats['C_drop']+=1 + self.peak_rank=max(self.peak_rank,self.rank);self.validate();return self + def amplitude(self,x): + need(0<=x<1<>k&1:a,b=piv[k];x^=a;y^=b + a,b=mul_i(self.ar,self.ai,qvalue(self.alpha,self.S,y));r=self.rank;t=F(1,1<<((r+1)//2));alpha=(t,t if r&1 else F());actual=(F(a,1<>i)&1)<>j&1);a[j],a[k]=a[k],a[j] + for i in range(n): + if i!=j and a[i]>>j&1:a[i]^=a[j] + assert [r&((1<>n for r in a) +def basis_extend(cols,n): + out=[] + for x in list(cols)+[1<len(out):out.append(x) + assert len(out)==n + return tuple(out) +def nullspace(rows,n): + a=list(rows);p=[];k=0 + for j in range(n): + t=next((i for i in range(k,len(a)) if a[i]>>j&1),None) + if t is None:continue + a[t],a[k]=a[k],a[t] + for i in range(len(a)): + if i!=k and a[i]>>j&1:a[i]^=a[k] + p.append(j);k+=1 + return tuple((1<>j)&1)<>i&1:out=pmul(out,T[i]) + for i in range(n): + if z>>i&1:out=pmul(out,T[n+i]) + return out +def compose(A,B):return tuple(apply(A,p) for p in B) +def inverse(T): + n=len(T)//2;cols=[x|(z<>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4)) + return tuple(out) +def qvalue(Q,alpha,x,n): + return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4 +def mul_i(a,p): + x,y=a;p%=4 + return [(x,y),(-y,x),(-x,-y),(y,-x)][p] +@dataclass +class Op: + n:int + tab:tuple + circuit:list + def then(self,b): + assert self.n==b.n + return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit) + def adjoint(self): + circ=[] + for e in reversed(self.circuit): + if e[0]=='P':circ.append(('P',inv(e[1],self.n))) + elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2]))) + elif e[0]=='C':circ.append(('C',e[1],-e[2])) + elif e[0]=='phase':circ.append(('phase',(-e[1])%4)) + else:circ.append(e) + return Op(self.n,inverse(self.tab),circ) + def zero_state(self,basis=0): + N=1<>i)&1 for i in range(n)) + assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n)) + return Op(n,tuple([(1<>i&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>i)&1)) for i in range(n)]),[('X',b)]) +def fourier(n,axes=None): + out=ident(n) + for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<len(selected):picks.append(j);selected.append(x) + assert len(picks)==r and all(x>>r==0 for x in Bcols) + Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<50. This refutes that generic inference, not the actual K construction. +The bound8 used by the author's C,Q,M constants remains valid. + +All remaining stages of one output cube are SWAP isometries and owned CLEAR +projections; OWN_ZERO is an isometric zero embedding. A suffix beginning +inside accumulation has a remaining partial B with the same bound. In the +reverse transpose, its corresponding prefixes have the same norm. Completed +cubes implement orthogonal K on mains and remove their private scratch. +Different cubes act on disjoint main blocks and clear scratch before reuse; +an incoming scratch error can reach the current cube's outputs, but cannot +flow through a cleared scratch into a later cube. Hence the prefix/suffix +bound for the complete sequential product-cube stage is8, rather than a +product of8 over all3375 cubes. + +The exact four chronological recoder receipts cover both original words and +both reversed transposes. A selector axis's120^2 batches act on disjoint +120-field blocks. After at most two complete selector axes, multiplying their +endpoint bounds by the active axis prefix bound gives the reported squared +bound14320735522816/15. Its exact integer square-root upper bound is977096; +it is not raised to43200. + +For each E or inverse code, two recoder stacks, one modal scale of at most1351, +and the corrected K bound give `C=8*1351*S^2`. Physical L maps are unitary. +Query gathering has two recoders and COPY norm at most2; scattering has two +recoders and shear norm at most1351. Thus `Qbound=2*1351*S^4` covers every +prefix/suffix, including the reverse owned transpose. The original-ground +queries remain full H25 calls; no modal support discount is used. + +Distinct source-owner contact copies have combined norm at most2, regardless +of how often each retained contact is subsequently read. The inverse target +stage has block row/column bound7, including partial ADD sums, giving8. +Two code stages, the query pair, and these two native passes give the existing +`M=16*C^2*Qbound`. Ordinary boundaries are monomial. The three-module plus +three-code bound remains `M^3*C^3`. The checker reproduces all existing exact +constants and advertised strict powers without evaluating the dense circuit. + +These are bounds at the declared whole-field primitive boundaries. A SWAP is +an exact SWAP primitive here, and a paid Gaussian is a completed unitary +child. If SWAP is lowered into3ADD+sign microcode or a Gaussian recursively +expanded, its internal error service/prefixes must be separately accounted. +No per-bit coordinate allocation is inferred from these field-l2 bounds. + +## Invoice orientation and source timing + +An independent census of the actual512-owner native inverse gives, per owner: + +| primitive | count | +|---|---:| +| ADD |76| +| COPY |1| +| CLEAR |1| +| P |15| +| D |15| +| X |17| +| phase |6| + +Its paid calls are one each of H8,H9,H15,H16 per owner. Transposing a COPY +adds one ADD and CLEAR; final CLEAR becomes OWN_ZERO. The forward monomial +boundary adds3 X operations per owner. Therefore the unified native upper +bill ADD77V, P15V, D15V, X20V, phase6V, COPY V, OWN_ZERO V, CLEAR2V covers +both orientations, with V=120^3. + +The query's extra+h ADD accounts for the transpose of modal COPY. Its h +OWN_ZERO accounts for transposed final mode CLEAR. Two E codes allocate and +clear V fields each. The resulting total OWN_ZERO is3V+h, not2V+h, and agrees +with the published module invoice. The script independently recomputes every +ordinary local/three-stage upper count and the V+h+512 owned peak. + +A metadata-only source version pass checks all512 actual source owners and +76 reads per owner. Each reverse source-Y COPY occurs at its actual unchanged +contact version, before that inverse source path finishes. Base120's8 query +calls precede the source-consuming native word; the emitted corrections are +-15 in backward and+15 in inverse. Thus the inverse acquires the authentic +native contacts first, restores ground Y by E, queries original Y, undoes the +correction, and then finishes native X inversion. + +Bilinear transpose retains every real ADD/SCALE coefficient once, reverses +chronology and exchanges ADD source and target. The review checks every such +non-address primitive against the emitted inverse. Address P transposes to +its inverse, Gaussian C is symmetric, D/X are symmetric and scalar phase is +unchanged; these phase identities remain the author's pinned physical science +and root's independent physical replay, rather than a new dense replay here. + +The displayed algebra uses only `[E,R]=0`, E real symmetric, and Q,D commuting +on their disjoint axes. It does not move E through Q separately. Inverse Y +restoration followed by original-ground correction has the stated order. +The boundary `diag(D^2,D^2) J (WB^-1)^T J^-1`, J=diag(Q^2,I), gives the forward +blocks `[[ED,0],[DEQ^-1,DE]]`; the first block uses commutation with R^2. +Owner coefficients act once; only physical address words tensor lift. + +No material invoice, direction or finite field-norm error was found beyond +the intermediate arbitrary-scratch explanation corrected above. The negative +terminal remains UNKNOWN. This review does not establish coordinate/TM +precision, all-size storage/routing, a complete new supplier, scientific +adoption or any new kappa. diff --git a/research/full120-e8-lowrank-e-native/review/check.py b/research/full120-e8-lowrank-e-native/review/check.py new file mode 100644 index 0000000000..9199662eec --- /dev/null +++ b/research/full120-e8-lowrank-e-native/review/check.py @@ -0,0 +1,149 @@ +"""Read-only independent norm/invoice review; no dense operator replay.""" +from pathlib import Path +from fractions import Fraction as F +from collections import Counter +from hashlib import sha256 +import json,gzip,math,argparse +HERE=Path(__file__).resolve().parent +AUTHOR=Path('/tmp/full-e8-e-adapter120-20261025-structural') +SEAL='cb40b9602eec2c4c8950af4f9e8a06ea0d99db5ca74ceafd8b7781acc0aaccf6' +def need(q,s): + if not q:raise ValueError(s) +def canon(x):return(json.dumps(x,sort_keys=True,separators=(',',':'))+'\n').encode() +def js(n):return json.loads((AUTHOR/n).read_bytes()) +def gz(n):return json.loads(gzip.decompress((AUTHOR/n).read_bytes())) +def pins(): + need(sha256((AUTHOR/'FILES.sha256').read_bytes()).hexdigest()==SEAL,'author seal unchanged') + n=0 + for line in (AUTHOR/'FILES.sha256').read_text().splitlines(): + h,p=line.split(' ',1);need(sha256((AUTHOR/p).read_bytes()).hexdigest()==h,'author bytes unchanged '+p);n+=1 + return n + +def norm_checks(): + pr=js('inputs/prefix/RECEIPT.json');r=js('PRECISION120.json') + need(set(pr['orientations'])=={'to_modal','from_modal','to_modal_transpose','from_modal_transpose'},'four chronological prefix orientations') + b=max(F(v['whole_three_axis_l2_amplification_squared_upper'])for v in pr['orientations'].values()) + c=(b.numerator+b.denominator-1)//b.denominator;S=math.isqrt(c) + if S*S=b and (S-1)**250 and ratio<64,'arbitrary-scratch generic sqrt50 inference rejected') + C=8*1351*S*S;Q=2*1351*S**4;M=16*C*C*Q;W=M**3*C**3 + need(str(C)==r['code_prefix_suffix_norm_bound'],'same code bound survives') + need(str(Q)==r['query_gather_scatter_prefix_suffix_norm_bound'],'query count of four recoders') + need(str(M)==r['local_module_prefix_suffix_norm_bound'],'native2*8 and two codes') + need(str(W)==r['three_modules_plus_three_positive_exit_codes_norm_bound'],'same three-stage constant') + need(M<1<<202 and W<1<<764,'advertised powers') + return {'S':S,'recoder_squared_bound':str(b),'actual_K_terms_each_row':76, + 'actual_K_row_column_l1':'7','arbitrary_scratch_shear_bound':8, + 'generic_sqrt50_counterexample_squared_ratio':str(ratio), + 'unchanged_C':str(C),'unchanged_Q':str(Q),'unchanged_M':str(M),'unchanged_whole':str(W), + 'scope':'All declared whole-field macro prefixes and suffixes; no lowering of SWAP or recursive Gaussian internal arithmetic is granted.'} + +def counter_add(*ds): + out=Counter() + for d in ds:out.update(d) + return out + +def invoice_checks(): + data=gz('ROOT512-CHECKPOINT-PROGRAM.json.gz');count=Counter();paid=Counter() + for op in data['native_inverse_program']: + if op[0]!='UNARY':count[op[0]]+=1;continue + q=data['events'][str(abs(op[2]))]['inverse_literal'] + if q['kind']=='MONOMIAL':word=data['monomial_definitions'][q['word']] + else:word=data['monomial_definitions'][q['before']]+[['C',q['positive_child_axes']]]+data['monomial_definitions'][q['after']] + for e in word: + if e[0]=='C':paid[len(e[1])]+=1 + else:count[e[0]]+=1 + per={k:F(v,512)for k,v in count.items()} + need(per=={'ADD':76,'COPY':1,'CLEAR':1,'P':15,'D':15,'X':17,'phase':6},'literal native inverse counts independent census') + need(paid=={8:512,9:512,15:512,16:512},'native paid profile') + V=120**3;h=22016;batches=3*120**2 + r=js('PRECISION120.json');kernel=gz('inputs/KERNEL-PROGRAM.json.gz') + for w in ['to_modal_kernel_word','from_modal_kernel_word']: + need(Counter(e[0]for e in kernel[w])=={'ADD':7042,'SCALE':84,'SWAP':91},'actual owner instruction census') + code={'ADD':2*batches*7042+76*V,'SCALE':2*batches*84+h,'SWAP':2*batches*91+V,'P':2*V,'D':2*V,'OWN_ZERO':V,'CLEAR':V} + # Query and its transpose: each COPY becomes ADD+owned CLEAR; each final + # owned CLEAR becomes OWN_ZERO. The explicit extra+h ADD covers this. + query={'ADD':4*batches*7042+2*h,'SCALE':4*batches*84,'SWAP':4*batches*91,'P':4*V,'D':4*V,'COPY':h,'OWN_ZERO':h,'CLEAR':2*h} + native={'ADD':77*V,'P':15*V,'D':15*V,'X':20*V,'phase':6*V,'COPY':V,'OWN_ZERO':V,'CLEAR':2*V} + module=counter_add(code,code,query,native) + whole=counter_add(*([module]*3),*([code]*3),{'SWAP':V,'SCALE':V}) + need(code==r['ordinary_E_or_inverse_code'],'E orientation upper invoice') + need(query==r['ordinary_query_or_adjoint_upper'],'query both orientations upper invoice') + need(native==r['ordinary_native_inverse_transpose_boundaries_upper'],'native both orientations upper invoice') + need(dict(module)==r['ordinary_local_module_upper']and dict(whole)==r['ordinary_N3_plus_positive_exit_upper'],'complete independent structured sums') + need(r['paid_N3']=={'8':3*V,'9':3*V,'15':3*V,'16':3*V,'25':3*h},'three-stage paid bill') + need(r['owned_local_and_N3_peak_upper']==V+h+512,'all contact/mode/Kscratch peak covered') + return {'literal_root512_inverse_counts':dict(count),'inverse_per_owner':{k:str(v)for k,v in per.items()}, + 'forward_extra_X_per_owner':3,'transpose_COPY_extra_ADD_per_owner':1, + 'ordinary_code':code,'query_upper':query,'native_upper':native,'module_upper':dict(module), + 'owned_peak_upper':V+h+512,'invoice_orientation':'Direct B needs fewer owned events; inverse requires COPY caches; forward transpose requires OWN_ZERO cache/modes and COPY-adjoint ADD. The unified bill covers each, without charging an owned field as productive mass.'} + +def contact_checks(): + source=gz('inputs/B-PROGRAM.json.gz');original=source['program'];versions=Counter();contacts={};reads=Counter() + for e in original: + if e[0]=='ADD': + need(e[1]=='X'and e[3]=='Y','source Y read only by targetADD') + owner=e[4];v=(versions[owner],e[7]);need(owner not in contacts or contacts[owner]==v,'one unchanged physical source contact') + contacts[owner]=v;reads[owner]+=1 + elif e[1]=='Y':versions[e[2]]+=1 + need(len(contacts)==512 and set(reads.values())=={76},'actual512 contact contact/read counts') + cp=gz('ROOT512-CHECKPOINT-PROGRAM.json.gz');current=Counter(versions);seen=set() + for e in cp['source_Y_only_pass']: + if e[0]=='UNARY': + q=cp['events'][str(abs(e[2]))]['original'];need(q[1]=='Y'and e[2]<0,'actual reverse source unary');current[q[2]]-=1 + else: + need(e[0]=='COPY'and e[1][0]=='cache'and e[2][0]=='Y','only actual source snapshots') + owner=e[2][1];need(current[owner]==contacts[owner][0]and owner not in seen,'cache captured at actual contact version');seen.add(owner) + need(len(seen)==512 and all(v==0 for v in current.values()),'source inverse completes after cache') + base=gz('MACROS120-PROGRAM.json.gz');back=base['backward'];inv=base['inverse'] + queries=[j for j,e in enumerate(back)if e[0]=='U'and e[4]=='original_ground_full_R9_query'] + native=[j for j,e in enumerate(back)if e[0]=='U'and e[4].startswith('actual_native_')] + need(len(queries)==8 and max(queries)

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QfB%R74+tZ(Wwc_P0DHWtk^lez literal 0 HcmV?d00001 diff --git a/research/full120-e8-lowrank-e-native/author/MACROS120.json b/research/full120-e8-lowrank-e-native/author/MACROS120.json new file mode 100644 index 0000000000..5251f2abce --- /dev/null +++ b/research/full120-e8-lowrank-e-native/author/MACROS120.json @@ -0,0 +1,150 @@ +{ + "actual_contact_inverse_and_transpose_all240_independent_operator_rows": "BASE120-CHECKPOINT.json", + "actual_native_paid_phase_object": "87d7cad7133ed0a2950b1d4fa2397e20e3c7bcedb90db95a15130aa03da543ae", + "all14400_common_chart_code_entries_each_direction": true, + "all_literal_owned_lifecycles": true, + "controls": { + "early_ground_mode_clear_rejected": true, + "missing_actual_source_cache_rejected": true + }, + "main_address_axes": 9, + "main_fields": 240, + "noncommuting_generic_operator_identity": { + "H": "H(T)=diag(T,Q_inverse T Q); R=D Q; E commutes R and is real symmetric. E generally does not commute Q or D.", + "backward": "[[E_inverse D, -E_inverse R],[0,D E_inverse]]=H(E_inverse) B0", + "forward": "[[E D,0],[D E Q_inverse,D E]]=H(E) F0", + "inverse": "[[D_inverse E,Q E D_inverse],[0,E D_inverse]]", + "mode_gather": "Actual original Y before backward precode. Inverse first finishes actual inverse source-Y pass with owned contact cache, then codes Y by E to acquire original ground." + }, + "noncommuting_physical_allcolumn_fixture": "OWNED-E.json:three lambdas15,225/2,-1350;16 independent maincolumns each", + "receipts": { + "backward": { + "maximum_scalar_absolute_coefficient": "30", + "ordinary_and_literal_counts": { + "ADD": 57784, + "CLEAR": 248, + "COPY": 8, + "OWN_ZERO": 240, + "SCALE": 688, + "SWAP": 968, + "U": 2288, + "physical_D": 2760, + "physical_P": 2840, + "physical_X": 1560, + "physical_phase": 720 + }, + "paid": { + "2": 120, + "3": 120, + "5": 120, + "6": 120, + "9": 8 + }, + "peak_owned_fields": 16 + }, + "forward": { + "maximum_scalar_absolute_coefficient": "30", + "ordinary_and_literal_counts": { + "ADD": 57912, + "CLEAR": 368, + "OWN_ZERO": 368, + "SCALE": 688, + "SWAP": 968, + "U": 2648, + "physical_D": 2760, + "physical_P": 2840, + "physical_X": 2400, + "physical_phase": 720 + }, + "paid": { + "2": 120, + "3": 120, + "5": 120, + "6": 120, + "9": 8 + }, + "peak_owned_fields": 128 + }, + "inverse": { + "maximum_scalar_absolute_coefficient": "30", + "ordinary_and_literal_counts": { + "ADD": 57784, + "CLEAR": 368, + "COPY": 128, + "OWN_ZERO": 240, + "SCALE": 688, + "SWAP": 968, + "U": 2288, + "physical_D": 2760, + "physical_P": 2840, + "physical_X": 2040, + "physical_phase": 720 + }, + "paid": { + "2": 120, + "3": 120, + "5": 120, + "6": 120, + "9": 8 + }, + "peak_owned_fields": 128 + }, + "linear_transpose_inverse": { + "maximum_scalar_absolute_coefficient": "30", + "ordinary_and_literal_counts": { + "ADD": 57912, + "CLEAR": 368, + "OWN_ZERO": 368, + "SCALE": 688, + "SWAP": 968, + "U": 2288, + "physical_D": 2760, + "physical_P": 2840, + "physical_X": 2040, + "physical_phase": 720 + }, + "paid": { + "2": 120, + "3": 120, + "5": 120, + "6": 120, + "9": 8 + }, + "peak_owned_fields": 128 + }, + "ordinary_E_X": { + "maximum_scalar_absolute_coefficient": "30", + "ordinary_and_literal_counts": { + "ADD": 14564, + "CLEAR": 120, + "OWN_ZERO": 120, + "SCALE": 176, + "SWAP": 302, + "U": 240, + "physical_D": 240, + "physical_P": 256 + }, + "paid": {}, + "peak_owned_fields": 8 + }, + "ordinary_E_inverse_X": { + "maximum_scalar_absolute_coefficient": "30", + "ordinary_and_literal_counts": { + "ADD": 14564, + "CLEAR": 120, + "OWN_ZERO": 120, + "SCALE": 176, + "SWAP": 302, + "U": 240, + "physical_D": 240, + "physical_P": 256 + }, + "paid": {}, + "peak_owned_fields": 8 + } + }, + "schema": "full120-literal-positive-E-owned-macro-review/v1", + "scientific_payload_sha256": "bea35cef68dc0fc09b7c8fbb590a2f84e63929ca2fd3057d6df00867fa376560", + "scope": "The emitted base120 primitive words are actual, including every paid child, ordinary address word and phase. Exact common-chart scalarcode replay plus sealed native phase science and actual native owned inverse/transpose prove composition. This checker does not propagate a122880-by122880 dense matrix. The odd3 family uses the explicit structured owner loop and its independently pinned512 native template. No negative E decoder, formal supplier or new kappa.", + "status": "PASS_ACTUAL_BASE120_E_MACRO_AND_STRUCTURED_COMPOSITION" +} diff --git a/research/full120-e8-lowrank-e-native/author/MODES120-PROGRAM.json b/research/full120-e8-lowrank-e-native/author/MODES120-PROGRAM.json new file mode 100644 index 0000000000..73ab07a830 --- /dev/null +++ b/research/full120-e8-lowrank-e-native/author/MODES120-PROGRAM.json @@ -0,0 +1,234 @@ +{ + "base_modal_scale": { + "E": "-1/14", + "E_inverse": "-14" + }, + "base_owner_recoder": { + "from": "inputs/KERNEL-PROGRAM.json.gz:from_modal_kernel_word", + "to": "inputs/KERNEL-PROGRAM.json.gz:to_modal_kernel_word" + }, + "code_recipe": [ + "Apply each actual physical L_i to its field.", + "Apply to-modal word in place on each selector axis.", + "SCALE active sectors by A_inverse_scale for E or A_scale for E_inverse.", + "Restore from-modal words in reverse axis order.", + "Apply actual scalar K (base8cube/odd3 512cube) into owned zero output scratch, read all inputs, SWAP outputs into mains, CLEAR old mains from scratch; reuse8/512 fields.", + "Apply L_i inverse." + ], + "global_owner_recoder": { + "ambient": 25, + "loop": "For axis a=0,1,2 and lexicographic other selector coordinates in0..119 apply the emitted120-field word on that axis. Restore in reverse axis order using the inverse word.", + "orthonormal_basis_raw27": [ + 262657, + 262658, + 262660, + 262664, + 262672, + 262688, + 262720, + 262784, + 262912, + 263679, + 264703, + 266751, + 270847, + 279039, + 295423, + 328191, + 393727, + 786431, + 1310719, + 2359295, + 4456447, + 8650751, + 17039359, + 33816575, + 67371007 + ], + "physical_normalizers": "Actual K-TEMPLATE U25 chart and q tuple; ordinary exact signed Clifford L_i from actual K native constructor. These address monomials commute with R25 with phase; no claim they commute Q or D separately.", + "scalar_coefficients": "Each owner coefficient acts once; only address monomials tensor lift with field width.", + "selector_shape": [ + 120, + 120, + 120 + ] + }, + "global_scalar_C": "(C1 C2+C1 C3+C2 C3-C1 C2 C3)/2; factors act on distinct owner selector axes.", + "global_scalar_K": "(K1+K2+K3-K1 K2 K3)/2; actual76-entry rows, row-l1=7.", + "invoices": { + "base120": { + "axis_word_batches_per_direction": 1, + "ordinary_code_E_or_inverse": { + "ADD": 14564, + "CLEAR": 120, + "OWN_ZERO": 120, + "SCALE": 176, + "SWAP": 302, + "peak_scratch": 8, + "physical_L_field_map": 240 + }, + "original_ground_query_plus_scatter": { + "ADD": 28176, + "CLEAR": 8, + "COPY": 8, + "SCALE": 336, + "SWAP": 364, + "paid": { + "9": 8 + }, + "physical_L_field_map": 480 + }, + "owned_inverse_peak_upper": 136, + "query_or_transpose_upper": { + "ADD": 28184, + "CLEAR": 16, + "COPY": 8, + "OWN_ZERO": 8, + "SCALE": 336, + "SWAP": 364, + "paid": { + "9": 8 + }, + "physical_L_field_map": 480 + } + }, + "odd3": { + "axis_word_batches_per_direction": 43200, + "ordinary_code_E_or_inverse": { + "ADD": 739756800, + "CLEAR": 1728000, + "OWN_ZERO": 1728000, + "SCALE": 7279616, + "SWAP": 9590400, + "peak_scratch": 512, + "physical_L_field_map": 3456000 + }, + "original_ground_query_plus_scatter": { + "ADD": 1216879616, + "CLEAR": 22016, + "COPY": 22016, + "SCALE": 14515200, + "SWAP": 15724800, + "paid": { + "25": 22016 + }, + "physical_L_field_map": 6912000 + }, + "owned_inverse_peak_upper": 1750528, + "query_or_transpose_upper": { + "ADD": 1216901632, + "CLEAR": 44032, + "COPY": 22016, + "OWN_ZERO": 22016, + "SCALE": 14515200, + "SWAP": 15724800, + "paid": { + "25": 22016 + }, + "physical_L_field_map": 6912000 + } + } + }, + "kernel_science_sha256": "0b526f1a38a73a82ae66e1b0182ed2fa8c14e16d703cd38fff4dc491d3b7c15b", + "native120_science_sha256": "87d7cad7133ed0a2950b1d4fa2397e20e3c7bcedb90db95a15130aa03da543ae", + "native512_science_sha256": "1aeba5ae2276ff58e24ed9ca84f08830c0bb7321432bc74e42472f0029bfb1c2", + "odd3_sectors": [ + { + "A_inverse_scale": "1", + "A_scale": "1", + "C_eigenvalue": "0", + "dimension": 1404928, + "modal_axis_flags": [ + 0, + 0, + 0 + ] + }, + { + "A_inverse_scale": "1", + "A_scale": "1", + "C_eigenvalue": "0", + "dimension": 100352, + "modal_axis_flags": [ + 0, + 0, + 1 + ] + }, + { + "A_inverse_scale": "1", + "A_scale": "1", + "C_eigenvalue": "0", + "dimension": 100352, + "modal_axis_flags": [ + 0, + 1, + 0 + ] + }, + { + "A_inverse_scale": "-2/223", + "A_scale": "-223/2", + "C_eigenvalue": "225/2", + "dimension": 7168, + "modal_axis_flags": [ + 0, + 1, + 1 + ] + }, + { + "A_inverse_scale": "1", + "A_scale": "1", + "C_eigenvalue": "0", + "dimension": 100352, + "modal_axis_flags": [ + 1, + 0, + 0 + ] + }, + { + "A_inverse_scale": "-2/223", + "A_scale": "-223/2", + "C_eigenvalue": "225/2", + "dimension": 7168, + "modal_axis_flags": [ + 1, + 0, + 1 + ] + }, + { + "A_inverse_scale": "-2/223", + "A_scale": "-223/2", + "C_eigenvalue": "225/2", + "dimension": 7168, + "modal_axis_flags": [ + 1, + 1, + 0 + ] + }, + { + "A_inverse_scale": "1/1351", + "A_scale": "1351", + "C_eigenvalue": "-1350", + "dimension": 512, + "modal_axis_flags": [ + 1, + 1, + 1 + ] + } + ], + "physical_operator_claim": "C_phys=L^-1 Cscalar L commutes R. E=K(I-C)^-1, E_inverse=K+C. The emitted ordinary code uses no Q-conjugation assumption. Backward output is H(E_inverse)B0, forward obtained from owned inverse transpose is H(E)F0. H(T)=diag(T,Q^-1 T Q).", + "query_recipe": [ + "On unchanged original ground Y apply L_i then to-modal selector words.", + "COPY every active coordinate into its owned mode; restore original Y exactly via inverse recoder and L_i inverse.", + "Apply one full positive R9 or R25 to each owned mode.", + "After native B but before postX(E_inverse), apply L_i and to-modal words to X, ADD -lambda times each retained mode at its active coordinate, then restore and L_i inverse.", + "CLEAR modes only after their final scatter. In inverse schedule original Y is first acquired using the actual source-contact inverse, before query." + ], + "schema": "full120-positive-E-structured-constructor/v1" +} diff --git a/research/full120-e8-lowrank-e-native/author/MODES120.json b/research/full120-e8-lowrank-e-native/author/MODES120.json new file mode 100644 index 0000000000..1d411bf557 --- /dev/null +++ b/research/full120-e8-lowrank-e-native/author/MODES120.json @@ -0,0 +1,114 @@ +{ + "base_E_and_inverse_all14400_entries": true, + "base_K_C_compatibility": true, + "base_local_module_paid": { + "2": 120, + "3": 120, + "5": 120, + "6": 120, + "9": 8 + }, + "base_recoder_replay_entries": 28800, + "global_C_eigenvalues": [ + "225/2", + "-1350" + ], + "global_E_eigenvalues_on_active": [ + "2/223", + "-1/1351" + ], + "global_dimension": 1728000, + "global_nonzero_modes": 22016, + "invoices": { + "base120": { + "axis_word_batches_per_direction": 1, + "ordinary_code_E_or_inverse": { + "ADD": 14564, + "CLEAR": 120, + "OWN_ZERO": 120, + "SCALE": 176, + "SWAP": 302, + "peak_scratch": 8, + "physical_L_field_map": 240 + }, + "original_ground_query_plus_scatter": { + "ADD": 28176, + "CLEAR": 8, + "COPY": 8, + "SCALE": 336, + "SWAP": 364, + "paid": { + "9": 8 + }, + "physical_L_field_map": 480 + }, + "owned_inverse_peak_upper": 136, + "query_or_transpose_upper": { + "ADD": 28184, + "CLEAR": 16, + "COPY": 8, + "OWN_ZERO": 8, + "SCALE": 336, + "SWAP": 364, + "paid": { + "9": 8 + }, + "physical_L_field_map": 480 + } + }, + "odd3": { + "axis_word_batches_per_direction": 43200, + "ordinary_code_E_or_inverse": { + "ADD": 739756800, + "CLEAR": 1728000, + "OWN_ZERO": 1728000, + "SCALE": 7279616, + "SWAP": 9590400, + "peak_scratch": 512, + "physical_L_field_map": 3456000 + }, + "original_ground_query_plus_scatter": { + "ADD": 1216879616, + "CLEAR": 22016, + "COPY": 22016, + "SCALE": 14515200, + "SWAP": 15724800, + "paid": { + "25": 22016 + }, + "physical_L_field_map": 6912000 + }, + "owned_inverse_peak_upper": 1750528, + "query_or_transpose_upper": { + "ADD": 1216901632, + "CLEAR": 44032, + "COPY": 22016, + "OWN_ZERO": 22016, + "SCALE": 14515200, + "SWAP": 15724800, + "paid": { + "25": 22016 + }, + "physical_L_field_map": 6912000 + } + } + }, + "kernel_science_sha256": "0b526f1a38a73a82ae66e1b0182ed2fa8c14e16d703cd38fff4dc491d3b7c15b", + "modal_inverse_sign_control_rejected": true, + "native_paid_per_local_module": { + "15": 1728000, + "16": 1728000, + "8": 1728000, + "9": 1728000 + }, + "negative_terminal": "UNKNOWN", + "original_ground_timing_control_rejected": true, + "query_paid_per_local_module": { + "25": 22016 + }, + "schema": "full120-E-modal-structured-proof/v1", + "scientific_payload_sha256": "2022a0164ebdb79d9cb76e363aaf5861afbb4a262f4a11a5feae94bc5e0d648a", + "scope": "Actual base native and512 native template pins, exact scalar recoder/mode proof, owned source checkpoint and small noncommuting-Q fulloperator fixture jointly compose this structured constructor. No1,728,000-by1,728,000 matrix or full3375 native phase stream is claimed expanded. 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"scope": "Exact complete small noncommuting-Q full operators, with original source acquisition, same paid profiles, owned lifecycle and absolute phase. Global all-port implementation uses separate actual root512 native checkpoint proof and rational spectral mode theorem. No negative E terminal decoding or complete caller claimed.", + "status": "PASS_LITERAL_BOTH_ORIENTATIONS_WITH_OWNED_SOURCE_CHECKPOINT" +} diff --git a/research/full120-e8-lowrank-e-native/author/PRECISION-SCOPE.md b/research/full120-e8-lowrank-e-native/author/PRECISION-SCOPE.md new file mode 100644 index 0000000000..362c237222 --- /dev/null +++ b/research/full120-e8-lowrank-e-native/author/PRECISION-SCOPE.md @@ -0,0 +1,69 @@ +# Field-l2 precision scope and ordinary work + +`precision120.py` replays every rational prefix of T,T^-1 and their actual +chronological linear transposes. For a matrix P, +||P||2^2 <= ||P||1 ||P||infinity. Max row-l1 times max column-l1 therefore +bounds every prefix. The120^2 batches within one selector axis act on +disjoint sets of fields, so their norm is the maximum block norm. After +three owner axes the largest squared bound over all four orientations is +14320735522816/15. The integer S=977096 bounds each full three-axis stack +and each of its prefixes. It is not raised to43200. + +Each physical L word, P/D/X/phase and positive Gaussian child is unitary +at every positive field width. Scalar owner coefficients act once. A +partial K output accumulation has absolute row and column sums at most7. +Keeping the unchanged mains and scratch together bounds its extended norm +by sqrt(1+7^2)<8. SWAP is unitary and CLEAR is contractive; completed +disjoint cubes have norm1. The same bound covers the reversed linear +adjoint. Ordinary zero scratch supplies no input error of its own. + +Use C=8*1351*S^2 for an E or Ei code and its linear adjoint. COPY of a +set of original coordinates has norm at most2, modal scatter has norm at +most1+max|lambda|=1351, and the gather/scatter recoders contribute S^4. +Thus Qbound=2*1351*S^4 bounds the query pair. Source contact snapshots have +norm at most2 as a set. The remaining native triangular ADD stage has +norm at most1+7=8, using absolute coefficient row and column sums, including +partial sums. Therefore16 covers native inverse contact acquisition and +its reverse transpose. Source/target halves can be separated by E code +and query because their factors2 and8 are applied to those separate passes. + +A uniform local module bound is M=16*C^2*Qbound <2^202. The three modules +and three positive ordinary exit codes are bounded by M^3*C^3 <2^764. +The four recoder orientations also bound reversed adjoint prefixes, hence +the corresponding suffix maps; COPY/CLEAR ownership is transposed exactly. +These are deliberately loose finite constants, with exact integers in +`PRECISION120.json`. + +If L primitive error injections each have l2 norm at most epsilon over +the collection of whole fields, final local l2 error is at most L*M*epsilon. +The bound is independent of positive address width. A per-coordinate +rounding convention can add a square-root dimension factor. This package +does not assert a fixed extra coordinate precision, storage bound, or +all-size Turing-machine closure; those require a separate allocation and +an admitted negative terminal. + +For the odd3 local module the conservative unified ordinary upper bill is: + +| operation | count | +|---|---:| +| ADD |2,829,471,232| +| SCALE |29,074,432| +| SWAP |34,905,600| +| P |39,744,000| +| D |39,744,000| +| X |34,560,000| +| phase |10,368,000| +| COPY |1,750,016| +| owned zero |5,206,016| +| CLEAR |6,956,032| + +This dominates both F and B orientations and keeps COPY/zero/CLEAR +separate from paid calls. The local paid bill is V each of H8,H9,H15,H16 +plus22016 H25, with V=120^3. The global inverse/forward owned peak is at +most V+22016+512=1,750,528 fields. Sequential three-stage reuse obeys the +same peak. The exact base120 primitive counts and smaller actual peaks +are in `MACROS120.json`; the global upper is a structured loop count. + +No owned field is counted as productive helper mass. No query is credited +below full H25 on the strength of modal support geometry. No conditional +budget margin is presented as a supplier, exponent, or scientific adoption. diff --git a/research/full120-e8-lowrank-e-native/author/PRECISION120.json b/research/full120-e8-lowrank-e-native/author/PRECISION120.json new file mode 100644 index 0000000000..077bfb96e9 --- /dev/null +++ b/research/full120-e8-lowrank-e-native/author/PRECISION120.json @@ -0,0 +1,86 @@ +{ + "K_partial_extended_stage_norm_bound": 8, + "actual_K_column_l1": "7", + "actual_K_row_l1": "7", + "actual_kernel_prefix_receipt_sha256": "37a49e5d31897b5b3a3b14382757f2afe29b59d4cd52a22df79054e266ca926b", + "code_prefix_suffix_norm_bound": "10318576939478528", + "error_ABI": "For any fixed emitted primitive word with L additive error injections, each of whole-field-collection l2 norm <=epsilon, output l2 error <=L*M*epsilon for a local module (or L*whole*epsilon for the N3 prefix). Paid Gaussian and signed address monomial operations are unitary at every positive width. Prefix/suffix bounds include linear adjoint orientations and owned zero/COPY/CLEAR.", + "local_module_prefix_suffix_norm_bound": "4195598123350366652959228020368364249142398869863956142358528", + "max_A_or_Ainverse_sector_scale": 1351, + "ordinary_E_or_inverse_code": { + "ADD": 739756800, + "CLEAR": 1728000, + "D": 3456000, + "OWN_ZERO": 1728000, + "P": 3456000, + "SCALE": 7279616, + "SWAP": 9590400 + }, + "ordinary_N3_plus_positive_exit_upper": { + "ADD": 10707684096, + "CLEAR": 26052096, + "COPY": 5250048, + "D": 129600000, + "OWN_ZERO": 20802048, + "P": 129600000, + "SCALE": 110790144, + "SWAP": 135216000, + "X": 103680000, + "phase": 31104000 + }, + "ordinary_local_module_upper": { + "ADD": 2829471232, + "CLEAR": 6956032, + "COPY": 1750016, + "D": 39744000, + "OWN_ZERO": 5206016, + "P": 39744000, + "SCALE": 29074432, + "SWAP": 34905600, + "X": 34560000, + "phase": 10368000 + }, + "ordinary_native_inverse_transpose_boundaries_upper": { + "ADD": 133056000, + "CLEAR": 3456000, + "COPY": 1728000, + "D": 25920000, + "OWN_ZERO": 1728000, + "P": 25920000, + "X": 34560000, + "phase": 10368000 + }, + "ordinary_normalizer_contract": "The odd3 actual constructor uses one ordinary P and one real D for each L or L inverse; the base120 normalizers can have one extra P, counted literally in MACROS120.", + "ordinary_query_or_adjoint_upper": { + "ADD": 1216901632, + "CLEAR": 44032, + "COPY": 22016, + "D": 6912000, + "OWN_ZERO": 22016, + "P": 6912000, + "SCALE": 14515200, + "SWAP": 15724800 + }, + "owned_local_and_N3_peak_upper": 1750528, + "paid_N3": { + "15": 5184000, + "16": 5184000, + "25": 66048, + "8": 5184000, + "9": 5184000 + }, + "query_gather_scatter_prefix_suffix_norm_bound": "2462829155624030016935616512", + "schema": "full120-positive-E-field-l2-and-ordinary-tariff/v1", + "scope": "Bounds are finite constants independent of positive address field width, measured in l2 of the collection of whole fields. Per-coordinate rounding can incur a square-root dimension factor and requires a separate precision allocation. No all-size TM/storage theorem, negative terminal decoding, target moment or exponent admission is claimed.", + "status": "PASS_FINITE_FIELD_L2_CONSTANTS_AND_STRUCTURED_INVOICE", + "strict_power_of_two_log2_upper": { + "N3_with_three_positive_exit_codes": 764, + "local_module": 202, + "ordinary_code": 54, + "query_pair": 91, + "three_axis_stack": 20 + }, + "three_axis_recoder_integer_norm_bound": 977096, + "three_axis_recoder_squared_bound": "14320735522816/15", + "three_modules_plus_three_positive_exit_codes_norm_bound": "81141133041756890830676282338769357372859981703386618959700866149464447236556963873826016155945436237186587569182988879143827605595679945966460024761976013937179110025345202902369242623848430396861038667044587222984681724579938304" +} diff --git a/research/full120-e8-lowrank-e-native/author/PROOF.md b/research/full120-e8-lowrank-e-native/author/PROOF.md new file mode 100644 index 0000000000..ac025f734a --- /dev/null +++ b/research/full120-e8-lowrank-e-native/author/PROOF.md @@ -0,0 +1,163 @@ +# Exact operator and construction proof + +Write Q for the common one-axis Gaussian, D for the fresh complement, +R=DQ, and use **H(T)=diag(T,Q^-1 T Q)**. Every actual physical L_i is a +real signed permutation commuting with R, including its absolute phase at +every positive field width. It need not commute with Q or D separately. +Scalar owner coefficients act once; physical address words tensor lift. + +## Scalar full120 data + +The pinned M has120 rows of squared norm4 and M^T M=60 I8. Put C=MM^T/4. +Thus C^2=15 C and rank C=8. The explicit15-cube partition supplies the +actual native scalar K with K^2=I, K^T=K, KM=-M, and KC=CK=-C. +For A=I-C, + +``` +E = K A^-1 = K + C/14, +Ei = E^-1 = K + C. +``` + +`modes120.py` checks all 14400 entries of both inverse products and of the +actual native K/C compatibility. For T=[M|N], the selected112 columns of N +are actual three-root kernel relations and the first8 rows of T^-1 are +M^T/60. The exact in-place words for T and T^-1 use 7042 ADD,84 SCALE and 91 +SWAP each, with no owned fields or paid Gaussian. The program replays both +words, checks both inverse matrices, and checks every kernel condition. + +E is executed as physical L normalization, T^-1, SCALE -1/14 on the first8 +coordinates, T, K, and L^-1. Ei replaces that scale with -14. These negative +modal scale signs differ from the positive E eigenvalue1/14. The actual +base macro independently replays every emitted elementary code operation +and K output-scratch operation in the common chart, all 14400 entries for +each code. The physical operator is consequently the block matrix +L_i^-1 E_ij L_j. This argument does not commute L_i through Q. + +For odd3 define, on the three distinct selector coordinates, + +``` +Cg = (C1 C2+C1 C3+C2 C3-C1 C2 C3)/2, +Kg = (K1+K2+K3-K1 K2 K3)/2. +``` + +Cg is zero on fewer than two modal coordinates. It has eigenvalue225/2 +on 21504 coordinates with two modal factors and eigenvalue-1350 on 512 +coordinates with three. On all these coordinates at least two K factors +are-1; hence Kg=-I there, Kg^2=I everywhere, and Kg Cg=-Cg. In particular, + +``` +Eg = Kg + (2/223) C_active2 - (1/1351) C_active3, +Eig = Kg + Cg. +``` + +The executable code uses A^-1 modal scales -2/223 and1/1351, or A modal +scales -223/2 and1351. The global physical chart is the actual pinned U25 +orthonormal basis of the raw27-bit equal-block-parity space. Recoding each +selector repeats the120-field elementary word for each of120^2 fixed +other selector pairs. This is43200 batches per direction, with no tensor +power of owner coefficients. Actual physical L_i are the normalized +q-tuple signed Clifford words of the pinned whole-family constructor. + +Kg has76 nonzero coefficients per row, with absolute row and column sums7. +It is applied in each actual 512-owner product cube by allocating512 zero +outputs, accumulating all76 terms per output, then swapping into mains +only after all original inputs have been read. Old main values now in +owned scratch are cleared. This scratch is reused between product cubes. +The base version uses the15 actual8-cubes, four terms per row, and 8 scratch. + +## Original-ground query and backward adapter + +The owned query reads original ground Y before any backward precode: +normalize L, recode T^-1 on selector axes, COPY all active coordinates, +restore T and L^-1, and pay one full R on each retained mode. To scatter +R C Y into X, normalize/recodify X, add each queried mode times its actual +eigenvalue, and restore. This gives exactly L^-1 T diag(lambda) R T^-1 L Y += R C_phys Y because L and the scalar owner code commute with R. + +No q-support span is used to discount these queries. There are 8 full H9 +queries at base and 22016 full H25 queries for odd3. Query fields are owned +temporaries and are cleared after their last scatter. The mode copy is +not counted as a productive original input or a helper contribution. + +The actual source-Y native companion is + +``` +B_K = [[D,-R K],[0,D]]. +``` + +Apply ordinary Ei to Y before B_K. Add -R C Y_original into native X, then +apply ordinary Ei to X. Since K Ei+C=I, the result is + +``` +WB = [[Ei D, -Ei R],[0,D Ei]] = H(Ei) B0. +``` + +The second diagonal entry is **D Ei**, not an assertion that H(Ei)'s +second bank is ordinary Ei: Q^-1 Ei Q D = Q^-1 Ei R = D Ei. We only use +[Ei,R]=0. Gathering after preY(Ei) would instead query C Ei Y=14 C Y at +base; this timing error is explicitly rejected. The same spectral +calculation separates the two nonzero global eigenvalues. + +## Actual source checkpoint, inverse and linear transpose + +The base and cube512 checkpoint compilers consume actual native B event +lists. All Y are source-only, with a single unchanged physical ADD +contact each. Each actual contact is read4 times at base or76 times in +the odd3 cube. Reverse the source-only unary Y pass, and at its contact +COPY that actual Y state into one owned cache. Continue the source inverse +until complete. Reverse X events using these cached contacts, then CLEAR +them after their final ADD read. No original source is assumed reusable +after its overwrite. The free noncommuting-operator replays prove both +inverse orders and the entire owned transpose on all 240/1024 rows. + +For the E inverse schedule, first precode X by E. Execute only that actual +native inverse Y pass with contact acquisition; Y now equals Ei times +original Y. Code Y by E to recover original ground Y. Gather/query this +original Y and scatter **+R C Y** into X. Finish the actual inverse X pass +using the retained native contacts, then clear contacts and mode fields. + +At the operator level this inverse is + +``` +WB^-1 = [[D^-1 E, Q E D^-1],[0,E D^-1]]. +``` + +All address primitives have an exact linear transpose: P transposes to its +inverse, D/X and every Gaussian child are symmetric, scalar phase is +unchanged. ADD swaps source/target with the same scalar. The adjoint of +owned CLEAR initializes a zero field; the adjoint of COPY adds the owned +field into the original source and clears the owned field. These are +linear transposes over complex numbers, not Hermitian adjoints. +Every inverse Gaussian child is implemented by its positive child followed +by the ordinary X mask, with absolute phase one at every width. + +Put J=diag(Q^2,I). The forward emitted boundary is + +``` +WF = diag(D^2,D^2) J (WB^-1)^T J^-1 + = [[E D,0],[D E Q^-1,D E]] = H(E) F0. +``` + +For the first diagonal block, D^2 Q^2 E D^-1 Q^-2=E D because E commutes +R^2. The other two blocks follow directly. Thus the forward word uses the +same paid profile as backward and includes all needed ordinary boundaries. +The small noncommuting-Q fixture independently verifies the full matrices, +all phases and owned lifecycles for all three actual spectral values. + +## Three fresh stages and the outstanding terminal + +Use three disjoint fresh complements and common Q in F/B/F order. Codes +from one stage commute with the other stages' fresh D operations. The +typed H bookkeeping gives the retained word E3 Ei2 E1. After the standard +signed swap and ordinary positive inverse code, the endpoints are + +``` +negative original X: Q^-1 (E3 Ei2 E1) D123, +positive original Y: D123 Q. +``` + +The global positive endpoint is a true H73. Ordinary inversion of the +negative code on its outside cannot be moved through Q. The actual small +64-column three-stage fixture rejects that invalid Gaussian endpoint. +The negative decoder is UNKNOWN, so the conditional two-half target grant +is not an actual caller admission. This package claims no new kappa. diff --git a/research/full120-e8-lowrank-e-native/author/README.md b/research/full120-e8-lowrank-e-native/author/README.md new file mode 100644 index 0000000000..e0d5f2dea0 --- /dev/null +++ b/research/full120-e8-lowrank-e-native/author/README.md @@ -0,0 +1,92 @@ +# Full120 positive E adapter + +This package constructs the positive E code, source-consuming low-rank +correction, inverse with actual native source checkpoints, and forward word +obtained by linear transposition for the new full120 E8 geometry. It is a +constructive component. The negative terminal decoder, complete supplier +admission, and any new kappa remain **UNKNOWN**. + +The literal n9 constructor acts on all 240 original base main fields and uses +the new 15-cube phase-complete native object. The odd3 constructor is an +explicit structured owner-loop proof with an actual 512-owner phase object; +the entire1,728,000-owner phase stream and a122880-square n9 address matrix +are not claimed expanded. + +## Reproduce + +Use Python3.10 or newer and the standard library only. All runtime inputs +are local to this package. From this directory run: + +``` +python3 -I -B e_adapter.py +python3 -I -B owned_e.py +python3 -I -B n3.py +python3 -I -B backward512.py +python3 -I -B checkpoint120.py --mode base120 +python3 -I -B checkpoint120.py --mode root512 +python3 -I -B modes120.py +python3 -I -B macros120.py +python3 -I -B precision120.py +``` + +Repeat with `-O` to verify that no scientific check relies on Python +assertions. The default commands compare exact recomputation with retained +receipts and do not rewrite science. `replay.py --write` runs both modes and +records command/output hashes in `REPLAY.json`; it writes transient logs to +a new directory outside the packet. `FILES.sha256` seals the payload. + +## Objects and checks + +* `MACROS120-PROGRAM.json.gz` contains actual primitive lists for backward, + inverse, inverse transpose, forward, E, and E inverse. Every address word, + ordinary phase and positive child is literal. `MACROS120.json` records + strict ownership/lifecycle checks and common-chart code replay of all + 14400 entries in both directions. Both local orientations pay exactly + 120 each of H2,H3,H5,H6 plus8 H9. The literal backward peak is16 owned + fields; inverse/forward peak is128. +* `BASE120-CHECKPOINT` and `ROOT512-CHECKPOINT` use the actual new native B + instructions. They verify left/right inverses and owned linear transpose + on all 240 and1024 independent field-operator rows with arbitrary + noncommuting unary operators. Every original source has one unchanged + physical contact, read4 or76 times; one owned snapshot retains it. +* `OWNED-E` propagates all 16 independent scalar-address input columns over + rational complex numbers, including absolute phases, for lambda15,225/2, + and-1350. Its controls reject missing queries, bad boundaries, missing + contacts, incorrect transpose signs and early CLEAR. +* `MODES120` independently replays the exact full120 modal/kernel word, + proves E and its inverse on all 14400 scalar entries, and specifies the + three-selector recoder, physical normalization, owned query and K scratch + construction. The actual odd3 rank is22016:21504 modes of eigenvalue225/2 + and 512 of eigenvalue-1350. Each module pays22016 full H25 queries. +* `N3` propagates all 64 original columns of a small three-fresh-stage + physical fixture. It verifies one Gaussian positive half after ordinary + inverse code and rejects the naive negative ordinary decoder. Its64 + columns are a fixture, not an enumeration of the global family. +* `PRECISION120` replays all four chronological orientations of the actual + owner recoder and supplies a complete conservative ordinary invoice and + finite whole-field l2 constants. See `PRECISION-SCOPE.md`. + +All owner coefficients are applied once to fields. Only address words +tensor lift with positive width. In particular, no owner-space tensor +power, packed query discount, or productive-helper credit is used. + +## Provenance + +The new base native canonical science is +`87d7cad7133ed0a2950b1d4fa2397e20e3c7bcedb90db95a15130aa03da543ae`. +The new odd3 cube512 native canonical science is +`1aeba5ae2276ff58e24ed9ca84f08830c0bb7321432bc74e42472f0029bfb1c2`. +The full120 triangle-kernel recoder canonical science is +`0b526f1a38a73a82ae66e1b0182ed2fa8c14e16d703cd38fff4dc491d3b7c15b`. +These objects and their actual required inputs are copied locally. + +The native source/phase construction comes from the three sealed full120 +geometry/native/family packages. `e_adapter.py`, `owned_e.py`, `n3.py`, and +`checkpoint120.py` adapt the retained E-native-author source protocol to +the new eigenvalues and actual native objects. `backward512.py` adapts the +retained inverse-transpose backward companion. The new modal word and its +prefix supplement are by joint_native_review; the supplement is a second +check by the same basis author, without an author-independence claim. + +No source package was modified. No external priority, scientific adoption, +outer-caller admission, or exponent improvement is asserted here. diff --git a/research/full120-e8-lowrank-e-native/author/REPLAY.json b/research/full120-e8-lowrank-e-native/author/REPLAY.json new file mode 100644 index 0000000000..ed36713d8a --- /dev/null +++ b/research/full120-e8-lowrank-e-native/author/REPLAY.json @@ -0,0 +1,223 @@ +{ + "cases": [ + { + "command": [ + "python3", + "-I", + "-B", + "e_adapter.py" + ], + "returncode": 0, + "stderr_sha256": "e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855", + "stdout_sha256": "8d9e7e03b979a0351c07302aaeb5c1ca1cc557f7dad0b8896935be02dd34e254" + }, + { + "command": [ + "python3", + "-O", + "-I", + "-B", + "e_adapter.py" + ], + "returncode": 0, + "stderr_sha256": "e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855", + "stdout_sha256": "8d9e7e03b979a0351c07302aaeb5c1ca1cc557f7dad0b8896935be02dd34e254" + }, + { + "command": [ + "python3", + "-I", + "-B", + 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mul_i(a,b,p):return[(a,b),(-b,a),(-a,-b),(b,-a)][p%4] +def qvalue(alpha,S,x): + value=0 + while x: + bit=x&-x;j=bit.bit_length()-1;x^=bit;value+=alpha[j]+2*parity(S[j]&x) + return value%4 +def support_map(B,x): + out=0 + while x: + bit=x&-x;out^=B[bit.bit_length()-1];x^=bit + return out +def echelon(B): + piv={} + for j,col in enumerate(B): + x=col;word=1<=0 and 0<=basis<1<>i)&1)==self.alpha[i]%2 for i in range(r)),'quadratic diagonal equals linear parity') + need(all(((self.S[i]>>j)&1)==((self.S[j]>>i)&1)for i in range(r)for j in range(i)),'symmetric binary quadratic form') + need((self.ar*self.ar+self.ai*self.ai)*(1<>j)&1)==((S[j]>>i)&1)for i in range(self.n)for j in range(i))and all(alpha[i]%2==((S[i]>>i)&1)for i in range(self.n)),'Clifford diagonal polynomial') + const,a,T=pullback(alpha,S,self.b,self.B);self.phase(const);self.alpha=[(x+y)%4 for x,y in zip(self.alpha,a)];self.S=[x^y for x,y in zip(self.S,T)] + else: + need(kind=='C'and isinstance(e[2],int)and e[2]in[-1,1]and isinstance(e[1],int)and 0<=e[1]<1<>j)&1))%4 for j,a in enumerate(self.alpha)];self.S=[row^(h if h>>j&1 else 0)for j,row in enumerate(self.S)];self.stats['C_same']+=1 + else: + need(h!=0,'odd derivative has nonzero support constraint');eta=((s-delta)//2)%2;p=(h&-h).bit_length()-1;y0=(1<>j&1 else 0)for j in range(r)if j!=p];const,a,T=pullback(self.alpha,self.S,y0,cols) + self.b^=support_map(self.B,y0);self.B=[support_map(self.B,c)for c in cols];self.alpha=a;self.S=T;self.phase(const);self.scalar(1,s);self.stats['C_drop']+=1 + self.peak_rank=max(self.peak_rank,self.rank);self.validate();return self + def amplitude(self,x): + need(0<=x<1<>k&1:a,b=piv[k];x^=a;y^=b + a,b=mul_i(self.ar,self.ai,qvalue(self.alpha,self.S,y));r=self.rank;t=F(1,1<<((r+1)//2));alpha=(t,t if r&1 else F());actual=(F(a,1<>i)&1)<>j&1);a[j],a[k]=a[k],a[j] + for i in range(n): + if i!=j and a[i]>>j&1:a[i]^=a[j] + assert [r&((1<>n for r in a) +def basis_extend(cols,n): + out=[] + for x in list(cols)+[1<len(out):out.append(x) + assert len(out)==n + return tuple(out) +def nullspace(rows,n): + a=list(rows);p=[];k=0 + for j in range(n): + t=next((i for i in range(k,len(a)) if a[i]>>j&1),None) + if t is None:continue + a[t],a[k]=a[k],a[t] + for i in range(len(a)): + if i!=k and a[i]>>j&1:a[i]^=a[k] + p.append(j);k+=1 + return tuple((1<>j)&1)<>i&1:out=pmul(out,T[i]) + for i in range(n): + if z>>i&1:out=pmul(out,T[n+i]) + return out +def compose(A,B):return tuple(apply(A,p) for p in B) +def inverse(T): + n=len(T)//2;cols=[x|(z<>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4)) + return tuple(out) +def qvalue(Q,alpha,x,n): + return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4 +def mul_i(a,p): + x,y=a;p%=4 + return [(x,y),(-y,x),(-x,-y),(y,-x)][p] +@dataclass +class Op: + n:int + tab:tuple + circuit:list + def then(self,b): + assert self.n==b.n + return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit) + def adjoint(self): + circ=[] + for e in reversed(self.circuit): + if e[0]=='P':circ.append(('P',inv(e[1],self.n))) + elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2]))) + elif e[0]=='C':circ.append(('C',e[1],-e[2])) + elif e[0]=='phase':circ.append(('phase',(-e[1])%4)) + else:circ.append(e) + return Op(self.n,inverse(self.tab),circ) + def zero_state(self,basis=0): + N=1<>i)&1 for i in range(n)) + assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n)) + return Op(n,tuple([(1<>i&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>i)&1)) for i in range(n)]),[('X',b)]) +def fourier(n,axes=None): + out=ident(n) + for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<len(selected):picks.append(j);selected.append(x) + assert len(picks)==r and all(x>>r==0 for x in Bcols) + Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<0 else'NEGATIVE_EVEN_WITH_ZERO_EXTRA_DECODER_COST'} + if L>0: + lo,hi=3*L/rho,3*U/rho;rec['whole_N3_H1_allowance_per_mode']=m.rounded((lo,hi));a,b=m.power(n);rec['full_Hn_query_integer_allowance_per_mode']=(lo/b).__floor__();m.need(hi/a Date: Sun, 25 Oct 2026 19:11:55 +0800 Subject: [PATCH 6/6] Construct full120 source-consuming E adapters with exact native checkpoints --- .../AUTHOR-SOURCES.json | 18 + .../full120-e8-lowrank-e-native/FROZEN.json | 284 ++ research/full120-e8-lowrank-e-native/LICENSE | 201 ++ .../full120-e8-lowrank-e-native/README.md | 90 + .../full120-e8-lowrank-e-native/SOURCES.json | 103 + .../full120-e8-lowrank-e-native/TASK.json | 80 + .../full120-e8-lowrank-e-native/VERIFY.json | 67 + .../author/BASE120-CHECKPOINT-PROGRAM.json.gz | Bin 0 -> 296954 bytes .../author/BASE120-CHECKPOINT.json | 34 + .../author/E-ADAPTER.json | 72 + .../author/FILES.sha256 | 45 + .../author/MACROS120-PROGRAM.json.gz | Bin 0 -> 1371124 bytes .../author/MACROS120.json | 150 + .../author/MODES120-PROGRAM.json | 234 ++ .../author/MODES120.json | 114 + .../author/N3-PROGRAM.json | 986 ++++++ .../author/N3.json | 34 + .../author/OWNED-E-PROGRAM.json | 3095 +++++++++++++++++ .../author/OWNED-E.json | 230 ++ .../author/PRECISION-SCOPE.md | 69 + .../author/PRECISION120.json | 86 + .../author/PROOF.md | 163 + .../author/README.md | 92 + .../author/REPLAY.json | 223 ++ .../author/ROOT512-CHECKPOINT-PROGRAM.json.gz | Bin 0 -> 2008213 bytes .../author/ROOT512-CHECKPOINT.json | 34 + .../author/backward512.py | 144 + .../author/checkpoint120.py | 163 + .../author/e_adapter.py | 102 + .../author/inputs/B-MODULE.json | 30 + .../author/inputs/B-PROGRAM.json.gz | Bin 0 -> 836583 bytes .../author/inputs/COVER.json | 1 + .../author/inputs/K-MODULE.json | 73 + .../author/inputs/K-PROGRAM.json.gz | Bin 0 -> 1328463 bytes .../author/inputs/K-TEMPLATE.json | 1637 +++++++++ .../author/inputs/KERNEL-PROGRAM.json.gz | Bin 0 -> 53970 bytes .../author/inputs/KERNEL-RESULT.json | 44 + 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This package +constructs both E orientations, using actual original ground source queries, +native source checkpoints and a genuine owned inverse/linear transpose. It +is a positive component, with no full negative decoder, complete Gaussian +supplier, new kappa or scientific promotion claim. + +At base120, C=MM^T/4 has rank8 and eigenvalue15, K^2=I, KC=-C, and +E=K+C/14, E_inverse=K+C. On Q=C0, D=C_[1,9), R=DQ, use +H(T)=diag(T,Q^-1 T Q). The emitted physical contracts are + +``` +WF = [[E D,0],[D E Q^-1,D E]] = H(E) F0 +WB = [[E_inverse D,-E_inverse R],[0,D E_inverse]] = H(E_inverse) B0 +paid per direction: H2/H3/H5/H6 each120, H9 eight times +``` + +All240 base mains are arbitrary independent original fields. The backward +mode gather precedes preY; inverse finishes the actual source-only inverse +pass and retains real common-frame contacts before querying its recovered +ground Y. Forward transposes that owned inverse with explicit COPY/CLEAR +dual rules and ordinary boundaries. No unavailable query on Q^-1 X is granted. +The emitted ordinary codes replay all14400 common-chart coefficients each; +actual native checkpoints and transpose are checked on all240 operator rows. +The complete physical address matrix is not expanded. + +For odd3, V=120^3=1728000 and h=22016. C eigenvalues are225/2 on21504 +modes and-1350 on512. Each local orientation pays V each of H8,H9,H15,H16 +and h full H25. The 120-owner in-place recoder has7042ADD,84SCALE,91SWAP +each way, repeated on disjoint selector-axis batches. Actual primitive K +uses reused512-owner output scratch. The constructor is an explicit +structured loop over all owners with a pinned actual512 native template; +no global dense matrix or all3375 literal native streams are claimed. + +The local unified ordinary upper includes2829471232ADD,29074432SCALE, +34905600SWAP, and all address operations/owned allocations in +author/PRECISION-SCOPE.md. Owned peak is at most V+h+512=1750528. +Four chronological recoder orientations yield finite whole-field-l2 macro +bounds, less than2^202 locally and2^764 for N3 plus positive exits. The +review corrects one prose estimate: arbitrary scratch error requires the +full shear bound1+7=8; the author's existing constant8 and all final bounds +remain valid. Exact SWAP and completed paid Gaussian calls are macro +interfaces; their recursive/microcode prefixes and coordinate rounding +allocation are not proved by these constants. + +The root peer imports no author script. It interprets every actual macro +primitive on six selected original inputs (old0 and new112,119 in both +banks), both F/B orientations and all four tensor-width phase residues, +checking all240 returned fields each time:3960 nonzero and7560 zero blocks. +It shares the pinned Clifford primitive and uses a separate polynomial +affine-support phase backend. The peer is not an all240-column or n25 +reconstruction. Separate review checks precision factors and the ordinary +invoice. These are AI-worker reviews, not independent human or kernel +acceptance. Owner scalar coefficients act once; only address words tensor lift. + +F1,B2,F3 has negative endpoint Q^-1 E3 E2^-1 E1 D123. The positive half +admits its ordinary inverse code to H73. The negative half remains UNKNOWN. +The earlier full120 conditional budget and12.6% density reduction are not +productive target credit. Existing ordinary-decoder obstructions and +pre-return-source predecessors remain credited. + +## Open next questions + +Can the actual negative bank yield independent Gaussian outputs with a +profitable paid decoder or changed caller inventory, including its K bulk? +Can the completed caller then admit coordinate precision, recursive child +errors, ordinary compilation, routing and storage? TASK.json gives the +concrete first steps and limits. These obligations remain unresolved. + +``` +python3.12 -B scripts/research_package.py --package research/full120-e8-lowrank-e-native +python3.12 -B scripts/check_research_commit.py --package research/full120-e8-lowrank-e-native +``` + +Python3.12 standard library suffices. Hooks run serially, normally and-O, +compare canonical decompressed scientific programs and enforce frozen bytes +before/after. author/ and peer/ are verbatim sealed closures; review/ is a +separate verbatim qualification. portable_review.py changes only its author +directory and normalizes the descriptive receipt path/digest back to the +original value for exact comparison. README discovery paths in retained source packages +are provenance, not runtime dependencies. + +Credit Ali Romman; Dugongue and Dillon Amburgey; Cao Yifan; Cinna Davis, zxv, +Jacob Alan Sussman; the retained Clifford/native/frame/compiler/analytic +lineage. The new full120 geometry, triangle-kernel recoder and phased native +objects are attributed in source proofs and seals. Prepared for THU New Media +Research Center (@thu-nmrc) with substantial OpenAI Codex assistance. +Apache-2.0; retained input notices apply. No exhaustive novelty/priority, +full outer admission, formal scientific adoption or new exponent is asserted. diff --git a/research/full120-e8-lowrank-e-native/SOURCES.json b/research/full120-e8-lowrank-e-native/SOURCES.json new file mode 100644 index 0000000000..75c80aae18 --- /dev/null +++ b/research/full120-e8-lowrank-e-native/SOURCES.json @@ -0,0 +1,103 @@ +{ + "base_commit": "32890bc5de034ab8fc93ac88ead7279a6a416d04", + "files": [ + { + "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602", + "path": "docs/research/agent-task-catalog.json", + "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72", + "usage": "provenance" + }, + { + "git_blob": "fc3d4ba105e1f097d0d7d051a308281e86ab1446", + "path": "certificates/selected-result.json", + "sha256": "66974efdced4083c00025f97d95d83909a226cdf801edb9301c195c6641f6903", + "usage": "provenance" + }, + { + "git_blob": "bca92c222c395d3d75c047fbb678f3cd0947c60f", + "path": "research/coded-native-caller/NORMALIZERS.json", + "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da", + "usage": "provenance" + }, + { + "git_blob": "166841a037f069249f6f7f6dedb89248812f59e2", + "path": "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py", + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "usage": "provenance" + }, + { + "git_blob": "7ec1c59b7daf19e5215e384fcb9055a497efe3ee", + "path": "research/odd-e8-whole-k-native/frame_tools.py", + "pin": "head:56ba6d7d609124d71c067d6a380caed573963f8f:research/odd-e8-whole-k-native/frame_tools.py", + "sha256": "e5b2ea1f60d554b3a285569602360c663ee8b387350424678b3bd0b0b5432bf4", + "usage": "provenance" + }, + { + "git_blob": "51c529874305069e2ca5f77888cd7610ec6ea165", + "path": "research/odd-e8-whole-k-native/geometry_tools.py", + "pin": "head:56ba6d7d609124d71c067d6a380caed573963f8f:research/odd-e8-whole-k-native/geometry_tools.py", + "sha256": "208d02ef131d0aad635bcb35e3db196fd3298fd5d4fbfbc7fadc672c81ca8261", + "usage": "provenance" + }, + { + "git_blob": "9d190e7b48e376ade8898a04cc9e1ae191e4e5d1", + "path": "research/odd-e8-whole-k-native/core.py", + "pin": "head:56ba6d7d609124d71c067d6a380caed573963f8f:research/odd-e8-whole-k-native/core.py", + "sha256": "482149e6efd593835c084d8e7552c70e4724d6aa6d643dc77c79dda03a1c57df", + "usage": "provenance" + }, + { + "git_blob": "bb41b66f667dc253bde49e6085a4b780240a533c", + "path": "research/odd-e8-lowrank-e-native/e_adapter.py", + "pin": "head:dcd9a877364dfe62ccdc154584574c048cac0deb:research/odd-e8-lowrank-e-native/e_adapter.py", + "sha256": "fd01fcd33e0915b32bfa75d53be5ddf10982391327f40dde3001b45d3a54107f", + "usage": "provenance" + }, + { + "git_blob": "f6b12f6245cc8150e220c2ef971a6c4d481d4aa1", + "path": "research/odd-e8-lowrank-e-native/owned_e.py", + "pin": "head:dcd9a877364dfe62ccdc154584574c048cac0deb:research/odd-e8-lowrank-e-native/owned_e.py", + "sha256": "8f6e04abb73904833d821968627f97021829354f77c4a8f1f872d2d71cfce17a", + "usage": "provenance" + }, + { + "git_blob": "5e705e1252de0798305a3b17068473b86dfbebec", + "path": "research/odd-e8-lowrank-e-native/n3.py", + "pin": "head:dcd9a877364dfe62ccdc154584574c048cac0deb:research/odd-e8-lowrank-e-native/n3.py", + "sha256": "454d1ac01ef00b79814e25287e5f3ad38fce0c5a1320659086f4ae0363d35ce2", + "usage": "provenance" + }, + { + "git_blob": "be1fb7b0acf616a85c8de1aa363529aef82abfc2", + "path": "research/odd-e8-lowrank-e-native/checkpoint.py", + "pin": "head:dcd9a877364dfe62ccdc154584574c048cac0deb:research/odd-e8-lowrank-e-native/checkpoint.py", + "sha256": "8b27e2553ab9cd5a0467c488b3c9bb72c0997d756f70736f0f01ff72a9591582", + "usage": "provenance" + }, + { + "git_blob": "8bb9b56b8d716f1e390bf558b495a8f94598ab61", + "path": "research/full120-e8-native/components/full-e8-native120-20261025-structural/NATIVE120-NATIVE-PROGRAM.json.gz", + "pin": "head:dcd9a877364dfe62ccdc154584574c048cac0deb:research/full120-e8-native/components/full-e8-native120-20261025-structural/NATIVE120-NATIVE-PROGRAM.json.gz", + "sha256": "594bd83ddfc834cc030acb2670ec3d6dd405e5e87edfda33156be40518fc7706", + "usage": "provenance" + }, + { + "git_blob": "10f7c1a513ec0de91821b51585623e086874919d", + "path": "research/full120-e8-native/components/full-e8-odd3-native120-20261025-structural/K-PROGRAM.json.gz", + "pin": "head:dcd9a877364dfe62ccdc154584574c048cac0deb:research/full120-e8-native/components/full-e8-odd3-native120-20261025-structural/K-PROGRAM.json.gz", + "sha256": "696c02bc2aefa0cd0dd0c92d40e0e821d9ae7c4e7798182a2c53861098d70fec", + "usage": "provenance" + } + ], + "local_author_sources": "AUTHOR-SOURCES.json", + "peer_scope": "Root peer independently interprets full n9 F/B literal macros on six original columns, both orientations and four tensor phase residues; no author imports, shared exact Clifford primitive and separate affine phase oracle. Review independently audits precision/tariff arithmetic; neither is human/kernel acceptance.", + "predecessors": { + "geometry": "Ali Romman #5439 oddE8 geometry; retained P112/E8 native/controller/compiler lineage.", + "native_phase": "Earlier wholeK and polarized frame/compiler implementations in ancestor #5464 head56ba6d7d609124d71c067d6a380caed573963f8f, adapted for explicit15cube partitions.", + "new_constructive_work": "Full120 root completion; exhaustive Weyl cube orbit and actual15cube cover; new8 phase normalizers; emitted240-input F/B native;3375cube geometry and n25 root512 native instance.", + "peer": "Separate AI-worker interpreter imports no author scripts; shared exact Clifford primitives and locally developed affine-support phase backend are explicitly retained. Not independent human or proof-kernel review." + }, + "runtime_policy": "All scripts, scientific programs and inputs are local vendored files. No sibling checkout, /tmp origin, network or Git is required to execute registered hooks.", + "schema_version": 1, + "scope": "Full120 source-consuming E components and scoped physical/precision reviews. No full negative Gaussian supplier or frontier promotion." +} diff --git a/research/full120-e8-lowrank-e-native/TASK.json b/research/full120-e8-lowrank-e-native/TASK.json new file mode 100644 index 0000000000..2c12c3feea --- /dev/null +++ b/research/full120-e8-lowrank-e-native/TASK.json @@ -0,0 +1,80 @@ +{ + "actual_scope": "Construct full120 physical E and inverse ordinary codes, source-consuming full-R correction, actual native checkpoint inverse and linear-transpose forward; explicit structured odd3 owner loops and paid/ordinary invoices.", + "ai_assistance": "Substantial OpenAI Codex assistance by a lead and separate geometry, physical-compiler and independent-review agents. This is not independent human or formal-kernel review.", + "author": "THU New Media Research Center (@thu-nmrc)", + "base_commit": "32890bc5de034ab8fc93ac88ead7279a6a416d04", + "bottleneck_link": "Completes the explicit E-mode integration left open by the full120 native K component. A full negative decoder and complete outer admission still remain.", + "budget_minutes": 60, + "evidence": "author/PROOF.md; author/MACROS120-PROGRAM.json.gz; author/MODES120-PROGRAM.json; author/PRECISION-SCOPE.md; peer/NOTE.md; review/REVIEW.md.", + "open_questions": [ + { + "blocked_by": "This package supplies neither that decoder nor a changed profitable target inventory.", + "first_step": "Emit a source-aware paid decoder with complete owned lifecycles and all-width phases on actual geometry. Removing only E defects while leaving K coding is insufficient.", + "question": "Can the actual returned negative E word be converted into independent Gaussian jobs with a favorable full invoice?", + "why_it_matters": "Only the positive three-stage half is decoded to trueH73." + }, + { + "blocked_by": "Whole-field macro l2 bounds do not implement coordinate/recursive Turing-machine admission.", + "first_step": "Bind actual macro/child interfaces and coordinate record/error schedules to the full terminal inventory, with exact storage/ordinary costs.", + "question": "Can coordinate rounding, recursive child allocation, storage and ordinary compiler costs be admitted for the completed caller?", + "why_it_matters": "No global precision or exponent theorem follows from finite macro norms." + } + ], + "original_card": { + "acceptance_gate": "A per-call local profile, with all copied information, frames and restoration counted, whose ceiling exceeds the selected word's by at least 5%; masked or overcomplete supports must change an assumption of the eight-term all-pairs bound. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "allowed_variations": [ + "One masked, overcomplete or block decoder family with exact labels and supports.", + "A scoped lower bound on effective rank for one alphabet.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "bottleneck_link": "Rank-1 children are about half of recursive cost; the selected word's effective child rank is about 3.9. Larger-rank delivery lowers recursive cost per unit of paid mass.", + "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin. Ideal budget: rank-16 delivery is 2.31x (levers.py).", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "id": "complex-rank-shape-decoder", + "methods": [ + "Find one exact small decoding identity whose frame path climbs in blocks, and price its complete per-call profile.", + "Bound the best effective child rank achievable for one fixed support alphabet, including copies, frames and restoration." + ], + "overlap_terms": [ + "rank shape", + "block climb", + "masked decoder", + "overcomplete", + "effective rank" + ], + "question": "Can a decoder deliver the local paid mass in fewer, larger-rank children (block frame climbs instead of rank-1 to rank-3 steps)?", + "scope_change_triggers": [ + "Repacking idle remainders of an unchanged word (covered by the packing ceiling).", + "Repeating the eight-term all-pairs search inside its proved scope.", + "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.", + "Searching below C=40 in the #2017 Eisenstein binary scalar-rectangle or fixed-support block-linear additive pairing model; specify a changed premise instead. This bound does not cover every complex decoder.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/complex-decoder-field-extension-seed44/README.md", + "research/complex-frame-pair-decoders/README.md", + "research/selected-k8-unrestricted-ends/README.md", + "research/eisenstein-reduction-copy-floor/README.md" + ] + }, + "outcome": "partial", + "priority_revision": 7, + "schema_version": 1, + "scope_change_reason": "Instantiate the new full120 spectrum and actual native objects, preserving original source versions, with newly emitted base240-main E macros and structured global22016-mode construction.", + "scope_status": "changed", + "stop_rule": "Freeze positive E components. Next frontier expansion must construct and price a full paid negative decoder or genuinely changed caller/target inventory, including K bulk, all input versions and outer costs. No conditional fullH73 grant is productive credit.", + "task_id": "complex-rank-shape-decoder", + "terminal_changed_premise_gate": "A pre-Q native readout, a fully priced same-stage/nonfitting E code, paid Gaussian correction, or changed caller/target/cohort protocol; terminal-only fixed finite ordinary decoding of the proper-K endpoint is excluded only in the theorem grammar.", + "terminal_scope_extension": "Existing properK and actualE ordinary-decoder obstructions are credited; this construction does not contradict them. Paid/changed producer mechanisms remain open." +} diff --git a/research/full120-e8-lowrank-e-native/VERIFY.json b/research/full120-e8-lowrank-e-native/VERIFY.json new file mode 100644 index 0000000000..7d21402eb4 --- /dev/null +++ b/research/full120-e8-lowrank-e-native/VERIFY.json @@ -0,0 +1,67 @@ +{ + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/run.py", + "--part", + "author" + ], + "checks": "Serial source science replay plus locked inventories.", + "timeout_seconds": 450 + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-W", + "error", + "-B", + "{package}/run.py", + "--part", + "author" + ], + "checks": "Serial source science replay plus locked inventories.", + "timeout_seconds": 450 + }, + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/run.py", + "--part", + "peer" + ], + "checks": "Separate physical literal F/B selected columns, all4 width phase residues, plus scoped precision/tariff review.", + "timeout_seconds": 120 + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-W", + "error", + "-B", + "{package}/run.py", + "--part", + "peer" + ], + "checks": "Separate physical literal F/B selected columns, all4 width phase residues, plus scoped precision/tariff review.", + "timeout_seconds": 120 + } + ], + "inputs": [], + "python": "3.12", + "requirements": [], + "schema_version": 1, + "status": "ready" +} diff --git a/research/full120-e8-lowrank-e-native/author/BASE120-CHECKPOINT-PROGRAM.json.gz b/research/full120-e8-lowrank-e-native/author/BASE120-CHECKPOINT-PROGRAM.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..8f79e18d83b82dc1b2b4044bf0368dad777c6d99 GIT binary patch literal 296954 zcmV)fK&8JQiwFP!000026YRZRkK{M9=J!4i^6I{zYbM+&QXNcXd^E8H=2e)ZNupnfWIpo_HRT@$kQW-T&qLpTAq* z|7HL1^Y=gg@b$Oto3Hmj?;n2o`Ri~0+t<H8nn z*WZ5qAO7S2{2%|rzyF8->FaO4{;xm&Fm;Nwy*!6Z~pdvzx>pH`1!9te!+MC@u%|${w93$ z@;C4&`|Gd2eD}Y6_m}T~`1NP``v3U<-toKdfB5;ApMIUcFbDj8?SJ|D+rTG^;V}c( z8Axw11MM;ck12RJ1ybH(4&F_|hi0LVpMU)GufOc?zF(l$_rLrr!|-pv>;JNU{y+as z{OW)B>iYYye)-e>;j91r-39Ib(trM^Z@&7k-~aNbum1X{{`3B7|4X00{P|zM`tgVT zRsZEH@b9O83>v=*h-VEjqy=_Sq?PFptGX=BWs_=cQpg{3`I*+C_Y z!)v{Zf&cUm|Nh^7_n-dZfBPT#5@GWFFW>+3{%-#1`#-PCb2EwQoBWM_Q@*L+7(-1s z{nOXqmXAf)Zx5Z9NQq)2@~L>*#b-&Wngv;X$9W|0WR^sA~H6RLOXWFa$ZK&RV(VE64?4*S_D$&)})}~BK z%9ge?pA@2_Dj8-uTd>rl zO%;t={IAO{v(J->z@vGbwS!40OLl!f9FIxtjM6H-<`&zk*29o;7`lD<(NKDdeOEhX zCGQZ@iE+=tFDfy9Ryh7`(DhR@5HQ`UJ4-Ap93z%CkD^(Ip5bY7=03qXICQj*8pz2$ z$Ed)p`^fRQ$uMv2nc zi_N2QmOPn)(!u#tdYLg%!Df{+a+_jjkej^C*}IOjbo#-DXbG<%rTBoREGQ!9N@aZ&NCLrx3LHVuz+Z2v65mIPou(1U z{J^5zOrQZ^>^<%{K*GM9m#maS8CvstZ>wk$@!(yHOyqe0 zbLwjV)vT;FHNw{dG<1%zXV{dAaj41fKXNIFDv<~w2gfOCF@|9-iUZuM7Ll>j&UrxA zBCksj2ZpWoI1|Ob-xnO)Gr;j_eiG|}Zb<66uLS%xcn7@elmvt8Ak{kMs9h3dfcSv` zkg3h;+2nA05*$}+0kS4_#+r8Tb!Homf6yA4ty>6X+AJ-3X$r8FvYU<>hlIFKdmV6; 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z;nGuJseAy_60qHL6m4%Jbbu+Y(9V&@-XQzOyrMF)Oa~Bz1|WN79D6rPxx4%=A(RIJA+c0 zce_$?)hH#W7B3onTw9vb{P7(NeDgz!mX?7aG(V|gFYZP-imB5*`nirp)QKJo87zc! zD~*cyA3qQh3OqBQ2&Vr(v3KVvckAg-dG~?PKL4krfQbM$6oQo_Mf9MZa-&WpEUXZ= zR~kzPTLyTCX#6Tk&o$=V`JXe!RR1(E=hos4{qB48$7g_|DR!J+0OuhRruPKu)sEWi6>}d&Gt-dE9@1h|KaD3W}>?~B7?Gln^o`#-QYG17ob4x z!SSLO^f$nWP8|FR1?&kuK)xzXgGYh%rW|lvN>T*De64OUN|ppF25z>Y15|{v7Z>oU z6_fA=5nU&r225~eascL{PB~UW$U8*AIkI5H1~Wd35Br8>{ta^=2}>X!Jua}iPX6++ z7S;4e@f%kG=HjAZ)zFk{B?3U@4%**3>2uiOd5axIJ+W%zx7>i)&1)<>j&1);a[j],a[k]=a[k],a[j] + for i in range(n): + if i!=j and a[i]>>j&1:a[i]^=a[j] + assert [r&((1<>n for r in a) +def basis_extend(cols,n): + out=[] + for x in list(cols)+[1<len(out):out.append(x) + assert len(out)==n + return tuple(out) +def nullspace(rows,n): + a=list(rows);p=[];k=0 + for j in range(n): + t=next((i for i in range(k,len(a)) if a[i]>>j&1),None) + if t is None:continue + a[t],a[k]=a[k],a[t] + for i in range(len(a)): + if i!=k and a[i]>>j&1:a[i]^=a[k] + p.append(j);k+=1 + return tuple((1<>j)&1)<>i&1:out=pmul(out,T[i]) + for i in range(n): + if z>>i&1:out=pmul(out,T[n+i]) + return out +def compose(A,B):return tuple(apply(A,p) for p in B) +def inverse(T): + n=len(T)//2;cols=[x|(z<>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4)) + return tuple(out) +def qvalue(Q,alpha,x,n): + return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4 +def mul_i(a,p): + x,y=a;p%=4 + return [(x,y),(-y,x),(-x,-y),(y,-x)][p] +@dataclass +class Op: + n:int + tab:tuple + circuit:list + def then(self,b): + assert self.n==b.n + return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit) + def adjoint(self): + circ=[] + for e in reversed(self.circuit): + if e[0]=='P':circ.append(('P',inv(e[1],self.n))) + elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2]))) + elif e[0]=='C':circ.append(('C',e[1],-e[2])) + elif e[0]=='phase':circ.append(('phase',(-e[1])%4)) + else:circ.append(e) + return Op(self.n,inverse(self.tab),circ) + def zero_state(self,basis=0): + N=1<>i)&1 for i in range(n)) + assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n)) + return Op(n,tuple([(1<>i&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>i)&1)) for i in range(n)]),[('X',b)]) +def fourier(n,axes=None): + out=ident(n) + for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<len(selected):picks.append(j);selected.append(x) + assert len(picks)==r and all(x>>r==0 for x in Bcols) + Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<>(9*j))&511).bit_count()%2 for j in range(3)})==1 for x in orth),'every chart generator lies in equal-block-parity U25') + characteristic=0 + for x in orth:characteristic^=x + need(characteristic==(1<<27)-1,'U25 characteristic equals raw allones') + raw=(HERE/'inputs/NORMALIZERS.json').read_bytes();need(hashlib.sha256(raw).hexdigest()==PIN,'exact frozen root/mode inputs');d=json.loads(raw);need(all(dot(p['q'],p['q'])==1 and p['q']!=511 for p in d['ports']),'all112 base labels normone noncharacteristic');M=[list(map(F,r))for r in zip(*d['mode_columns'])];n=112 + need(len(M)==112 and all(sum(M[i][a]*M[i][b]for i in range(n))==(56 if a==b else 0)for a,b in product(range(8),repeat=2)),'actual M^T M=56I') + # Deterministic independent pivot rows of M, only eight-dimensional algebra. + piv=[];R=[] + for i,row in enumerate(M): + v=row[:] + for j,b in R: + if v[j]:q=v[j];v=[x-q*y for x,y in zip(v,b)] + j=next((j for j,x in enumerate(v)if x),None) + if j is not None: + q=v[j];v=[x/q for x in v];R.append((j,v));piv.append(i) + if len(piv)==8:break + free=[i for i in range(n)if i not in piv];Hinv=inverse([[M[piv[j]][a]for j in range(8)]for a in range(8)]) + N=[[F(i==f)for f in free]for i in range(n)] + for k,f in enumerate(free): + for j,p in enumerate(piv):N[p][k]=-sum(Hinv[j][a]*M[f][a]for a in range(8)) + need(all(sum(M[i][a]*N[i][b]for i in range(n))==0 for a in range(8)for b in range(104)),'explicit104-dimensional rational kernel') + T=[M[i]+N[i]for i in range(n)] + Ti=[[M[j][a]/56 for j in range(n)]for a in range(8)]+[[F(f==j)-sum(M[f][a]*M[j][a]for a in range(8))/56 for j in range(n)]for f in free] + need(all(sum(T[i][k]*Ti[k][j]for k in range(n))==F(i==j)for i,j in product(range(n),repeat=2)),'all112^2 rational inverse entries') + # Efficient rank-eight block elimination rather than dense112 elimination. + # Modal c=M^T y/56 first overwrites only the8 pivot rows invertibly; + # free y are consumed before their kernel-coordinate updates. + A8=[[M[piv[j]][a]/56 for j in range(8)]for a in range(8)] + local=inverse_ops(elementary_to_inverse(A8));invops=[] + for e in local: + if e[0]=='SWAP':invops.append(['SWAP',piv[e[1]],piv[e[2]]]) + elif e[0]=='SCALE':invops.append(['SCALE',piv[e[1]],e[2],e[3]]) + else:invops.append(['ADD',piv[e[1]],piv[e[2]],e[3],e[4]]) + for a,p in enumerate(piv): + for f in free: + if M[f][a]:q=M[f][a]/56;invops.append(['ADD',p,f,q.numerator,q.denominator]) + for f in free: + for a,p in enumerate(piv): + if M[f][a]:q=-M[f][a];invops.append(['ADD',f,p,q.numerator,q.denominator]) + current=list(range(112));desired=piv+free + for i in range(112): + j=current.index(desired[i]) + if i!=j:invops.append(['SWAP',i,j]);current[i],current[j]=current[j],current[i] + fwdops=inverse_ops(invops) + need(matrix_apply_ops(eye(n),invops)==Ti,'literal in-place T^-1 recoder') + need(matrix_apply_ops(eye(n),fwdops)==T,'literal in-place T recoder') + # Bind K/C compatibility using all14 actual localcube matrices. + groups={} + for i,r in enumerate(M):groups.setdefault(tuple(j for j,x in enumerate(r)if x),[]).append(i) + need(len(groups)==14 and all(len(g)==8 for g in groups.values()),'14 actualeight cubes') + for g in groups.values(): + K=[[F(i==j)-sum(M[g[i]][a]*M[g[j]][a]for a in range(8))/4 for j in range(8)]for i in range(8)] + need(all(sum(K[i][j]*K[j][k]for j in range(8))==F(i==k)for i,k in product(range(8),repeat=2)),'all actual Kcube involutions') + need(all(sum(K[i][j]*M[g[j]][a]for j in range(8))==-M[g[i]][a]for i in range(8)for a in range(8)),'actual K acts minusidentity on globalC modes') + sectors=[];rank=0 + for flags in product([0,1],repeat=3): + active=sum(flags);dim=8**active*104**(3-active);lam=98 if active==2 else(-1078 if active==3 else 0) + if lam:rank+=dim + sectors.append({'active_C_axes':list(flags),'dimension':dim,'F_C_eigenvalue':lam,'A_eigenvalue':1-lam,'A_inverse_eigenvalue':str(F(1,1-lam))}) + need(rank==20480,'exact globalF3 rank20480') + # Structured global loops are explicit; do not expand all v*GL operations. + glcounts=Counter(e[0]for e in invops)+Counter(e[0]for e in fwdops);v=112**3;axis_batches=3*112**2 + gather_scatter_counts={k:2*axis_batches*c for k,c in glcounts.items()} + gather_scatter_counts.update({'field_monomial_pass':4*v,'mode_COPY':rank,'mode_ADD':rank,'mode_CLEAR':rank}) + # Every elementary ADD/SCALE and COPY has a finite field-l2 norm bound. + # Gaussian children and P/D/X/phase have norm1 at every width. + glgrowth=F(1) + for e in invops+fwdops: + if e[0]=='ADD':glgrowth*=1+abs(F(e[3],e[4])) + elif e[0]=='SCALE':glgrowth*=max(F(1),abs(F(e[2],e[3]))) + with localcontext()as c: + c.prec=70;a=Decimal('0.003027288235');sigma=1-a;p=lambda r:(Decimal(r).ln()*sigma).exp();allow=Decimal(2)/3*p(73)-sum(p(r)for r in [8,9,15,16]);cost=Decimal(rank)/v*p(25);costold=Decimal(22016)/v*p(25) + preflight={'a':str(a),'N':3,'target_grant':{'73':2*v},'base_K_paid':{str(r):3*v for r in [8,9,15,16]},'correction_paid':{'25':3*rank},'per_port_local_K_only_allowance':str(allow),'per_port_local20480H25_cost':str(cost),'conditional_margin20480':str(allow-cost),'conditional_margin22016':str(allow-costold),'certified_margin20480_interval':bounded_margin(20480),'certified_margin22016_interval':bounded_margin(22016),'scope':'Conditional preflight grants both coded E terminals as independent H73. This terminal grant is UNKNOWN and is not a constructed supplier, numerical kappa or formal admission.'} + need(F(preflight['certified_margin20480_interval'][0])>0 and F(preflight['certified_margin22016_interval'][0])>0,'strict rational positive conditional margins') + program={'schema':'global-F3-rational-mode-algorithm/v1','normalizer_pin':PIN,'global_orthonormal_basis_raw27':orth,'global_normalizer_rule':['For globalport triple(a,b,c), raw q=q_a | (q_b<<9) | (q_c<<18) from pinned base NORMALIZERS ports.','Its25-bit coordinate is sum(dot(rawq,orth[j])<0 with q_j=0 and G=T_(ej+q) T_(e0+ej).','T_v x=x+(v dot x)v. Put z_j=(wt(row_j G)-1)/2 mod2 and L=Z_z P_G.','Orthogonality and weight congruence prove L R25 L^-1=R25 with exact phase for all positive widths. All scalar owner coefficients act once; only address monomials tensor lift.'],'mode_matrix112x8':encode(M),'kernel_pivot_rows':piv,'kernel_free_rows':free,'T112':encode(T),'T_inverse112':encode(Ti),'literal_T_inverse_elementary_word':invops,'literal_T_elementary_word':fwdops,'global_owner_basis':'T tensor T tensor T, acting on three owner selector coordinates. Each elementary112-owner word repeats for every one of112^2 fixed other-axis coordinates. No tensor power of owner sums in field width.','nonzero_modes':[x for x in sectors if x['F_C_eigenvalue']],'owned_query_word':['Apply each physical L_i to original Y_i (ordinary signed monomial).','For axis0,1,2 and every fixed pair of other owner indices in0..111, apply emitted T_inverse112 word in place.','COPY each coordinate with at least2 modal indices<8 into its own zero field g_t; there are20480.','Restore all original Y by inverse owner-axis words then L_i^-1. All source reads finish before native/precode overwrites.','Apply one native full R25 positive Gaussian to every g_t.','To add -R F_C Y into existing X, apply L_i and T_inverse owner-axis words to X, ADD -lambda_t g_t at each nonzero mode coordinate, restore T words then L_i^-1.','CLEAR every owned g_t after its final scatter.'],'code_E_word':['Normalize each main-bank owner by L_i.','Apply T_inverse on each owner axis.','SCALE each modal sector by (1-lambda_t)^-1 for E or by (1-lambda_t) for E^-1.','Restore T on each owner axis.','Apply actual block-diagonal K_odd on every8x8x8 cube using its literal76-per-row coefficients, owned512-field output scratch; after every source read, SWAP each completed output with its main field, then CLEAR the old main value now in owned scratch. Reuse the512 scratch fields.','Apply L_i^-1 to restore physical coordinates.'],'operator_claim':'F_C=L^-1 T^tensor3 diag(lambda) (T_inverse)^tensor3 L. It commutes with R because every L_i does. K_odd F_C=-F_C and K_odd^2=I, so E=K_odd(I-F_C)^-1 is real symmetric, invertible and commutes with R.'} + result={'schema':'global20480-mode-query-proof/v1','status':'PASS_EXPLICIT_RATIONAL_MODES_AND_INPLACE_ORDINARY_WORD','normalizer_pin':PIN,'base_dimension':112,'base_C_rank':8,'kernel_dimension':104,'literal_T_inverse_counts':dict(Counter(e[0]for e in invops)),'literal_T_counts':dict(Counter(e[0]for e in fwdops)),'rational_T_inverse_entries_checked':112**2,'global_dimension':v,'sectors':sectors,'nonzero_global_modes':rank,'query_paid_profile_per_full':{'25':rank},'gather_scatter_ordinary_counts':gather_scatter_counts,'query_owned_fields':rank,'ordinary_E_code_per_evaluation':{'ADD':axis_batches*glcounts['ADD']+76*v,'SCALE':axis_batches*glcounts['SCALE']+rank,'SWAP':axis_batches*glcounts['SWAP']+v,'field_monomial_pass':2*v,'OWN_ZERO':v,'CLEAR':v,'reusable_owned_fields':512},'ordinary_query_both_orientations_upper':{'ADD':2*axis_batches*glcounts['ADD']+2*rank,'SCALE':2*axis_batches*glcounts['SCALE'],'SWAP':2*axis_batches*glcounts['SWAP'],'field_monomial_pass':4*v,'COPY':rank,'OWN_ZERO':rank,'CLEAR':2*rank},'ordinary_native_inverse_transpose_and_boundaries_upper':{'ADD':77*v,'P':15*v,'D':15*v,'X':20*v,'phase':6*v,'COPY':v,'OWN_ZERO':v,'CLEAR':2*v},'ordinary_local_module_upper_recipe':'Two ordinary E/E^-1 code evaluations plus one query upper bill plus native inverse-transpose/boundary upper bill. This conservative unified bound covers both orientations; some COPY/ZERO/CLEAR counts intentionally dominate either orientation. Structured loop counts, not an expanded global event list. N3 uses3 modules and3 extra positive-output inverse-code evaluations.','global_inverse_owned_peak_upper':v+rank+512,'field_l2_query_prefix_log2_upper':6*glgrowth.numerator.bit_length()+12,'field_l2_Ecode_prefix_log2_upper':3*glgrowth.numerator.bit_length()+14,'source_contact_extra_owned_for_inverse':v,'reusable_scalar_K_scratch_fields':512,'gather_scatter_GL_norm_product_numerator_bits':glgrowth.numerator.bit_length(),'gather_scatter_GL_norm_product_denominator_bits':glgrowth.denominator.bit_length(),'finite_precision_statement':'Each fixed ordinary elementary ADD norm<=1+abs(c), SCALE norm<=max(1,abs(c)), owned COPY norm<=2, CLEAR norm<=1. Their explicitly counted finite product bounds field-l2 error growth uniformly in positive width; paid Gaussians and signed monomials are unitary. This supplies a finite precision offset, not the unproved outer TM/rounding/storage admission.','preflight':preflight,'scientific_program_sha256':hashlib.sha256(canonical(program)).hexdigest(),'whole_caller_or_kappa':False} + return json.loads(canonical(result)),program +if __name__=='__main__': + ap=argparse.ArgumentParser();ap.add_argument('--write',action='store_true');a=ap.parse_args();r,p=calculate() + if a.write:(HERE/'MODES.json').write_text(json.dumps(r,sort_keys=True,indent=2)+'\n');(HERE/'MODES-PROGRAM.json').write_text(json.dumps(p,sort_keys=True,indent=2)+'\n') + else:need(json.loads((HERE/'MODES.json').read_bytes())==r,'readonly modes receipt');need(json.loads((HERE/'MODES-PROGRAM.json').read_bytes())==p,'readonly actual rational basis and elementary words') + print(json.dumps({k:r[k]for k in ['status','nonzero_global_modes','query_paid_profile_per_full','literal_T_counts','literal_T_inverse_counts','scientific_program_sha256','preflight']},sort_keys=True)) diff --git a/research/odd-e8-lowrank-e-native/n3.py b/research/odd-e8-lowrank-e-native/n3.py new file mode 100644 index 0000000000..5e705e1252 --- /dev/null +++ b/research/odd-e8-lowrank-e-native/n3.py @@ -0,0 +1,97 @@ +"""Three distinct fresh stages: literal owned typed E caller and positive exit.""" +import argparse,hashlib,importlib.util,json,sys +from collections import Counter +from fractions import Fraction as F +from pathlib import Path +HERE=Path(__file__).resolve().parent +spec=importlib.util.spec_from_file_location('n3_owned',HERE/'owned_e.py');oe=importlib.util.module_from_spec(spec);sys.modules[spec.name]=oe;spec.loader.exec_module(oe) +C=oe.C;N=16;W=64;MAIN=oe.MAIN + +def need(q,s): + if not q:raise ValueError(s) +def eye(n):return [[C(i==j)for j in range(n)]for i in range(n)] +def zeros(n,m=None):return [[C()for j in range(n if m is None else m)]for i in range(n)] +def plus(A,B):return [[a+b for a,b in zip(r,s)]for r,s in zip(A,B)] +def times(c,A):return [[c*x for x in r]for r in A] +def left(A,B): + out=zeros(len(A),len(B[0])) + for i,r in enumerate(A): + for k,c in enumerate(r): + if c: + for j,x in enumerate(B[k]): + if x:out[i][j]+=c*x + return out +def prod(*As): + r=eye(len(As[0])) + for A in As:r=left(r,A) + return r +def block(A,B,D,E):return [a+b for a,b in zip(A,B)]+[a+b for a,b in zip(D,E)] +def diag(A,B):return block(A,zeros(len(A)),zeros(len(A)),B) +def perm(fun): + A=zeros(N) + for x in range(N):A[fun(x)][x]=C(1) + return A +def X(q):return perm(lambda x:x^q) +def gate(q,sgn=1):return plus(times(C(F(1,2),F(sgn,2)),eye(N)),times(C(F(1,2),F(-sgn,2)),X(q))) +def swap(x,s): + b0=x&1;bs=(x>>s)&1 + return x^((1|(1<>1)<>1)&1)][x]=C(1) +def translation(q): + O=zeros(4) + for x in range(4):O[x^q][x]=C(1) + return O +def gate(q,s=1):return add(scale(C(F(1,2),F(s,2)),I4),scale(C(F(1,2),F(-s,2)),translation(q))) +MAP={'I':I4,'P':P,**{'X'+str(q):translation(q)for q in [1,2,3]},'C0':gate(1),'C1':gate(2),'R':mul(gate(1),gate(2))} +def left(A,B):return [[sum((A[i][k]*B[k][j]for k in range(len(A))),C())for j in range(len(B[0]))]for i in range(len(A))] +def ownzero():return [[C()for j in range(16)]for i in range(4)] +def coded(bank,a,b,label): + f,g=bank;u,v=label+'a',label+'b' + return [['COPY',u,f],['COPY',v,g],['SCALE',f,a.numerator,a.denominator],['SCALE',g,a.numerator,a.denominator],['ADD',f,v,b.numerator,b.denominator,'P'],['ADD',g,u,b.numerator,b.denominator,'P'],['CLEAR',u],['CLEAR',v]] +def modes(lam,sign,label): + # FC=(lambda/2)[I;-P][I,-P]. Source Y is read before any overwrite. + g=label+'g' + return [['OWN_ZERO',g],['ADD',g,'Y0',1,1,'I'],['ADD',g,'Y1',-1,1,'P'],['PAID',g,'R',2],['ADD','X0',g,(sign*F(lam,2)).numerator,(sign*F(lam,2)).denominator,'I'],['ADD','X1',g,(-sign*F(lam,2)).numerator,(-sign*F(lam,2)).denominator,'P'],['CLEAR',g]] +def nativeB(): + # Exact inverse-transpose of F=[[D,0],[Pswap,D]], with ordinary X powers. + out=[['MONO',f,'X1']for f in ['X0','X1']] + for f in ['Y0','Y1']:out.extend([['PAID',f,'C1',1],['MONO',f,'X2']]) + out.extend([['ADD','X0','Y1',-1,1,'P'],['ADD','X1','Y0',-1,1,'P']]) + for f in ['X0','X1']:out.extend([['PAID',f,'C1',1],['MONO',f,'X2']]) + out.extend([['MONO',f,'X3']for f in ['X0','X1']]);out.extend([['MONO',f,'X2']for f in ['Y0','Y1']]) + return out +def programs(lam): + ei_a=F(lam,2);ei_b=1-ei_a;e_a=F(lam,2*(lam-1));e_b=F(lam-2,2*(lam-1)) + # Gather and transform the original Y mode first; retain it across nativeB. + q=modes(lam,-1,'back_mode_');split=4 + back=q[:split]+coded(['Y0','Y1'],ei_a,ei_b,'by')+nativeB()+q[split:-1]+coded(['X0','X1'],ei_a,ei_b,'bx')+q[-1:] + inv=coded(['X0','X1'],e_a,e_b,'ix') + inv.extend([['MONO',f,'X2']for f in ['Y0','Y1']]) + inv.extend([['COPY','cache0','Y0'],['COPY','cache1','Y1']]) + inv.extend([['PAID',f,'C1',1]for f in ['Y0','Y1']]) + inv+=coded(['Y0','Y1'],e_a,e_b,'iy')+modes(lam,1,'inverse_mode_') + inv.extend([['MONO',f,'X3']for f in ['X0','X1']]);inv.extend([['PAID',f,'C1',1]for f in ['X0','X1']]) + inv.extend([['ADD','X0','cache1',1,1,'P'],['ADD','X1','cache0',1,1,'P']]) + inv.extend([['MONO',f,'X1']for f in ['X0','X1']]);inv.extend([['CLEAR','cache0'],['CLEAR','cache1']]) + tr=[] + for e in reversed(inv): + if e[0]=='COPY':tr.extend([['ADD',e[2],e[1],1,1,'I'],['CLEAR',e[1]]]) + elif e[0]=='CLEAR':tr.append(['OWN_ZERO',e[1]]) + elif e[0]=='OWN_ZERO':tr.append(['CLEAR',e[1]]) + elif e[0]=='ADD':tr.append(['ADD',e[2],e[1],e[3],e[4],e[5]]) # I,P are symmetric. + elif e[0]=='SCALE':tr.append(list(e)) + else:need(e[0]in ['MONO','PAID'],True,'transpose known symmetric fixture primitive');tr.append(list(e)) + forward=[['MONO',f,'X1']for f in ['X0','X1']]+tr+[['MONO',f,'X3']for f in ['X0','X1']]+[['MONO',f,'X2']for f in ['Y0','Y1']] + return back,inv,tr,forward + +def run(program,initial=None): + vals={f:[[C(int(4*j+i==k))for k in range(16)]for i in range(4)]for j,f in enumerate(MAIN)}if initial is None else{f:[list(r)for r in initial[4*j:4*j+4]]for j,f in enumerate(MAIN)} + live=set(MAIN);peak=0;paid=Counter();ops=Counter() + for e in program: + op=e[0];ops[op]+=1 + if op in ['OWN_ZERO','COPY']: + f=e[1];need(f not in live and f not in MAIN,True,'owned destination must be fresh and zero') + if op=='COPY':need(e[2]in live,True,'COPY source initialized');vals[f]=[list(r)for r in vals[e[2]]] + else:vals[f]=ownzero() + live.add(f);peak=max(peak,len(live)-4) + elif op=='CLEAR':need(e[1]in live and e[1]not in MAIN,True,'owned only CLEAR after use');vals[e[1]]=ownzero();live.remove(e[1]) + elif op=='SCALE':need(e[1]in live,True,'SCALE initialized');vals[e[1]]=scale(F(e[2],e[3]),vals[e[1]]) + elif op=='ADD': + f,g=e[1:3];need(f in live and g in live,True,'ADD initialized owned/source');vals[f]=add(vals[f],scale(F(e[3],e[4]),left(MAP[e[5]],vals[g]))) + else: + need(op in ['MONO','PAID']and e[1]in live,True,'known initialized unary');vals[e[1]]=left(MAP[e[2]],vals[e[1]]) + if op=='PAID':paid[e[3]]+=1 + need(live,set(MAIN),'all owned temporaries cleaned') + return sum([vals[f]for f in MAIN],[]),{'paid':dict(sorted(paid.items())),'ordinary':dict(sorted((k,v)for k,v in ops.items()if k!='PAID')),'peak_owned_fields':peak} +def matrix_json(M):return [[[str(z.a),str(z.b)]for z in r]for r in M] +def targets(lam): + Q=diag(gate(1),gate(1));Qi=diag(gate(1,-1),gate(1,-1));D=diag(gate(2),gate(2));I=ident(8);Z=zeros(4) + K=block(Z,P,P,Z);Pm=scale(F(1,2),add(I,scale(-1,K)));FC=scale(lam,Pm);A=add(I,scale(-1,FC));Ai=add(I,scale(F(lam,1-lam),Pm));E=mul(K,Ai);Ei=mul(K,A) + HF=diag(E,prod(Qi,E,Q));HB=diag(Ei,prod(Qi,Ei,Q));WF=mul(HF,mul(diag(D,D),lower(Qi)));WB=mul(HB,mul(diag(D,D),upper(scale(-1,Q)))) + return WF,WB + +def calculate(): + cases=[];payload=[] + for lam in [14,98,-1078]: + back,inv,tr,forward=programs(lam);B,bi=run(back);Bi,ii=run(inv);T,ti=run(tr);FF,fi=run(forward);WF,WB=targets(lam) + need(B,WB,'literal owned backward E adapter all16 input columns and phases') + need(mul(Bi,B),ident(16),'literal owned inverse left all16columns') + need(mul(B,Bi),ident(16),'literal owned inverse right all16columns') + need(T,list(map(list,zip(*Bi))),'literal owned transpose all256 operatorentries') + need(FF,WF,'literal owned forward E adapter all16 inputcolumns absolutephase') + need(bi['paid'],{1:4,2:1},'back paid native4H1 +rH2') + need(ii['paid'],bi['paid'],'inverse same Gaussian paidprofile');need(fi['paid'],bi['paid'],'forward same Gaussian paidprofile') + controls={} + bad=[e for e in back if not(e[0]=='PAID'and e[2]=='R')];controls['missing_owned_R_query_rejected']=run(bad)[0]!=WB + bad=[list(e)for e in forward];bad[-4]=['MONO','X0','X1'];controls['wrong_forward_Dsquare_boundary_rejected']=run(bad)[0]!=WF + bad=[list(e)for e in inv];i=next(i for i,e in enumerate(bad)if e[0]=='COPY'and e[1]=='cache0');bad[i]=['OWN_ZERO','cache0'];controls['lost_actual_source_contact_rejected']=run(bad)[0]!=Bi + bad=[list(e)for e in tr];i=next(i for i,e in enumerate(bad)if e[0]=='ADD');bad[i]=list(bad[i]);bad[i][3]=-bad[i][3];controls['wrong_transpose_ADD_sign_rejected']=run(bad)[0]!=T + bad=[list(e)for e in inv];i=next(i for i,e in enumerate(bad)if e[0]=='ADD'and e[2]=='cache0');bad.insert(i,['CLEAR','cache0']) + try:run(bad) + except ValueError:controls['owned_source_early_CLEAR_rejected']=True + need(all(controls.values())and len(controls)==5,True,'all physical/phase/owned controls') + cases.append({'lambda':lam,'backward':bi,'inverse':ii,'transpose':ti,'forward':fi,'all16_arbitrary_main_columns_exact':True,'absolute_phases_exact':True,'all256_transpose_operator_entries_exact':True,'controls':controls,'backward_matrix_sha256':hashlib.sha256(json.dumps(matrix_json(B),separators=(',',':')).encode()).hexdigest(),'forward_matrix_sha256':hashlib.sha256(json.dumps(matrix_json(FF),separators=(',',':')).encode()).hexdigest()}) + payload.append({'lambda':lam,'backward':back,'inverse':inv,'transpose':tr,'forward':forward}) + result={'schema':'owned-E-adapter-fulloperator-fixture/v1','status':'PASS_LITERAL_BOTH_ORIENTATIONS_WITH_OWNED_SOURCE_CHECKPOINT','field_width':1,'address_axes':2,'arbitrary_independent_main_fields':4,'main_operator_dimension':16,'cases':cases,'scope':'Exact complete small noncommuting-Q full operators, with original source acquisition, same paid profiles, owned lifecycle and absolute phase. Global all-port implementation uses separate actual root512 native checkpoint proof and rational spectral mode theorem. No negative E terminal decoding or complete caller claimed.'} + return json.loads(json.dumps(result)),json.loads(json.dumps(payload)) +if __name__=='__main__': + ap=argparse.ArgumentParser();ap.add_argument('--write',action='store_true');a=ap.parse_args();r,p=calculate();rpath=HERE/'OWNED-E.json';ppath=HERE/'OWNED-E-PROGRAM.json' + if a.write:rpath.write_text(json.dumps(r,sort_keys=True,indent=2)+'\n');ppath.write_text(json.dumps(p,sort_keys=True,indent=2)+'\n') + else:need(r,json.loads(rpath.read_bytes()),'read-only owned E receipt');need(p,json.loads(ppath.read_bytes()),'read-only owned E program') + print(json.dumps(r,sort_keys=True)) diff --git a/research/odd-e8-lowrank-e-native/peer_review.py b/research/odd-e8-lowrank-e-native/peer_review.py new file mode 100644 index 0000000000..6df8b98c53 --- /dev/null +++ b/research/odd-e8-lowrank-e-native/peer_review.py @@ -0,0 +1,186 @@ +"""AI peer review controls; no author code imported, package read-only. + +The reviewer authored only the package's separate two_cube_native fixture. +This is not an independent human review, formal proof kernel or priority audit. +""" +from pathlib import Path +from fractions import Fraction as F +from collections import Counter,defaultdict +from itertools import product +from hashlib import sha256 +from functools import lru_cache +import argparse,gzip,json +HERE=Path(__file__).resolve().parent +DEFAULT=HERE +AUTHOR_METADATA={'FILES.json':'AUTHOR-FILES.json','SOURCES.json':'AUTHOR-SOURCES.json','VERIFY.json':'AUTHOR-VERIFY.json','README.md':'AUTHOR-README.md'} +def author_path(package,name): + return package/AUTHOR_METADATA.get(name,name) +def need(ok,why): + if not ok:raise ValueError(why) +def canon(x):return(json.dumps(x,sort_keys=True,separators=(',',':'))+'\n').encode() +def q(a=0,b=0):return(F(a),F(b)) +ZERO=q();ONE=q(1) +def qa(x,y):return(x[0]+y[0],x[1]+y[1]) +def qn(x):return(-x[0],-x[1]) +def qm(x,y):return(x[0]*y[0]-x[1]*y[1],x[0]*y[1]+x[1]*y[0]) +def qi(x): + a,b=x;d=a*a+b*b;return(a/d,-b/d) +def zero(n):return[[ZERO for j in range(n)]for i in range(n)] +def eye(n):return[[ONE if i==j else ZERO for j in range(n)]for i in range(n)] +def add(A,B):return[[qa(a,b)for a,b in zip(r,s)]for r,s in zip(A,B)] +def scale(c,A):return[[qm(c,x)for x in r]for r in A] +def mm(A,B): + O=zero(len(A));br=[[(j,x)for j,x in enumerate(r)if x!=ZERO]for r in B] + for i,r in enumerate(A): + for k,a in enumerate(r): + if a!=ZERO: + for j,b in br[k]:O[i][j]=qa(O[i][j],qm(a,b)) + return O +def prod(*As): + R=eye(len(As[0])) + for A in As:R=mm(R,A) + return R +def tr(A):return list(map(list,zip(*A))) +def inv(A): + n=len(A);R=[r[:]+eye(n)[i]for i,r in enumerate(A)] + for j in range(n): + p=next(i for i in range(j,n)if R[i][j]!=ZERO);R[p],R[j]=R[j],R[p];c=qi(R[j][j]);R[j]=[qm(c,x)for x in R[j]] + for i in range(n): + if i!=j and R[i][j]!=ZERO:c=qn(R[i][j]);R[i]=[qa(a,qm(c,b))for a,b in zip(R[i],R[j])] + return[r[n:]for r in R] +def block(A,B,C,D):return[a+b for a,b in zip(A,B)]+[a+b for a,b in zip(C,D)] +def diag(A,B):return block(A,zero(len(A)),zero(len(A)),B) +def upper(A):return block(eye(len(A)),A,zero(len(A)),eye(len(A))) +def lower(A):return block(eye(len(A)),zero(len(A)),A,eye(len(A))) +def controls(): + n=4;I4=eye(n) + def X(v):return[[ONE if i==j^v else ZERO for j in range(n)]for i in range(n)] + def C(v,s=1):return add(scale(q(F(1,2),F(s,2)),I4),scale(q(F(1,2),F(-s,2)),X(v))) + P=[[ONE if i==((j&1)<<1)|((j>>1)&1)else ZERO for j in range(n)]for i in range(n)] + Q=diag(C(1),C(1));D=diag(C(2),C(2));R=mm(D,Q);K=block(zero(4),P,P,zero(4));I=eye(8);Qi=inv(Q) + need(mm(K,K)==I and mm(K,R)==mm(R,K),'independent actual small K/R') + need(mm(K,Q)!=mm(Q,K),'noncommuting control') + FK=mm(diag(D,D),lower(mm(K,Qi)));BK=mm(diag(D,D),upper(scale(q(-1),mm(Q,K))));F0=mm(diag(D,D),lower(Qi));B0=mm(diag(D,D),upper(scale(q(-1),Q))) + out=[] + for lam in [4,98]: + Cc=scale(q(F(lam,2)),add(I,scale(q(-1),K)));A=add(I,scale(q(-1),Cc));E=mm(K,inv(A));Ei=inv(E) + need(tr(E)==E and mm(E,R)==mm(R,E)and mm(E,Q)!=mm(Q,E),'symmetric real E, exact R centralization, noncommuting Q') + H=lambda T:diag(T,prod(Qi,T,Q)) + before=prod(diag(Ei,I),BK,diag(I,Ei));scatter=block(zero(8),scale(q(-1),prod(Ei,R,Cc)),zero(8),zero(8));WB=add(before,scatter) + need(WB==mm(H(Ei),B0),'actual original-ground backward scatter sign/order') + Wi=inv(WB);need(mm(Wi,WB)==eye(16),'independent Gaussian-elimination inverse') + Q2=mm(Q,Q);D2=mm(D,D);J=diag(Q2,I);Jinv=inv(J);WF=prod(diag(D2,D2),J,tr(Wi),Jinv) + need(WF==mm(H(E),F0),'independent inverse-transpose D2/J boundary') + badsign=add(before,scale(q(-1),scatter));badacquire=add(before,block(zero(8),scale(q(-1),prod(Ei,R,Cc,Ei)),zero(8),zero(8))) + need(badsign!=WB and badacquire!=WB,'wrong sign and gathering overwritten E^-1Y rejected') + need(prod(diag(D2,D2),tr(Wi))!=WF,'omitted J boundary rejected') + dagger=lambda M:[[ (x[0],-x[1])for x in r]for r in tr(M)] + need(prod(diag(D2,D2),J,dagger(Wi),Jinv)!=WF,'conjugate transpose is not linear transpose') + out.append({'lambda':lam,'all_16x16_operator_entries':True,'original_ground_scatter':True,'inverse_transpose_boundary':True,'wrong_sign_wrong_acquire_omitted_J_and_dagger_mutants_rejected':True}) + return out +@lru_cache(None) +def gf_inv(rows): + n=len(rows);A=[x|(1<<(n+i))for i,x in enumerate(rows)] + for j in range(n): + p=next(i for i in range(j,n)if A[i]>>j&1);A[p],A[j]=A[j],A[p] + for i in range(n): + if i!=j and A[i]>>j&1:A[i]^=A[j] + return tuple(x>>n for x in A) +def transform(word,transpose=False): + O=[] + for e in reversed(word): + if e[0]=='P':O.append(['P',list(gf_inv(tuple(e[1])))]) + elif e[0]=='D':O.append(['D',e[1],e[2]if transpose else[(-x)%4 for x in e[2]]]) + elif e[0]=='X':O.append(e) + else:need(e[0]=='phase','monomial-only definition');O.append(['phase',e[1]if transpose else(-e[1])%4]) + return O +def calculate(package): + manifest_raw=author_path(package,'FILES.json').read_bytes();need(sha256(manifest_raw).hexdigest()=='2253b65bc0dbccb7c232b555bcf59987082c1babc84b815998f4680de0453496','precision-clarified author package seal');manifest=json.loads(manifest_raw) + for f,meta in manifest['files'].items(): + raw=author_path(package,f).read_bytes();need(len(raw)==meta['bytes']and sha256(raw).hexdigest()==meta['sha256'],'sealed file '+f) + files=['PROOF.md','PRECISION-SCOPE.md','README.md','checkpoint.py','owned_e.py','modes.py','n3.py','e_adapter.py','MODES-PROGRAM.json','MODES.json','ROOT-CHECKPOINT-PROGRAM.json.gz','inputs/NORMALIZERS.json','inputs/B-PROGRAM.json.gz','inputs/K-TEMPLATE.json'] + pins={f:sha256(author_path(package,f).read_bytes()).hexdigest()for f in files} + normal=json.loads((package/'inputs/NORMALIZERS.json').read_bytes());mp=json.loads((package/'MODES-PROGRAM.json').read_bytes());M=[[F(x)for x in r]for r in mp['mode_matrix112x8']];T=[[F(x)for x in r]for r in mp['T112']];Ti=[[F(x)for x in r]for r in mp['T_inverse112']];free=mp['kernel_free_rows'] + need(M==[list(map(F,r))for r in zip(*normal['mode_columns'])],'modal matrix binds actual roots') + need(all(sum(r[i]*r[j]for r in M)==56*int(i==j)for i,j in product(range(8),repeat=2)),'independent M^TM=56I') + need(all(T[i][:8]==M[i]for i in range(112)),'first T columns M') + need(all(sum(M[i][a]*T[i][8+b]for i in range(112))==0 for a in range(8)for b in range(104)),'independent M^TN=0') + need(all(T[f][8+b]==int(j==b)for j,f in enumerate(free)for b in range(104)),'free N block identity') + need(Ti[:8]==[[M[i][a]/56 for i in range(112)]for a in range(8)],'top inverse block') + need(Ti[8:]==[[F(f==j)-sum(M[f][a]*M[j][a]for a in range(8))/56 for j in range(112)]for f in free],'bottom inverse block') + sectors=[] + for flags in product([0,1],repeat=3): + v=[14*x for x in flags];lam=F(v[0]*v[1]+v[0]*v[2]+v[1]*v[2]-v[0]*v[1]*v[2],2);dim=8**sum(flags)*104**(3-sum(flags));sectors.append((flags,lam,dim)) + for signs in product([-1,1],repeat=3): + if all(not flags[i]or signs[i]==-1 for i in range(3))and lam:need(F(sum(signs)-signs[0]*signs[1]*signs[2],2)==-1,'Kodd=-I on every nonzero C sector') + need(sum(dim for flags,lam,dim in sectors if lam)==20480,'independent global modal rank') + orth=mp['global_orthonormal_basis_raw27'];need(len(orth)==25,'25-axis chart');dot=lambda a,b:(a&b).bit_count()&1 + need(all(dot(a,b)==int(i==j)for i,a in enumerate(orth)for j,b in enumerate(orth)),'orthonormal raw27 basis') + chi=0 + for b in orth:chi^=b + need(chi==(1<<27)-1,'global characteristic is raw chi27') + need(all(dot(p['q'],p['q'])==1 and p['q']!=(1<<9)-1 for p in normal['ports']),'all base normone noncharacteristic labels') + original=json.loads(gzip.decompress((package/'inputs/B-PROGRAM.json.gz').read_bytes()));owned=json.loads(gzip.decompress((package/'ROOT-CHECKPOINT-PROGRAM.json.gz').read_bytes()));need(sha256(canon(original)).hexdigest()=='f6b26f28f2a8f2dcfbf81f98c7ca18f967384b7b61518766494f8e821d5bf56f','actual source B science') + def tv(v):return[(1<>j&1 else 0)for j in range(25)] + def matmul(A,B): + out=[] + for row in A: + value=0 + for j,b in enumerate(B): + if row>>j&1:value^=b + out.append(value) + return out + root_L=0 + for e in original['program']: + if e[0]!='MONOMIAL'or e[1]!='Y'or e[4]!='inverse_transpose_real_reader_entry':continue + p=e[2];digits=[p//112**2,(p//112)%112,p%112];raw=sum(normal['ports'][x]['q']<<(9*j)for j,x in enumerate(digits));qp=sum(dot(raw,b)<>j&1));G=matmul(tv((1<0 else-1)*(abs(e[2])+1000000)]) + elif e[0]=='ADD':tt.append(['ADD',e[2],e[1],e[3],e[4]]) + elif e[0]=='CLEAR':tt.append(['ZERO_OWNED',e[1]]) + else:tt.extend([['ADD',e[2],e[1],1,1],['CLEAR',e[1]]]) + need(tt==owned['native_inverse_transpose_program'],'owned transpose is adjoint accumulation, not inverse CLEAR') + result={'schema':'E-adapter-AI-peer-static-and-identity-review/v1','status':'PASS_SCOPED_LOCAL_ALGEBRA_AND_STRUCTURED_NATIVE_COMPILATION','reviewer_role':'AI peer, author of two_cube_native fixture only; no claim of independent human/formal-kernel acceptance','reviewed_author_package_seal':sha256(manifest_raw).hexdigest(),'sealed_payload_file_count':len(manifest['files']),'source_package_file_sha256':pins,'small_independent_Qi_controls':controls(),'global_modes':{'M_Gram56I':True,'T_inverse_block_proof':True,'polynomial':'F3(C)=(C1C2+C1C3+C2C3-C1C2C3)/2','nonzero_rank':20480,'Kodd_minus_identity_on_C_modes':True,'global_noncharacteristic_chart':True,'physical_normalizer_rule_matches_actual_root_B':root_L},'actual_native_checkpoint':{'source_contacts':len(contacts),'source_reads':sum(reads.values()),'literal_inverse_and_inverse_transpose_events':physical,'source_inverse_order_and_snapshot_versions':True,'X_reverse_order_and_cache_last_read':True,'owned_transpose_rules':True},'cost_review':'Structured ordinary upper profiles and owned peak v+20480+512 are conservative for the local module. N3 needs3 modules and3 extra code inverses. Mode queries are not productive outputs. Full TM/rounding/routing/storage admission is not supplied.','precision_scope':'Operator norm growth is a finite width-independent field-l2 ABI constant. Per-coordinate fixed-point rounding to field-l2 can require a dimension-dependent precision increment; no uniform componentwise/TM closure is established.','blocking_claims':['Negative Q^-1 B_E D Gaussian admission remains UNKNOWN.','Conditional both-H73 moment is not a constructed supplier or kappa bound.','A public precision claim must retain the field-l2 ABI qualification.'],'theoretical_local_blocker_found':False,'scope':'No author Python code was imported or full package suite repeated. Exact new controls use independently implemented Q(i) matrices; structural native literals, source snapshots and global mode facts are checked independently from serialized inputs.'} + return result +if __name__=='__main__': + ap=argparse.ArgumentParser();ap.add_argument('--package',type=Path,default=DEFAULT);ap.add_argument('--write',action='store_true');a=ap.parse_args();r=calculate(a.package);f=HERE/'PEER-REVIEW.json' + if a.write:f.write_text(json.dumps(r,sort_keys=True,indent=2)+'\n') + else:need(json.loads(f.read_bytes())==r,'readonly review receipt') + print(json.dumps({k:r[k]for k in ['status','theoretical_local_blocker_found','actual_native_checkpoint','blocking_claims']},sort_keys=True)) diff --git a/research/odd-e8-lowrank-e-native/run.py b/research/odd-e8-lowrank-e-native/run.py new file mode 100644 index 0000000000..8b47450d00 --- /dev/null +++ b/research/odd-e8-lowrank-e-native/run.py @@ -0,0 +1,33 @@ +"""Self-contained, Git-free, read-only cold replay of the local E construction.""" +import argparse,gzip,hashlib,importlib.util,json,sys +from pathlib import Path +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent +def need(q,s): + if not q:raise ValueError(s) +def normal(x):return json.loads(json.dumps(x)) +def load(name): + spec=importlib.util.spec_from_file_location('local_E_'+name,HERE/(name+'.py'));m=importlib.util.module_from_spec(spec);sys.modules[spec.name]=m;spec.loader.exec_module(m);return m +def old(name): + p=HERE/name + return json.loads(gzip.decompress(p.read_bytes()))if name.endswith('.gz')else json.loads(p.read_bytes()) +def calculate(): + before={str(p.relative_to(HERE)):hashlib.sha256(p.read_bytes()).hexdigest()for p in HERE.rglob('*')if p.is_file()} + reports={} + x=load('e_adapter').calc();need(normal(x)==old('E-ADAPTER.json'),'exact local E adapter receipt');reports['local_exact']=x['status'] + for name,receipt,program in [('checkpoint','ROOT-CHECKPOINT.json','ROOT-CHECKPOINT-PROGRAM.json.gz'),('owned_e','OWNED-E.json','OWNED-E-PROGRAM.json'),('modes','MODES.json','MODES-PROGRAM.json'),('n3','N3.json','N3-PROGRAM.json'),('two_cube_native','TWO-CUBE-NATIVE.json','TWO-CUBE-NATIVE-PROGRAM.json.gz')]: + m=load(name);r,p=m.calculate(m.SOURCE)if name=='checkpoint'else m.calculate();need(normal(r)==old(receipt),name+' exact science receipt');need(normal(p)==old(program),name+' complete canonical literal program');reports[name]=r.get('status',r.get('schema')) + if name=='modes':modes=r + if name=='checkpoint':checkpoint=r + if name=='two_cube_native':twocube=r + files=['run.py','e_adapter.py','checkpoint.py','owned_e.py','modes.py','n3.py','two_cube_native.py','two_cube_frame_tools.py','inputs/B-PROGRAM.json.gz','inputs/K-TEMPLATE.json','inputs/NORMALIZERS.json','inputs/clifford_exact.py'] + result={'schema':'source-consuming-E-local-positive-cold-replay/v1','status':'PASS_LOCAL_BOTH_ORIENTATION_E_AND_TYPED_N3','components':reports,'global_paid_per_full':{'8':112**3,'9':112**3,'15':112**3,'16':112**3,'25':20480},'actual_root_source_contacts':checkpoint['source_contacts_checked'],'actual_root_source_reads':checkpoint['actual_source_ADD_reads_checked'],'global_nonzero_modes':modes['nonzero_global_modes'],'N3_negative_endpoint':'Q^-1 E3 E2^-1 E1 D123; Gaussian admission UNKNOWN','N3_positive_endpoint':'D123 Q after ordinary code inverse; rank73','conditional_margin_interval':modes['preflight']['certified_margin20480_interval'],'whole_caller_Gaussian_admission':False,'new_kappa':False,'code_and_input_sha256':{p:hashlib.sha256((HERE/p).read_bytes()).hexdigest()for p in files},'scope':'Pure same-folder Python standard library. Default does not write. Full physical local E word and inverse/transpose source-contact mechanism plus typed N3; independent Gaussian negative terminal and outer TM/precision/storage admission remain UNKNOWN.'} + after={str(p.relative_to(HERE)):hashlib.sha256(p.read_bytes()).hexdigest()for p in HERE.rglob('*')if p.is_file()} + need(before==after,'default combined calculation leaves every package file byte-identical') + result['all_package_files_readonly']=True + return normal(result) +if __name__=='__main__': + ap=argparse.ArgumentParser();ap.add_argument('--write',action='store_true');a=ap.parse_args();r=calculate() + if a.write:(HERE/'RESULT.json').write_text(json.dumps(r,sort_keys=True,indent=2)+'\n') + else:need(r==old('RESULT.json'),'frozen combined local-positive receipt') + print(json.dumps(r,sort_keys=True)) diff --git a/research/odd-e8-lowrank-e-native/two_cube_frame_tools.py b/research/odd-e8-lowrank-e-native/two_cube_frame_tools.py new file mode 100644 index 0000000000..7ec1c59b7d --- /dev/null +++ b/research/odd-e8-lowrank-e-native/two_cube_frame_tools.py @@ -0,0 +1,56 @@ +"""Exact low-rank phases and analytic full-Gaussian native conjugation. + +Source Clifford compiler credit retained. No dense 2^n state is allocated. +""" +def install(ce,need,peak): + def sparse_zero(op,basis_state=0): + vec={basis_state:(1,0)};den=0 + for e in op.circuit: + k=e[0] + if k=='P':vec={ce.mv(e[1],x):a for x,a in vec.items()} + elif k=='X':vec={x^e[1]:a for x,a in vec.items()} + elif k=='D':vec={x:ce.mul_i(a,ce.qvalue(e[1],e[2],x,op.n))for x,a in vec.items()} + elif k=='phase':vec={x:ce.mul_i(a,e[1])for x,a in vec.items()} + else: + need(k=='C','literal sparse phase primitive');q,s=e[1:];out={} + for x in set(vec)|{x^q for x in vec}: + a,b=vec.get(x,(0,0));c,d=vec.get(x^q,(0,0));v=(a-s*b+c+s*d,b+s*a+d-s*c) + if v!=(0,0):out[x]=v + vec=out;den+=1 + peak[0]=max(peak[0],len(vec));need(len(vec)<=(1<<18),'bounded low-rank phase support') + while den and all(not(a&1)and not(b&1)for a,b in vec.values()):vec={x:(a//2,b//2)for x,(a,b)in vec.items()};den-=1 + return vec,den + ce.Op.zero_state=sparse_zero + def monomial(op,known_zero=None): + n=op.n;T=op.tab;need(all(x==0 and p%2==0 for x,z,p in T[n:]),'physical map is actually monomial') + G=ce.transpose([x for x,z,p in T[:n]],n);b=ce.mv(G,sum((p//2)<=((1-i)/2)^n sum_x i^wt(x)|x>. Thus R K_G R^-1|0>=(-i)^wt(d)|d>. Signed tableau fixes the remaining monomial.', + 'native_G_columns':cols} diff --git a/research/odd-e8-lowrank-e-native/two_cube_native.py b/research/odd-e8-lowrank-e-native/two_cube_native.py new file mode 100644 index 0000000000..87430cf7d1 --- /dev/null +++ b/research/odd-e8-lowrank-e-native/two_cube_native.py @@ -0,0 +1,154 @@ +"""Actual two-cube E8 n9 native F/B words, including absolute phases. + +Phase tools are credited copies of the whole-K PR5464 predecessor. All +32 original main fields are independent; no helper or supplied query is +assumed. Default reads and verifies its semantic payload without writing. +""" +from pathlib import Path +from fractions import Fraction as F +from collections import Counter +from hashlib import sha256 +import argparse,gzip,importlib.util,json,sys +HERE=Path(__file__).resolve().parent +sys.dont_write_bytecode=True +def need(ok,why): + if not ok:raise ValueError(why) +def canonical(x):return(json.dumps(x,sort_keys=True,separators=(',',':'))+'\n').encode() +def load(name,path): + s=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(s);sys.modules[name]=m;s.loader.exec_module(m);return m +def basis(rows): + p={} + for x in rows: + for j in sorted(p,reverse=True): + if x>>j&1:x^=p[j] + if x:p[x.bit_length()-1]=x + return tuple(p[j]for j in sorted(p,reverse=True)) +def calculate(): + pins={'inputs/NORMALIZERS.json':'ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da','inputs/clifford_exact.py':'2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962','two_cube_frame_tools.py':'e5b2ea1f60d554b3a285569602360c663ee8b387350424678b3bd0b0b5432bf4'} + for f,p in pins.items():need(sha256((HERE/f).read_bytes()).hexdigest()==p,'source pin '+f) + ce=load('two_cube_clifford',HERE/'inputs/clifford_exact.py');frames=load('two_cube_frames',HERE/'two_cube_frame_tools.py');peak=[1];sparse,monomial=frames.install(ce,need,peak) + normal=json.loads((HERE/'inputs/NORMALIZERS.json').read_bytes());roots=list(zip(*normal['mode_columns']));groups={} + for p,row in enumerate(roots):groups.setdefault(tuple(j for j,v in enumerate(row)if v),[]).append(p) + chosen=sorted(groups.items())[:2];ports=sum([ps for _,ps in chosen],[]);n=9;R=ce.fourier(n);Q=ce.fourier(n,[0]);D=ce.fourier(n,range(1,n));defs={};anchors=[] + def define(word): + word=json.loads(json.dumps(word));key=sha256(canonical(word)).hexdigest();defs[key]=word;return key + def literal(word): + op=ce.ident(n) + for e in word: + if e[0]=='P':a=ce.perm(n,e[1]) + elif e[0]=='D':a=ce.diag(n,e[1],e[2]) + elif e[0]=='X':a=ce.xgate(n,e[1]) + elif e[0]=='phase':a=ce.Op(n,ce.identity(n),[tuple(e)]) + else:need(e[0]=='C','known literal');a=ce.cgate(n,e[1],e[2]) + op=op.then(a) + return op + phase_checks=[0] + def equal(A,B,label): + need(A.tab==B.tab,label+' signed tableau');need(sparse(A)==sparse(B),label+' absolute zero column');phase_checks[0]+=1 + def path(before,axes,after,expected): + need(all(e[0]in('P','D','X','phase')for e in before+after),'ordinary-only path wrappers') + actual=literal(before).then(ce.fourier(n,axes)).then(literal(after));equal(actual,expected,'actual paid path') + need(ce.rank([x for x,z,p in actual.tab[n:]])==len(axes),'paid rank') + return {'before_monomial':define(before),'child_axes':list(axes),'after_monomial':define(after),'rank':len(axes)} + normalizers={p:literal(normal['ports'][p]['K_word'])for p in ports};qs={p:normal['ports'][p]['q']for p in ports} + for p,L in normalizers.items():equal(L.then(R),R.then(L),'actual old normalizer centralizes full R') + Krows={};group_records=[];program=[] + def mono(role,p,word,label):program.append(['MONOMIAL',role,p,define(word),label]) + def paid(role,p,old,new,rec):program.append(['PAID_PATH',role,p,old,new,rec]) + for p in ports: + own=ce.canonical_frame(n,[qs[p]]) + mono('X',p,monomial(Q.adjoint().then(normalizers[p]).then(own)).circuit,'virtual_Q_source_entry') + mono('Y',p,normalizers[p].circuit,'original_ground_reader_entry') + for g,(support,ps)in enumerate(chosen): + parity={p:sum(roots[p][j]*roots[p][support[0]]<0 for j in support[1:])&1 for p in ps} + for r in ps:Krows[r]={s:F(int(r==s))-F(sum(a*b for a,b in zip(roots[r],roots[s])),4)for s in ps};Krows[r]={s:v for s,v in Krows[r].items()if v} + need(all(len(Krows[r])==4 and all(abs(v)==F(1,2)for v in Krows[r].values())for r in ps),'actual four signed half K rows') + for parity_bit in [0,1]: + sources=[p for p in ps if parity[p]==parity_bit];readers=[p for p in ps if parity[p]!=parity_bit];S=list(basis(qs[p]for p in sources));other=basis(qs[p]for p in readers) + need(len(S)==len(other)==3 and all(not((a&b).bit_count()&1)for a in S for b in other),'actual orthogonal S3 classes') + Phi=ce.canonical_frame(n,S);cols=ce.basis_extend(S,n);K=frames.native_K(ce,cols);T,anchor=frames.native_full_conjugate(ce,need,monomial,cols);anchors.append(anchor);chart='cube%d:S3:%d'%(g,parity_bit) + entry=path(K.adjoint().circuit,range(3),K.circuit,Phi);exit=path(K.adjoint().circuit,range(3,n),T.circuit,Phi.adjoint().then(R)) + for p in sources: + own=ce.canonical_frame(n,[qs[p]]);flag=[qs[p]] + for v in S: + if len(basis(flag+[v]))>len(flag):flag.append(v) + flags=ce.basis_extend(flag,n);Ks=frames.native_K(ce,flags);small=frames.flag_frame(ce,flags,1);wide=frames.flag_frame(ce,flags,3) + before=monomial(own.adjoint().then(small));after=monomial(wide.adjoint().then(Phi));rec=path(before.circuit+Ks.adjoint().circuit,range(1,3),Ks.circuit+after.circuit,own.adjoint().then(Phi));paid('X',p,'line:'+str(p),chart,rec) + for p in readers:paid('Y',p,'ground',chart,entry) + for r in readers: + for s,v in sorted(Krows[r].items()):need(s in sources,'actual K cross-parity');program.append(['ADD','Y',r,'X',s,v.numerator,v.denominator,chart]) + for p in sources:paid('X',p,chart,'full9',exit) + for p in readers: + V=S[:] + for v in ce.nullspace((qs[p],),n): + if len(basis(V+[v]))>len(V):V.append(v) + need(len(V)==8,'qperp8');vc=ce.basis_extend(V,n);Kv=frames.native_K(ce,vc);low=frames.flag_frame(ce,vc,3);target=frames.flag_frame(ce,vc,8) + before=monomial(Phi.adjoint().then(low));rec=path(before.circuit+Kv.adjoint().circuit,range(3,8),Kv.circuit,Phi.adjoint().then(target));paid('Y',p,chart,'qperp8:'+str(p),rec) + Tv,anchor=frames.native_full_conjugate(ce,need,monomial,vc);anchors.append(anchor) + wrapper=monomial(Kv.adjoint().then(ce.fourier(n,[8])).then(Tv).then(normalizers[p].adjoint()).then(Q.adjoint()));equal(wrapper,target.adjoint().then(normalizers[p].adjoint()).then(D),'reader output wrapper') + mono('Y',p,wrapper.circuit,'reader_D_output') + group_records.append({'cube':g,'source_parity':parity_bit,'sources':sources,'readers':readers,'S3':S}) + for p in ports:mono('X',p,normalizers[p].adjoint().circuit,'source_D_output') + def conjugate(word): + out=[] + for e in word: + if e[0]=='D':out.append(['D',e[1],[(-v)%4 for v in e[2]]]) + elif e[0]=='phase':out.append(['phase',(-e[1])%4]) + else:need(e[0]in('P','X'),'conjugated monomial');out.append(e) + return out + backward=[] + for p in ports:backward.append(['MONOMIAL','X',p,define([['X',1]]),'input_Q_minus2']) + for e in program: + if e[0]=='MONOMIAL':backward.append(['MONOMIAL',e[1],e[2],define(conjugate(defs[e[3]])),'inverse_transpose_'+e[4]]) + elif e[0]=='ADD':backward.append(['ADD',e[3],e[4],e[1],e[2],-e[5],e[6],'conjugate:'+e[7]]) + else: + rec=e[5];new={'before_monomial':define(conjugate(defs[rec['before_monomial']])),'child_axes':rec['child_axes'],'after_monomial':define([['X',sum(1< Date: Sun, 25 Oct 2026 18:49:10 +0800 Subject: [PATCH 5/6] Construct full120 E8 native K from a fifteen-cube cover --- .../full120-e8-native/AUTHOR-PACKAGES.json | 19 + research/full120-e8-native/COLD-REPLAY.json | 165 ++ research/full120-e8-native/FROZEN.json | 225 +++ research/full120-e8-native/LICENSE | 201 ++ research/full120-e8-native/README.md | 78 + research/full120-e8-native/SOURCES.json | 59 + research/full120-e8-native/TASK.json | 80 + research/full120-e8-native/VERIFY.json | 67 + .../COVER.json | 1 + .../FILES.json | 16 + .../NORMALIZERS120.json | 1 + .../PROOF.md | 69 + .../README.md | 64 + .../inputs/NORMALIZERS112.json | 126 ++ .../inputs/clifford_exact.py | 149 ++ .../normalizers120.py | 71 + .../orbit_cover.py | 108 ++ .../FILES.json | 17 + .../NATIVE120-NATIVE-PROGRAM.json.gz | Bin 0 -> 236505 bytes .../NATIVE120-NATIVE.json | 196 ++ .../PROOF.md | 61 + .../README.md | 59 + .../frame_tools.py | 56 + .../inputs/COVER.json | 1 + .../inputs/NORMALIZERS120.json | 1 + .../inputs/clifford_exact.py | 149 ++ .../native120.py | 160 ++ .../FAMILY-GEOMETRY120.json | 1 + .../FILES.json | 21 + .../K-MODULE.json | 73 + .../K-PROGRAM.json.gz | Bin 0 -> 1328463 bytes .../K-TEMPLATE.json | 1637 +++++++++++++++++ .../PROOF.md | 105 ++ .../README.md | 60 + .../core.py | 226 +++ .../family_geometry120.py | 48 + .../frame_tools.py | 56 + .../geometry_tools.py | 91 + .../inputs/COVER.json | 1 + .../inputs/NORMALIZERS.json | 1 + .../inputs/clifford_exact.py | 149 ++ .../full120-e8-native/peer/AFFINE-REPLAY.json | 1 + research/full120-e8-native/peer/FILES.json | 57 + research/full120-e8-native/peer/NOTE.md | 56 + .../full120-e8-native/peer/ODD-BUDGET.json | 1 + research/full120-e8-native/peer/RESULT.json | 1 + .../full120-e8-native/peer/affine_replay.py | 65 + research/full120-e8-native/peer/check.py | 94 + .../full120-e8-native/peer/inputs/COVER.json | 1 + .../inputs/NATIVE120-NATIVE-PROGRAM.json.gz | Bin 0 -> 236505 bytes .../peer/inputs/NORMALIZERS112.json | 126 ++ .../peer/inputs/NORMALIZERS120.json | 1 + .../peer/inputs/affine_oracle.py | 125 ++ .../peer/inputs/clifford_exact.py | 149 ++ research/full120-e8-native/peer/odd_budget.py | 31 + research/full120-e8-native/run.py | 24 + 56 files changed, 5400 insertions(+) create mode 100644 research/full120-e8-native/AUTHOR-PACKAGES.json create mode 100644 research/full120-e8-native/COLD-REPLAY.json create mode 100644 research/full120-e8-native/FROZEN.json create mode 100644 research/full120-e8-native/LICENSE create mode 100644 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/research/full120-e8-native/README.md b/research/full120-e8-native/README.md new file mode 100644 index 0000000000..37771bf7c5 --- /dev/null +++ b/research/full120-e8-native/README.md @@ -0,0 +1,78 @@ +# Full120 E8 native K from a fifteen-cube cover + +The previous odd-E8 native family used112 root lines in14 coordinate-support +cubes. This package includes all120 E8 root lines, finds an explicit15-cube +partition, and compiles its native operators with physical phases. It supplies +a new constructive component. **There is no new kappa or complete Gaussian +supplier claim.** + +Adding eight actual roots2e_i gives M^T M=60I. The exact Weyl-reflection cube +orbit has9450 members; the stored cover partitions all120 roots into15 valid +eight-port native blocks. Each block has two four-port classes with source +and reader q-spans3 and cross-orthogonality. The resulting scalar K satisfies +K^2=I, KM=-M and KC=-C for C=MM^T/4. The new eight ordinary normalizers and +their32 entry/exit wrappers include their absolute phases. + +The emitted n9 forward/backward word has240 arbitrary independent main +inputs, no helpers/COPY/CLEAR, and paid H2/H3/H5/H6 each120 in either direction. +All1440 nonzero main-operator blocks, all zero blocks and four rejecting +mutants are checked. A separate AI-worker interpreter verifies those1440 +blocks with an independent polynomial affine phase backend. The normalized +contracts remain F_K=diag(D,D)L(C_K Q^-1) and +B_K=diag(D,D)U(-Q C_K); Q=C0,D=C_[1,9). + +The odd3 family has3375 product cubes and1,728,000 actual labels in dimension25. +All labels,6750 common S9 classes and15,552,000 q/basis dot products are checked. +One512-owner n25 native instance is fully emitted and replayed, with paid +H8/H9/H15/H16 each512. The generic constructor defines the other cubes; their +complete literal streams were not all materialized. All-width tensor lifting +retains the absolute phase multiplied by width and scalar owner coefficients +applied once. + +The new C_odd nonzero spectrum is225/2 on21504 modes and−1350 on512 modes. +The modal-query density is43/3375, versus5/343 previously: about12.6% lower +per port. Absolute mode count increases to22016 because there are more ports. +If both three-stage halves were independent H73 outputs and the stated +source-consuming E correction were available, the exact price screen leaves +0.08928848513036617 per port per local call, versus0.04382074131724228 before. +This conditional grant is not productive target credit. The negative E +decoder and complete caller are still missing. The separate factor5 price +screen is planning evidence, not an executed factor5 supplier. + +`components/*/PROOF.md` give the source proofs. `peer/NOTE.md` states independent +coverage and the rational price bounds. The sealed source inventories are +retained unchanged; their /tmp discovery paths are provenance, not imports. +`COLD-REPLAY.json` records ten serial isolated normal/optimized source checks +in a fresh directory with all30 payloads unchanged. It does not claim an +OS-readonly filesystem. The registered replay repeats science, not just hashes. + +```sh +python3.12 -I -W error -B research/full120-e8-native/run.py +python3.12 -I -O -W error -B research/full120-e8-native/run.py +python3.12 -B scripts/research_package.py --package research/full120-e8-native +python3.12 -B scripts/check_research_commit.py --package research/full120-e8-native +``` + +Python3.12 and the standard library suffice. Checks are serial. Source gzip +programs compare canonical decompressed content; container hashes authenticate +the frozen bytes only. + +## Open next questions + +The structured questions in TASK.json require a complete paid or changed-target +negative decoder, original-input acquisition, helper ownership, and an actual +whole-caller invoice. Removing low-rank E defects while leaving a pureK-coded +bank is insufficient. Existing ordinary-decoder obstructions, including +[#5508](https://github.com/CrocSwap/integer-mult-bounds/pull/5508), remain credited. +Full E-mode construction, numerical precision, storage/compiler and outer +admission must be separately bound before a Gaussian supplier can be selected. + +Credits: Ali Romman; Dugongue and Dillon Amburgey; Cao Yifan; Cinna Davis, zxv, +Jacob Alan Sussman; the retained real-root/Clifford/native/frame/compiler and +analytic lineage. Generic Weyl and Clifford algebra are classical; the new +work is this exact native-compatible120-root cover and its executable phase +interfaces. Bounded PR/Discussion keyword checks found no identical package; +there is no exhaustive literature or unpublished priority claim. Prepared for +THU New Media Research Center (@thu-nmrc) with substantial OpenAI Codex +assistance, including separate AI-worker review. Apache-2.0; not independent +human, formal-kernel or maintainer scientific acceptance. diff --git a/research/full120-e8-native/SOURCES.json b/research/full120-e8-native/SOURCES.json new file mode 100644 index 0000000000..d22cd031fc --- /dev/null +++ b/research/full120-e8-native/SOURCES.json @@ -0,0 +1,59 @@ +{ + "base_commit": "32890bc5de034ab8fc93ac88ead7279a6a416d04", + "files": [ + { + "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602", + "path": "docs/research/agent-task-catalog.json", + "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72", + "usage": "provenance" + }, + { + "git_blob": "fc3d4ba105e1f097d0d7d051a308281e86ab1446", + "path": "certificates/selected-result.json", + "sha256": "66974efdced4083c00025f97d95d83909a226cdf801edb9301c195c6641f6903", + "usage": "provenance" + }, + { + "git_blob": "bca92c222c395d3d75c047fbb678f3cd0947c60f", + "path": "research/coded-native-caller/NORMALIZERS.json", + "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da", + "usage": "provenance" + }, + { + "git_blob": "166841a037f069249f6f7f6dedb89248812f59e2", + "path": "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py", + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "usage": "provenance" + }, + { + "git_blob": "7ec1c59b7daf19e5215e384fcb9055a497efe3ee", + "path": "research/odd-e8-whole-k-native/frame_tools.py", + "pin": "head:56ba6d7d609124d71c067d6a380caed573963f8f:research/odd-e8-whole-k-native/frame_tools.py", + "sha256": "e5b2ea1f60d554b3a285569602360c663ee8b387350424678b3bd0b0b5432bf4", + "usage": "provenance" + }, + { + "git_blob": "51c529874305069e2ca5f77888cd7610ec6ea165", + "path": "research/odd-e8-whole-k-native/geometry_tools.py", + "pin": "head:56ba6d7d609124d71c067d6a380caed573963f8f:research/odd-e8-whole-k-native/geometry_tools.py", + "sha256": "208d02ef131d0aad635bcb35e3db196fd3298fd5d4fbfbc7fadc672c81ca8261", + "usage": "provenance" + }, + { + "git_blob": "9d190e7b48e376ade8898a04cc9e1ae191e4e5d1", + "path": "research/odd-e8-whole-k-native/core.py", + "pin": "head:56ba6d7d609124d71c067d6a380caed573963f8f:research/odd-e8-whole-k-native/core.py", + "sha256": "482149e6efd593835c084d8e7552c70e4724d6aa6d643dc77c79dda03a1c57df", + "usage": "provenance" + } + ], + "predecessors": { + "geometry": "Ali Romman #5439 oddE8 geometry; retained P112/E8 native/controller/compiler lineage.", + "native_phase": "Earlier wholeK and polarized frame/compiler implementations in ancestor #5464 head56ba6d7d609124d71c067d6a380caed573963f8f, adapted for explicit15cube partitions.", + "new_constructive_work": "Full120 root completion; exhaustive Weyl cube orbit and actual15cube cover; new8 phase normalizers; emitted240-input F/B native;3375cube geometry and n25 root512 native instance.", + "peer": "Separate AI-worker interpreter imports no author scripts; shared exact Clifford primitives and locally developed affine-support phase backend are explicitly retained. Not independent human or proof-kernel review." + }, + "runtime_policy": "All imports and scientific inputs are vendored under this package; no local /tmp origin or sibling repository is needed. README absolute discovery paths in sealed sources are historical provenance only. Canonical decompressed science is compared for gzip artifacts.", + "schema_version": 1, + "scope": "New full120 geometry and native K components. No whole E Gaussian supplier, selected frontier or formal acceptance." +} diff --git a/research/full120-e8-native/TASK.json b/research/full120-e8-native/TASK.json new file mode 100644 index 0000000000..83ab9bbc77 --- /dev/null +++ b/research/full120-e8-native/TASK.json @@ -0,0 +1,80 @@ +{ + "actual_scope": "Construct full120 E8 fifteen-cube native K geometry and phase-complete n9 F/B, with structured odd3 n25 family; independently review phases and conditional modal-density budgets.", + "ai_assistance": "Substantial OpenAI Codex assistance by a lead and separate geometry, physical-compiler and independent-review agents. This is not independent human or formal-kernel review.", + "author": "THU New Media Research Center (@thu-nmrc)", + "base_commit": "32890bc5de034ab8fc93ac88ead7279a6a416d04", + "bottleneck_link": "This changes the base root inventory and native partition while preserving actual paid interfaces. It widens the conditional decoding budget; formal supplier admission still requires a paid decoder or changed caller.", + "budget_minutes": 60, + "evidence": "Components sealed files; exact15-cube cover; NATIVE120 word; n25 root512 word and all3375 binary geometry; independent affine replay and rational intervals.", + "open_questions": [ + { + "blocked_by": "No such decoder is supplied.", + "first_step": "Emit a complete original-input/source-history-aware paid decoder and test every independent column and its physical phases; keep the pureK bulk in the contract.", + "question": "Can the negative E-coded bank be decoded with a profitable actual paid program?", + "why_it_matters": "The positive E half alone does not provide2V independent Gaussian outputs." + }, + { + "blocked_by": "This package is a K component; E and outer admission are separate.", + "first_step": "Instantiate the new225/2 and\u22121350 spectral sectors and actual source-consuming query/inverse/transpose code, then charge the whole caller.", + "question": "Can the new native family be integrated with explicit E modes, numerical precision and the whole compiler?", + "why_it_matters": "K phase words and a favorable conditional density do not close caller/precision/storage obligations." + } + ], + "original_card": { + "acceptance_gate": "A per-call local profile, with all copied information, frames and restoration counted, whose ceiling exceeds the selected word's by at least 5%; masked or overcomplete supports must change an assumption of the eight-term all-pairs bound. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "allowed_variations": [ + "One masked, overcomplete or block decoder family with exact labels and supports.", + "A scoped lower bound on effective rank for one alphabet.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "bottleneck_link": "Rank-1 children are about half of recursive cost; the selected word's effective child rank is about 3.9. Larger-rank delivery lowers recursive cost per unit of paid mass.", + "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin. Ideal budget: rank-16 delivery is 2.31x (levers.py).", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "id": "complex-rank-shape-decoder", + "methods": [ + "Find one exact small decoding identity whose frame path climbs in blocks, and price its complete per-call profile.", + "Bound the best effective child rank achievable for one fixed support alphabet, including copies, frames and restoration." + ], + "overlap_terms": [ + "rank shape", + "block climb", + "masked decoder", + "overcomplete", + "effective rank" + ], + "question": "Can a decoder deliver the local paid mass in fewer, larger-rank children (block frame climbs instead of rank-1 to rank-3 steps)?", + "scope_change_triggers": [ + "Repacking idle remainders of an unchanged word (covered by the packing ceiling).", + "Repeating the eight-term all-pairs search inside its proved scope.", + "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.", + "Searching below C=40 in the #2017 Eisenstein binary scalar-rectangle or fixed-support block-linear additive pairing model; specify a changed premise instead. This bound does not cover every complex decoder.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/complex-decoder-field-extension-seed44/README.md", + "research/complex-frame-pair-decoders/README.md", + "research/selected-k8-unrestricted-ends/README.md", + "research/eisenstein-reduction-copy-floor/README.md" + ] + }, + "outcome": "partial", + "priority_revision": 7, + "schema_version": 1, + "scope_change_reason": "Replace the original112 roots in14 coordinate-support cubes with all120 E8 root lines repartitioned into15 Weyl cubes. Main native paid shape is preserved; nonzero odd3 modal-query density falls from5/343 to43/3375. No negative decoder or admitted Gaussian target is granted.", + "scope_status": "changed", + "stop_rule": "Freeze constructive full120 components. Next expansion must emit a full paid/changed-target negative decoder with input versions and a complete invoice. Conditional screens and modal support alone do not count as admission.", + "task_id": "complex-rank-shape-decoder", + "terminal_changed_premise_gate": "A pre-Q native readout, a fully priced same-stage/nonfitting E code, paid Gaussian correction, or changed caller/target/cohort protocol; terminal-only fixed finite ordinary decoding of the proper-K endpoint is excluded only in the theorem grammar.", + "terminal_scope_extension": "Existing properK and actualE ordinary-decoder obstructions are credited; this construction does not contradict them. Paid/changed producer mechanisms remain open." +} diff --git a/research/full120-e8-native/VERIFY.json b/research/full120-e8-native/VERIFY.json new file mode 100644 index 0000000000..7d80c328ca --- /dev/null +++ b/research/full120-e8-native/VERIFY.json @@ -0,0 +1,67 @@ +{ + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/run.py", + "--part", + "author" + ], + "checks": "Serial exact source geometry/native replay and unchanged files.", + "timeout_seconds": 450 + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-W", + "error", + "-B", + "{package}/run.py", + "--part", + "author" + ], + "checks": "Serial exact source geometry/native replay and unchanged files.", + "timeout_seconds": 450 + }, + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/run.py", + "--part", + "peer" + ], + "checks": "Independent1440-block affine phase interpretation, exact geometry and conditional rational budget; no author imports.", + 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,94,95,109,111,115],[49,50,52,53,59,60,62,63],[49,50,52,53,70,71,73,74],[49,50,52,53,105,106,108,109],[49,50,54,55,59,60,64,65],[49,50,54,55,68,69,73,74],[49,50,54,55,105,106,110,111],[49,50,59,60,96,97,101,102],[49,50,68,69,96,97,108,109],[49,50,70,71,96,97,110,111],[49,51,54,57,59,61,64,115],[49,51,54,69,72,74,76,115],[49,51,54,103,105,107,110,115],[49,52,59,62,93,94,98,99],[49,52,70,73,93,94,104,107],[49,52,72,75,93,94,106,109],[49,53,56,57,59,63,66,115],[49,53,56,67,70,74,76,115],[49,53,56,103,105,109,115,119],[49,54,59,64,93,95,98,100],[49,54,68,73,93,95,103,107],[49,54,72,76,93,95,106,111],[49,56,59,66,93,97,98,102],[49,56,68,75,93,97,103,109],[49,56,70,76,93,97,104,111],[49,57,59,94,96,99,101,115],[49,67,70,94,96,107,110,115],[49,69,72,94,96,109,115,119],[50,51,55,57,60,61,65,115],[50,51,55,68,72,73,76,115],[50,51,55,103,106,107,111,115],[50,52,56,57,60,62,66,115],[50,52,56,67,71,73,76,115],[50,52,56,103,106,108,115,119],[50,53,60,63,93,94,98,99],[50,53,71,74,93,94,104,107],[50,53,72,75,93,94,105,108],[50,55,60,65,93,95,98,100],[50,55,69,74,93,95,103,107],[50,55,72,76,93,95,105,110],[50,56,60,66,93,96,98,101],[50,56,69,75,93,96,103,108],[50,56,71,76,93,96,104,110],[50,57,60,94,97,99,102,115],[50,67,71,94,97,107,111,115],[50,68,72,94,97,108,115,119],[51,52,55,56,61,62,65,66],[51,52,55,56,67,68,71,72],[51,52,55,56,107,108,111,119],[51,52,61,62,95,96,100,101],[51,52,67,68,95,96,104,105],[51,52,74,75,95,96,111,119],[51,53,54,56,61,63,64,66],[51,53,54,56,67,69,70,72],[51,53,54,56,107,109,110,119],[51,53,61,63,95,97,100,102],[51,53,67,69,95,97,104,106],[51,53,73,75,95,97,110,119],[51,54,61,64,94,96,99,101],[51,54,67,70,94,96,103,105],[51,54,74,76,94,96,109,119],[51,55,61,65,94,97,99,102],[51,55,67,71,94,97,103,106],[51,55,73,76,94,97,108,119],[51,57,61,93,95,98,100,115],[51,58,67,92,94,98,103,116],[51,64,73,92,94,101,108,116],[51,65,74,92,94,102,109,116],[51,68,73,93,95,105,110,115],[51,69,74,93,95,106,111,115],[52,53,54,55,62,63,64,65],[52,53,54,55,68,69,70,71],[52,53,54,55,108,109,110,111],[52,53,62,63,96,97,101,102],[52,53,68,69,96,97,105,106],[52,53,73,74,96,97,110,111],[52,54,62,64,94,95,99,100],[52,54,68,70,94,95,103,104],[52,54,75,76,94,95,109,111],[52,56,62,66,94,97,99,102],[52,56,68,72,94,97,103,106],[52,56,73,76,94,97,107,111],[52,57,62,93,96,98,101,115],[52,67,73,93,96,104,110,115],[52,69,75,93,96,106,115,119],[53,55,63,65,94,95,99,100],[53,55,69,71,94,95,103,104],[53,55,75,76,94,95,108,110],[53,56,63,66,94,96,99,101],[53,56,69,72,94,96,103,105],[53,56,74,76,94,96,107,110],[53,57,63,93,97,98,102,115],[53,67,74,93,97,104,111,115],[53,68,75,93,97,105,115,119],[54,55,64,65,96,97,101,102],[54,55,70,71,96,97,105,106],[54,55,73,74,96,97,108,109],[54,56,64,66,95,97,100,102],[54,56,70,72,95,97,104,106],[54,56,73,75,95,97,107,109],[54,58,70,92,96,98,105,116],[54,61,73,92,96,99,108,116],[54,65,76,92,96,102,116,119],[55,56,65,66,95,96,100,101],[55,56,71,72,95,96,104,105],[55,56,74,75,95,96,107,108],[55,58,71,92,97,98,106,116],[55,61,74,92,97,99,109,116],[55,64,76,92,97,101,116,119],[56,77,100,103,113,114,117,118],[57,58,62,64,69,71,75,76],[57,58,62,64,103,104,108,110],[57,58,63,65,68,70,75,76],[57,58,63,65,103,104,109,111],[57,58,68,70,99,100,108,110],[57,58,69,71,99,100,109,111],[57,59,61,64,69,72,74,76],[57,59,61,64,103,105,107,110],[57,59,63,66,67,70,74,76],[57,59,63,66,103,105,109,119],[57,59,67,70,99,101,107,110],[57,59,69,72,99,101,109,119],[57,60,61,65,68,72,73,76],[57,60,61,65,103,106,107,111],[57,60,62,66,67,71,73,76],[57,60,62,66,103,106,108,119],[57,60,67,71,99,102,107,111],[57,60,68,72,99,102,108,119],[57,61,68,73,98,100,105,110],[57,61,69,74,98,100,106,111],[57,62,67,73,98,101,104,110],[57,62,69,75,98,101,106,119],[57,63,67,74,98,102,104,111],[57,63,68,75,98,102,105,119],[57,64,71,75,102,105,107,112],[57,64,72,74,102,104,108,112],[57,65,70,75,101,106,107,112],[57,65,72,73,101,104,109,112],[57,66,70,74,100,106,108,112],[57,66,71,73,100,105,109,112],[58,59,61,62,71,72,74,75],[58,59,61,62,104,105,107,108],[58,59,65,66,67,68,74,75],[58,59,65,66,104,105,111,119],[58,59,67,68,100,101,107,108],[58,59,71,72,100,101,111,119],[58,60,61,63,70,72,73,75],[58,60,61,63,104,106,107,109],[58,60,64,66,67,69,73,75],[58,60,64,66,104,106,110,119],[58,60,67,69,100,102,107,109],[58,60,70,72,100,102,110,119],[58,61,70,73,98,99,105,108],[58,61,71,74,98,99,106,109],[58,62,69,76,102,105,107,112],[58,62,72,74,102,103,110,112],[58,63,68,76,101,106,107,112],[58,63,72,73,101,103,111,112],[58,64,67,73,98,101,103,108],[58,64,71,76,98,101,106,119],[58,65,67,74,98,102,103,109],[58,65,70,76,98,102,105,119],[58,66,68,74,99,106,110,112],[58,66,69,73,99,105,111,112],[59,60,62,63,70,71,73,74],[59,60,62,63,105,106,108,109],[59,60,64,65,68,69,73,74],[59,60,64,65,105,106,110,111],[59,60,68,69,101,102,108,109],[59,60,70,71,101,102,110,111],[59,61,69,76,102,104,108,112],[59,61,71,75,102,103,110,112],[59,62,70,73,98,99,104,107],[59,62,72,75,98,99,106,109],[59,63,67,76,100,106,108,112],[59,63,71,73,100,103,112,119],[59,64,68,73,98,100,103,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This does not claim a full native phase word, terminal E decoder, productive caller, new kappa or scientific adoption.","source_pins":{"COVER_semantic":"151c03c9f527e1bc242e0e6d50bee51f7db3163e4a7ae6a9e54e129328f09f89","NORMALIZERS112":"ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da","clifford":"2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962"},"status":"PASS_FULL120_WEYL_PHASE_LIFTS_AND_NEW8_NORMALIZERS","weyl_permutation_rows":[[1,2,496,8,484,468,436,372,244],[1,2,488,484,16,460,428,364,236],[1,2,472,468,460,32,412,348,220],[1,2,440,436,428,412,64,316,188],[1,2,376,372,364,348,316,128,124],[1,2,248,244,236,220,188,124,256],[1,496,4,8,482,466,434,370,242],[1,488,4,482,16,458,426,362,234],[1,472,4,466,458,32,410,346,218],[1,440,4,434,426,410,64,314,186],[1,376,4,370,362,346,314,128,122],[1,248,4,242,234,218,186,122,256],[1,468,466,8,454,32,406,342,214],[1,436,434,8,422,406,64,310,182],[1,372,370,8,358,342,310,128,118],[1,244,242,8,230,214,182,118,256],[1,460,458,454,16,32,398,334,206],[1,428,426,422,16,398,64,302,174],[1,364,362,358,16,334,302,128,110],[1,236,234,230,16,206,174,110,256],[1,348,346,342,334,32,286,128,94],[1,220,218,214,206,32,158,94,256],[1,316,314,310,302,286,64,128,62],[1,188,186,182,174,158,64,62,256],[1,124,122,118,110,94,62,128,256],[496,2,4,8,481,465,433,369,241],[488,2,4,481,16,457,425,361,233],[472,2,4,465,457,32,409,345,217],[440,2,4,433,425,409,64,313,185],[376,2,4,369,361,345,313,128,121],[248,2,4,241,233,217,185,121,256],[484,2,481,8,16,453,421,357,229],[436,2,433,8,421,405,64,309,181],[372,2,369,8,357,341,309,128,117],[244,2,241,8,229,213,181,117,256],[460,2,457,453,16,32,397,333,205],[364,2,361,357,16,333,301,128,109],[236,2,233,229,16,205,173,109,256],[412,2,409,405,397,32,64,285,157],[348,2,345,341,333,32,285,128,93],[220,2,217,213,205,32,157,93,256],[316,2,313,309,301,285,64,128,61],[188,2,185,181,173,157,64,61,256],[124,2,121,117,109,93,61,128,256],[482,481,4,8,16,451,419,355,227],[466,465,4,8,451,32,403,339,211],[370,369,4,8,355,339,307,128,115],[242,241,4,8,227,211,179,115,256],[426,425,4,419,16,395,64,299,171],[362,361,4,355,16,331,299,128,107],[234,233,4,227,16,203,171,107,256],[410,409,4,403,395,32,64,283,155],[346,345,4,339,331,32,283,128,91],[218,217,4,211,203,32,155,91,256],[314,313,4,307,299,283,64,128,59],[186,185,4,179,171,155,64,59,256],[122,121,4,115,107,91,59,128,256],[454,453,451,8,16,32,391,327,199],[422,421,419,8,16,391,64,295,167],[358,357,355,8,16,327,295,128,103],[230,229,227,8,16,199,167,103,256],[406,405,403,8,391,32,64,279,151],[342,341,339,8,327,32,279,128,87],[214,213,211,8,199,32,151,87,256],[310,309,307,8,295,279,64,128,55],[182,181,179,8,167,151,64,55,256],[118,117,115,8,103,87,55,128,256],[398,397,395,391,16,32,64,271,143],[334,333,331,327,16,32,271,128,79],[206,205,203,199,16,32,143,79,256],[302,301,299,295,16,271,64,128,47],[174,173,171,167,16,143,64,47,256],[110,109,107,103,16,79,47,128,256],[286,285,283,279,271,32,64,128,31],[158,157,155,151,143,32,64,31,256],[94,93,91,87,79,32,31,128,256],[62,61,59,55,47,31,64,128,256],[2,1,4,8,16,32,64,128,256],[4,2,1,8,16,32,64,128,256],[8,2,4,1,16,32,64,128,256],[16,2,4,8,1,32,64,128,256],[32,2,4,8,16,1,64,128,256],[64,2,4,8,16,32,1,128,256],[128,2,4,8,16,32,64,1,256],[256,2,4,8,16,32,64,128,1],[1,4,2,8,16,32,64,128,256],[1,8,4,2,16,32,64,128,256],[1,16,4,8,2,32,64,128,256],[1,32,4,8,16,2,64,128,256],[1,64,4,8,16,32,2,128,256],[1,128,4,8,16,32,64,2,256],[1,256,4,8,16,32,64,128,2],[1,2,8,4,16,32,64,128,256],[1,2,16,8,4,32,64,128,256],[1,2,32,8,16,4,64,128,256],[1,2,64,8,16,32,4,128,256],[1,2,128,8,16,32,64,4,256],[1,2,256,8,16,32,64,128,4],[1,2,4,16,8,32,64,128,256],[1,2,4,32,16,8,64,128,256],[1,2,4,64,16,32,8,128,256],[1,2,4,128,16,32,64,8,256],[1,2,4,256,16,32,64,128,8],[1,2,4,8,32,16,64,128,256],[1,2,4,8,64,32,16,128,256],[1,2,4,8,128,32,64,16,256],[1,2,4,8,256,32,64,128,16],[1,2,4,8,16,64,32,128,256],[1,2,4,8,16,128,64,32,256],[1,2,4,8,16,256,64,128,32],[1,2,4,8,16,32,128,64,256],[1,2,4,8,16,32,256,128,64],[1,2,4,496,488,472,440,376,248],[1,484,482,8,16,454,422,358,230],[468,2,465,8,453,32,405,341,213],[458,457,4,451,16,32,395,331,203],[434,433,4,8,419,403,64,307,179],[428,2,425,421,16,397,64,301,173],[1,412,410,406,398,32,64,286,158],[1,2,4,8,16,32,64,256,128]]} diff --git a/research/full120-e8-native/components/full-e8-cube-cover-20261025-structural/PROOF.md b/research/full120-e8-native/components/full-e8-cube-cover-20261025-structural/PROOF.md new file mode 100644 index 0000000000..472446b2e1 --- /dev/null +++ b/research/full120-e8-native/components/full-e8-cube-cover-20261025-structural/PROOF.md @@ -0,0 +1,69 @@ +# Exact root closure, cube cover and Weyl physical lift + +Let M112 be the retained actual integer root rows, all norm squared4. Add +r_(112+i)=2e_i. The supplied binary labels q for the additional roots are +7,25,42,52,76,82,97,127. The verifier checks every14,400 pair: all q are +norm one and distinct, and for i!=j, real root inner product nonzero is +equivalent to binary q_i.q_j=0. All real roots have squared norm4. + +For each actual root r, reflection sends s to s-(s.r)r/2. Every coefficient +is integral, and the reflected vector equals one of the120 retained roots +up to sign. The120 projective root actions are exact involutory permutations. +The complete Gram M^T M is60I8, checked on all64 entries. + +An original eight-root support cube has C_b=M_b M_b^T/4 with C_b^2=2C_b. +Reflection preserves its Gram up to root row signs, preserving this identity. +The verifier nevertheless checks every9450 orbit cube directly. Trace C_b=8 +then gives rank4. K_b=I-C_b is a symmetric involution, zero diagonal, with +four signed-half entries per row, whose graph is complete bipartite4-by4. +For both actual q parity classes it verifies rank3 of the binary span and +orthogonality of the two spans. It does not assume that a Weyl transformation +preserves the old four-coordinate support grouping. + +Algorithm X uses the finite9450-cube orbit and searches the smallest +uncovered root column. The emitted15-cube cover is verified by sorting all +120 covered port indices and checking each appears once. Each selected cube +also retains its root-reflection route from an original cube. No search +failure or floating point judgment is involved: a full exact cover is output. + +For every selected block, C_b M_b=2M_b, hence K_b M_b=-M_b. Concatenating +blocks gives KM=-M. Since K is symmetric, KC=CK=-C. Together with K^2=I +and C^2=15C this proves + + (K+C/14)(K+C)=I. + +The program independently checks all14,400 actual K^2 and KC blocks and all +960 KM entries. This changes the whole owner scalar code; it does not make +Q^-1 E Q ordinary or solve the negative terminal bank. + +For the physical lift put c=511 and u=q_r+c. Every actual u has weight2 or6. +The binary transvection O_r=I+u u^T is orthogonal and maps + + q_s -> q_s+(1+q_s.q_r)(q_r+c), + +which is checked against every actual real-root permutation action. If +u.x=1, its Hamming-weight change is wt(u)-2wt(u&x), divisible by4 because +wt(u)=2 mod4 and the overlap is odd. Otherwise x is unchanged. Thus O_r +preserves weight modulo4 at every address. The exact full Gaussian kernel +only depends on the weight of the address difference modulo4, so the +ordinary permutation P(O_r) commutes with R9 including scalar phase. +All61,440 address congruences,120 signed tableaux and120 exact zero columns +are checked with the retained Gaussian-dyadic Clifford compiler. + +To reach a new axis root choose an actual old root s and reflection r with +s_r(s)=the new root up to sign. Set L_new=P(O_r)L_old. This is an emitted +ordinary word, commutes with R9 exactly and maps the central line to the +new q line. For canonical own-line Phi_q and hyperplane Phi_(q-perp), the +four forward wrappers are + + Phi_q L Q^-1, L, L^-1, D L^-1 Phi_(q-perp)^-1. + +Each is compiled to literal P/D/X/phase, with its signed tableau and +absolute zero column checked. There is no hidden paid Gaussian in a wrapper. + +Every single-address-column identity lifts columnwise to all positive field +widths; a scalar phase i^theta becomes i^(f theta). Each owner coefficient +is applied once outside this tensor power. Nothing tensors an owner sum. +The explicit cube partition supplies the generic source line->S3->R and +reader ground->S3->q-perp flags, with Gaussian ranks2,6,3,5 respectively. +Actual phase-native emission is a separate successor package. diff --git a/research/full120-e8-native/components/full-e8-cube-cover-20261025-structural/README.md b/research/full120-e8-native/components/full-e8-cube-cover-20261025-structural/README.md new file mode 100644 index 0000000000..cfe6b0ecbc --- /dev/null +++ b/research/full120-e8-native/components/full-e8-cube-cover-20261025-structural/README.md @@ -0,0 +1,64 @@ +# Full120 E8: a new15-cube native inventory with actual physical normalizers + +The actual P112 geometry extends to all120 projective E8 roots by appending +2e_i for i=0..7, with binary labels7,25,42,52,76,82,97,127. The full set is +closed under every one of its120 root reflections. The 14 original cubes +generate an orbit of9450 eight-root cubes. Every cube in this orbit passes +the actual binary native geometry test, and an exact cover partitions all +120 roots into15 cubes. The eight additional roots are mixed into seven +new blocks; they are not assumed to form an involutory isolated block. + +COVER.json contains all exact root/reflection/orbit/cover data. The complete +real mode Gram is60I, so C=MM^T/4 has eigenvalue15 on eight modes. For the +new block native K, K^2=I, KM=-M and KC=CK=-C. Thus A=I-C has eigenvalues +1 and-14, A^-1=(A+13I)/14, E=K+C/14 and E^-1=K+C. + +NORMALIZERS120.json preserves the `mode_columns`, `ports[*].q` and +`ports[*].K_word` consumer interface. It adds the explicit `cover15` +partition, which must replace grouping by four-coordinate root support. +All120 Weyl lifts are ordinary binary P matrices preserving weight modulo4, +and commute exactly with full R9. Each of the eight new normalizers is one +old normalizer followed by one such actual P. All32 new forward frame +wrappers are emitted as literal ordinary P/D/X/phase words, with absolute +phase checked. + +The generic native rank profile for this actual base inventory is120 +children of each H2,H3,H5,H6, with240 arbitrary original main fields. +The complete phase-native F/B word is separate work in +`/tmp/full-e8-native120-20261025-structural`. + +The odd3 geometry has120^3=1,728,000 owners and modal rank22,016, reducing +the modal ratio from5/343 to43/3375. Its nonzero C spectrum is225/2 on +21,504 modes and-1350 on512 modes. Global physical cube geometry and a +phase-complete n25 representative are separate work in +`/tmp/full-e8-odd3-native120-20261025-structural`. + +There is no terminal E decoder, complete productive caller, new kappa, +scientific adoption or selected-frontier change in this package. + +Read-only reproduction, Python3.11+ standard library: + +``` +python3.11 orbit_cover.py +python3.11 -O orbit_cover.py +python3.11 normalizers120.py +python3.11 -O normalizers120.py +``` + +All four normal/optimized checks pass. Default commands compare semantic +receipts and do not write. `--write` is explicit author mode. + +Credit the retained E8/P112 root data, Dugongue's PR4929 coded source, the +coded-native-caller normalizers and original Clifford/compiler lineage, +and Ali Romman's odd-E8 direct-sum framework. New material uses substantial +OpenAI Codex assistance. Apache-2.0; no independent human or kernel review +is claimed. + +## Open next questions + +- Install the explicit15-cube partition in the actual phase-native source; + verify all240 independent main columns, paid paths and inverse-transpose. +- Verify the entire15^3 family in one global I25 coordinate chart and emit + a phase-complete product cube containing the added roots. +- Retain the uncancelled terminal code E. A paid decoder or changed target + caller remains necessary before any improved multiplication bound. diff --git a/research/full120-e8-native/components/full-e8-cube-cover-20261025-structural/inputs/NORMALIZERS112.json b/research/full120-e8-native/components/full-e8-cube-cover-20261025-structural/inputs/NORMALIZERS112.json new file mode 100644 index 0000000000..bca92c222c --- /dev/null +++ b/research/full120-e8-native/components/full-e8-cube-cover-20261025-structural/inputs/NORMALIZERS112.json @@ -0,0 +1,126 @@ +{ + "clifford_sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "code_sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0", + "finite_checks": {"absolute_phase_mutations_rejected":112,"exact_endpoint_factor_identities":896,"gaussian_free_compiled_wrappers":896,"monomial_wrappers":896,"omitted_phase_rejections":112,"ports":112,"scalar_basis_recodings":224,"weight_congruence_addresses":57344}, + "local_gauge_bill": 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+ ], + "recoding_bill": {"forward_prefix_component_l1_upper":57,"forward_update_coefficient":"-1/4","inverse_output_prefix_component_l1_upper":"69/13","inverse_prefix_component_l1_upper":56,"inverse_update_coefficient":"-1/52","monomial_field_maps":224,"output_scaled_adds":448,"owned_fields":8,"owned_initial_clears":8,"owned_terminal_clears":8,"signed_mode_adds":448}, + "schema": "coded-native-real-normalizers/1", + "scope": "Exact physical central ABI and local gauges; not full-controller or multiplication admission.", + "source_payload_sha256": "cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd", + "status": "PASS_CODED_NATIVE_REAL_NORMALIZERS" +} diff --git a/research/full120-e8-native/components/full-e8-cube-cover-20261025-structural/inputs/clifford_exact.py b/research/full120-e8-native/components/full-e8-cube-cover-20261025-structural/inputs/clifford_exact.py new file mode 100644 index 0000000000..166841a037 --- /dev/null +++ b/research/full120-e8-native/components/full-e8-cube-cover-20261025-structural/inputs/clifford_exact.py @@ -0,0 +1,149 @@ +"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals. +Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d. +The tableau is supplemented by a literal circuit, so global phases are kept. +""" +from dataclasses import dataclass + +def parity(x):return x.bit_count()&1 +def rank(rows): + p={} + for x in rows: + while x: + b=x.bit_length()-1 + if b not in p:p[b]=x;break + x^=p[b] + return len(p) +def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<>j&1);a[j],a[k]=a[k],a[j] + for i in range(n): + if i!=j and a[i]>>j&1:a[i]^=a[j] + assert [r&((1<>n for r in a) +def basis_extend(cols,n): + out=[] + for x in list(cols)+[1<len(out):out.append(x) + assert len(out)==n + return tuple(out) +def nullspace(rows,n): + a=list(rows);p=[];k=0 + for j in range(n): + t=next((i for i in range(k,len(a)) if a[i]>>j&1),None) + if t is None:continue + a[t],a[k]=a[k],a[t] + for i in range(len(a)): + if i!=k and a[i]>>j&1:a[i]^=a[k] + p.append(j);k+=1 + return tuple((1<>j)&1)<>i&1:out=pmul(out,T[i]) + for i in range(n): + if z>>i&1:out=pmul(out,T[n+i]) + return out +def compose(A,B):return tuple(apply(A,p) for p in B) +def inverse(T): + n=len(T)//2;cols=[x|(z<>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4)) + return tuple(out) +def qvalue(Q,alpha,x,n): + return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4 +def mul_i(a,p): + x,y=a;p%=4 + return [(x,y),(-y,x),(-x,-y),(y,-x)][p] +@dataclass +class Op: + n:int + tab:tuple + circuit:list + def then(self,b): + assert self.n==b.n + return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit) + def adjoint(self): + circ=[] + for e in reversed(self.circuit): + if e[0]=='P':circ.append(('P',inv(e[1],self.n))) + elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2]))) + elif e[0]=='C':circ.append(('C',e[1],-e[2])) + elif e[0]=='phase':circ.append(('phase',(-e[1])%4)) + else:circ.append(e) + return Op(self.n,inverse(self.tab),circ) + def zero_state(self,basis=0): + N=1<>i)&1 for i in range(n)) + assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n)) + return Op(n,tuple([(1<>i&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>i)&1)) for i in range(n)]),[('X',b)]) +def fourier(n,axes=None): + out=ident(n) + for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<len(selected):picks.append(j);selected.append(x) + assert len(picks)==r and all(x>>r==0 for x in Bcols) + Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<>j&1 else 0)for j in range(n));P=ce.perm(n,G) + need(u.bit_count()%4==2,'all root Weyl transvection weights2mod4') + for j,qs in enumerate(q): + need(ce.mv(G,qs)==q[cover['reflection_permutations'][ri][j]],'binary Weyl action equals actual realroot reflection') + need(all((ce.mv(G,x).bit_count()-x.bit_count())%4==0 for x in range(512)),'actual all-address weight modulo4') + need(P.then(R).tab==R.then(P).tab and P.then(R).zero_state()==R.then(P).zero_state(),'Weyl P exact signed tableau and absolute phase commutation') + ref.append(G);checks+=1 + def literal(word): + U=ce.ident(n) + for e in word: + if e[0]=='P':V=ce.perm(n,e[1]) + elif e[0]=='D':V=ce.diag(n,e[1],e[2]) + elif e[0]=='X':V=ce.xgate(n,e[1]) + else:need(e[0]=='phase','ordinary literal only');V=ce.Op(n,ce.identity(n),[tuple(e)]) + U=U.then(V) + return U + ports=[dict(p)for p in old['ports']];new=[] + for p in range(112,120): + found=next((j,r)for j in range(112)for r,perm in enumerate(cover['reflection_permutations'])if perm[j]==p) + j,r=found;word=old['ports'][j]['K_word']+[['P',list(ref[r])]];L=literal(word) + need(ce.mv(ref[r],q[j])==q[p],'actual newly reached rootlabel') + need(L.then(R).tab==R.then(L).tab and L.then(R).zero_state()==R.then(L).zero_state(),'actual new Li fullR exactcommutation') + need(L.tab[0][0]==q[p]and L.tab[0][1]==0,'actual Li maps central X translation to q') + own=ce.canonical_frame(n,[q[p]]);hyper=ce.canonical_frame(n,ce.nullspace([q[p]],n)) + maps={'input_X':Q.adjoint().then(L).then(own),'input_Y':L,'output_X':L.adjoint(),'output_Y':hyper.adjoint().then(L.adjoint()).then(D)} + compiled={} + for name,U in maps.items(): + need(ce.rank([x for x,z,t in U.tab[n:]])==0,'actual newly normalized wrapper ordinary') + out,recipe=ce.monomial(U);need(out.tab==U.tab and out.zero_state()==U.zero_state(),'actual wrapper full signed tableau and absolute phase') + need(all(e[0]in ['P','D','X','phase']for e in out.circuit),'no hidden Gaussian wrapper') + compiled[name]={'word':out.circuit,'recipe':recipe} + rec={'port':p,'q':q[p],'K_word':word,'origin_old_port':j,'weyl_root_reflection':r,'weyl_orthogonal_matrix_rows':ref[r],'compiled_wrappers':compiled} + ports.append(rec);new.append(rec) + # Independent actual full scalar K,C proof after the new cube recoding. + K=[{}for i in range(120)] + for block in cover['cover15']: + for i in block['ports']: + for j in block['ports']: + a=F(i==j)-F(sum(x*y for x,y in zip(M[i],M[j])),4) + if a:K[i][j]=a + C=[[F(sum(x*y for x,y in zip(a,b)),4)for b in M]for a in M] + need(all(sum(co*F(M[j][a])for j,co in K[i].items())==-M[i][a]for i,a in product(range(120),range(8))),'actual global K M=-M') + need(all(sum(co*K[j].get(k,F())for j,co in K[i].items())==int(i==k)for i,k in product(range(120),repeat=2)),'actual full120 K squaredI') + need(all(sum(co*C[j][k]for j,co in K[i].items())==-C[i][k]for i,k in product(range(120),repeat=2)),'all14400 actual K C=-C blocks') + Ei=[[K[i].get(j,F())+C[i][j]for j in range(120)]for i in range(120)];E=[[K[i].get(j,F())+C[i][j]/14 for j in range(120)]for i in range(120)] + # Efficient identity follows exactly from the independently checked KC, + # K^2 and C^2=15C; verify the latter on all blocks using M^TM=60I. + need(all(F(sum(M[i][a]*60*M[j][a]for a in range(8)),16)==15*C[i][j]for i,j in product(range(120),repeat=2)),'actual allblocks C squared15C') + payload={'schema':'full120-actual-Weyl-lift-and-normalizers/v1','status':'PASS_FULL120_WEYL_PHASE_LIFTS_AND_NEW8_NORMALIZERS','mode_columns':[list(x)for x in zip(*M)],'ports':ports,'new8':new,'weyl_permutation_rows':ref,'cover15':cover['cover15'],'scalar_K_rows':[[[j,str(a)]for j,a in sorted(row.items())]for row in K],'scalar_C':'MM^T/4','scalar_E':'K+C/14','scalar_E_inverse':'K+C','identity':'K^2=I, KC=CK=-C, C^2=15C; (K+C/14)(K+C)=I','finite_checks':{'all_reflections':120,'weight_congruence_addresses':120*512,'actual_q_actions':120**2,'phase_complete_new8_normalizers':8,'phase_complete_new8_wrappers':32,'global_KM_entries':120*8,'global_KC_entries':120**2,'global_K_squared_entries':120**2},'source_pins':{'NORMALIZERS112':sha256((HERE/'inputs/NORMALIZERS112.json').read_bytes()).hexdigest(),'clifford':CEP,'COVER_semantic':sha256(canon(cover)).hexdigest()},'phase_scope':'Every Weyl lift is an actual ordinary binary P matrix, weight-preserving modulo4, hence fullR commutation including absolute phase for every positive column width. Old Li is followed chronologically by P_Weyl; new8 output/input wrappers are compiled literal P/D/X/phase only. Owner scalar coefficients are applied once outside address tensor powers.','scope':'Actual full120 cube geometry and compatible normalizer/frame data. This does not claim a full native phase word, terminal E decoder, productive caller, new kappa or scientific adoption.','new_kappa':False} + return json.loads(canon(payload)) +if __name__=='__main__': + ap=argparse.ArgumentParser();ap.add_argument('--write',action='store_true');a=ap.parse_args();d=calculate();p=HERE/'NORMALIZERS120.json' + if a.write:p.write_bytes(canon(d)) + else:need(json.loads(p.read_bytes())==d,'read-only new120 normalizer receipt') + print(json.dumps({k:d[k]for k in ['status','finite_checks','scalar_E','scalar_E_inverse','new_kappa']},sort_keys=True)) diff --git a/research/full120-e8-native/components/full-e8-cube-cover-20261025-structural/orbit_cover.py b/research/full120-e8-native/components/full-e8-cube-cover-20261025-structural/orbit_cover.py new file mode 100644 index 0000000000..cb7e82d547 --- /dev/null +++ b/research/full120-e8-native/components/full-e8-cube-cover-20261025-structural/orbit_cover.py @@ -0,0 +1,108 @@ +"""Full120 E8 projective roots: exact Weyl cube orbit and exact cover. +Apache-2.0; retained P112/E8 lineage, substantial OpenAI Codex assistance. +""" +from pathlib import Path +from fractions import Fraction as F +from collections import Counter,deque +from hashlib import sha256 +from itertools import product +import argparse,json,time +HERE=Path(__file__).resolve().parent +PIN='ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da' +NEW_Q=[7,25,42,52,76,82,97,127] +def need(a,b): + if not a:raise ValueError(b) +def canon(x):return(json.dumps(x,sort_keys=True,separators=(',',':'))+'\n').encode() +def dot(a,b):return sum(x*y for x,y in zip(a,b)) +def binarydot(a,b):return(a&b).bit_count()&1 +def oriented(r): + r=tuple(r) + return tuple(-x for x in r)if next(x for x in r if x)<0 else r +def basis(rows): + p={} + for x in rows: + for j in sorted(p,reverse=True): + if x>>j&1:x^=p[j] + if x:p[x.bit_length()-1]=x + return tuple(p[j]for j in sorted(p,reverse=True)) +def calculate(): + start=time.monotonic();raw=(HERE/'inputs/NORMALIZERS112.json').read_bytes();need(sha256(raw).hexdigest()==PIN,'actual112 input pin');d=json.loads(raw) + M=[tuple(r)for r in zip(*d['mode_columns'])]+[tuple(2*int(i==j)for j in range(8))for i in range(8)] + q=[p['q']for p in d['ports']]+NEW_Q;roots={oriented(r):i for i,r in enumerate(M)} + need(len(M)==len(q)==len(roots)==len(set(q))==120,'full120 roots and binarylabels distinct') + need(all(dot(r,r)==4 for r in M)and all(binarydot(x,x)==1 for x in q),'norms') + need(all(sum(M[k][i]*M[k][j]for k in range(120))==60*int(i==j)for i,j in product(range(8),repeat=2)),'full real mode Gram60I') + pairtypes=Counter() + for i,j in product(range(120),repeat=2): + rdot=dot(M[i],M[j]);qd=binarydot(q[i],q[j]);pairtypes[rdot,qd,i==j]+=1 + need((not qd)==(i!=j and rdot!=0),'full A exact nonzero support iff q orthogonal') + # Every projective Weyl reflection is an actual full120 permutation. + perms=[] + for r in M: + perm=[] + for s in M: + a=dot(s,r);need(a%2==0,'integral E8 reflection coefficient');t=oriented(tuple(x-a//2*y for x,y in zip(s,r)));need(t in roots,'actual full E8 reflection closes');perm.append(roots[t]) + need(sorted(perm)==list(range(120))and all(perm[perm[j]]==j for j in range(120)),'actual involutory root permutation');perms.append(tuple(perm)) + initial={} + for i,row in enumerate(M[:112]):initial.setdefault(tuple(j for j,x in enumerate(row)if x),[]).append(i) + seeds=[tuple(ps)for _,ps in sorted(initial.items())];need(len(seeds)==14 and all(len(s)==8 for s in seeds),'actual14 original cubes') + # The orbit under all projective root reflections, not a root-support guess. + seen=set(seeds);todo=list(seeds);parents={s:None for s in seeds};pos=0 + while pos0,'actual nativegood cube candidates') + # Algorithm X with smallest uncovered column, deterministic exact cover. + masks={i:sum(1<

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