From 29fe88ba218b5d2192d8e31f07a01d1141afdacd Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Sun, 25 Oct 2026 16:09:38 -0500 Subject: [PATCH 1/6] Improve conditional kappa with independent P104 helper splits --- research/p104-helper-subspace-splits/NOTICE | 20 + research/p104-helper-subspace-splits/PROOF.md | 204 ++++++++ .../p104-helper-subspace-splits/README.md | 145 +++++ .../p104-helper-subspace-splits/RESULT.json | 495 ++++++++++++++++++ .../p104-helper-subspace-splits/SOURCES.json | 104 ++++ .../p104-helper-subspace-splits/SPLITS.json | 457 ++++++++++++++++ .../p104-helper-subspace-splits/TASK.json | 72 +++ .../p104-helper-subspace-splits/VALIDATION.md | 37 ++ .../p104-helper-subspace-splits/VERIFY.json | 41 ++ .../p104-helper-subspace-splits/WORD.json.gz | Bin 0 -> 108157 bytes .../p104-helper-subspace-splits/construct.py | 157 ++++++ .../inputs/PR5580-WORD.json.gz | Bin 0 -> 105115 bytes research/p104-helper-subspace-splits/local.py | 206 ++++++++ .../p104-helper-subspace-splits/pricing.py | 169 ++++++ .../p104-helper-subspace-splits/search.py | 155 ++++++ .../p104-helper-subspace-splits/verify.py | 130 +++++ 16 files changed, 2392 insertions(+) create mode 100644 research/p104-helper-subspace-splits/NOTICE create mode 100644 research/p104-helper-subspace-splits/PROOF.md create mode 100644 research/p104-helper-subspace-splits/README.md create mode 100644 research/p104-helper-subspace-splits/RESULT.json create mode 100644 research/p104-helper-subspace-splits/SOURCES.json create mode 100644 research/p104-helper-subspace-splits/SPLITS.json create mode 100644 research/p104-helper-subspace-splits/TASK.json create mode 100644 research/p104-helper-subspace-splits/VALIDATION.md create mode 100644 research/p104-helper-subspace-splits/VERIFY.json create mode 100644 research/p104-helper-subspace-splits/WORD.json.gz create mode 100644 research/p104-helper-subspace-splits/construct.py create mode 100644 research/p104-helper-subspace-splits/inputs/PR5580-WORD.json.gz create mode 100644 research/p104-helper-subspace-splits/local.py create mode 100644 research/p104-helper-subspace-splits/pricing.py create mode 100644 research/p104-helper-subspace-splits/search.py create mode 100644 research/p104-helper-subspace-splits/verify.py diff --git a/research/p104-helper-subspace-splits/NOTICE b/research/p104-helper-subspace-splits/NOTICE new file mode 100644 index 0000000000..a3f5136a05 --- /dev/null +++ b/research/p104-helper-subspace-splits/NOTICE @@ -0,0 +1,20 @@ +New helper-subspace construction, proof and replay: +Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. +The same assistant performed the construction and author-side checks. + +Retained contributions: +Ali Romman: PR5580 contact step and PR5544/5545 complete P104 caller. +Joel Pulikkan (GamingPuzzled): PR5569 priced helper handoff. +DreamingOfClouds: PR5561 free helper endpoints and PR5568 search tools. +thu-nmrc: PR5551 contact improvements. +Gareth Davidson (bitplane): PR2305 source composition. +David Arias: PR2152 coalesced P104 word. +Cinna Davis: PR2219 private reuse and the controller lineage. +Jacob Alan Sussman: productive mixed-target recursion. +zxv and Cao Yifan: exact intervals, compiler and native/pricing lineage. +GamingPuzzled: PR5472 successor handoff, a predecessor to the split concept. +The retained source notices preserve earlier geometry, BIT and analytic credit. + +The elementary rank-one basis identity is not claimed as a new general +linear-algebra theorem. The contribution is its explicit independent-target +use on this P104 word and the complete conditional kappa improvement. diff --git a/research/p104-helper-subspace-splits/PROOF.md b/research/p104-helper-subspace-splits/PROOF.md new file mode 100644 index 0000000000..e479b15351 --- /dev/null +++ b/research/p104-helper-subspace-splits/PROOF.md @@ -0,0 +1,204 @@ +# Independent helper splits and the complete cost + +This proof changes the helper input and output contract of the exact PR5580 +word. It retains every main endpoint, paid Gaussian call and owned lifetime. +All scalar identities below are over the rationals. The native check supplies +exact phases and the rule for every positive tensor width. + +## 1. A split criterion + +Let a group of helpers have the same initial chart U and final chart V. +The complete source word returns each of these helpers unchanged in normalized +coordinates and has no helper contribution to any other output. +Let F be a strict intermediate chart, with U contained in F and F contained +in V. At one chronological cut, let P be the scalar prefix matrix and S the +scalar suffix matrix. The matrices include every public input and output. +Owned fields follow the source initialization and erasure contract. + +Suppose a row a and a column b use only fields at chart F. Suppose c and d +use only the specified helper group, and + +```math +aP=c,\qquad Sb=d,\qquad ab=cd=1. +``` + +Choose a helper role p at F. There are invertible scalar matrices G and J +with + +```math +e_p^T G=c,\quad Gd=e_p,\qquad e_p^T J=a,\quad Jb=e_p. +``` + +Here G acts only on helpers with boundary charts U and V. J acts only on +fields at F. The construction emits these matrices as ADD and dyadic-unit +SCALE operations. Its row and column elimination uses the unit pairings. +The emitted program and its inverse are explicit; no dense matrix operation +is assigned zero implementation cost. + +Apply G inverse at the input. At the cut, apply J. Role p then contains the +independent coordinate t=c h. Retain p as an output at F. Introduce one new +independent input z at F. Use its new role in place of p in J inverse and in +the complete suffix. Finally apply G at V, with the same role substitution. +The suffix state changes by b(z-a P h), so its helper output is + +```math +h+d(z-ch). +``` + +The final change of basis gives + +```math +G[h+d(z-ch)]=Gh+e_p(z-t). +``` + +Thus the former p coordinate is replaced by the independent z coordinate; +all other helper coordinates and every main output retain their required +values. The old t coordinate has already been returned at F. This replaces +one U-to-V target by a U-to-F target and an F-to-V target. + +This uses a new input, not two outputs computed from one input. It does not +assume a helper is zero. The early output is a public field and stays live +until the caller returns. The successor input is public from the start and +is first used at the cut. No new COPY, CLEAR or owned lifetime is introduced. +The source's owned erasures remain charged under the inherited contract. + +All three basis changes use common physical charts. They therefore commute +with the relevant chart operator. Native normalization gives ranks +`dim(F)-dim(U)` and `dim(V)-dim(F)` with their exact phases. Scalar coefficients +stay outside the tensor substitution. The frame induction applies at every +positive width; it is not a test at width one alone. + +## 2. The first explicit split + +The source is PR5580 at `6efa248cf456d6101d757e9d09ba29711d18a13a`. +Use the cut after zero-based event 13778, chart 120 of dimension five, and +pivot 648. The boundary group has initial chart 3 (dimension zero) and final +chart 127 (dimension nine). With e_r the coordinate at role r, the exact +vectors are + +```math +a=e_{651}^T+(e_{648}^T+e_{649}^T)/2,\quad +b=e_{648}+e_{649}-e_{650}-e_{652}, +``` + +```math +c=(e_{648}^T+e_{649}^T)/2,\quad +d=e_{648}+e_{649}-e_{650}-e_{652}+2e_{205}. +``` + +The complete prefix gives aP=c; the complete suffix gives Sb=d. +Both pairings are one. The first basis change uses five ADDs, the local +basis uses five ADDs, and their two inverses use ten more ADDs. The first +split therefore adds 20 scalar events and replaces H9 by H5 and H4. +A later split divides this particular H5 target further. The full sequence, +including each updated event index, is in `SPLITS.json`. + +`check_cut` reconstructs each prefix functional and propagates each suffix +column. It checks that all other input and output coefficients are zero. +The verifier then checks every public and owned row after each complete +split. A separate dense-integer transpose replay checks all 574,564 entries +of the final 758 by 758 interface. + +## 3. The complete target change + +The fifteen splits are + +- six H9 to H4 + H5; +- five H9 to H2 + H7; +- three H9 to H1 + H8; +- one H5 to H1 + H4. + +They add 15 independent helper inputs. The source's 735 public fields become +750, of which 542 are helpers and 208 are main fields. Eight owned lifetime +roles remain; only one is live at a time. The 25,140 source events become +25,502. Every source paid occurrence remains, with the same ordered pair of +charts, rank and ownership. Some register names change to identify the +successor input. The new local helper profile is + +```text +{1:4, 2:5, 4:90, 5:10, 7:5, 8:18, 9:410}. +``` + +For every 0(a+b)^t`. Each split strictly increases the target moment and leaves +the paid moment fixed. The signed local target change is + +```math +4H_1+5H_2+7H_4+5H_5+5H_7+3H_8-14H_9. +``` + +Its rank mass is zero, as required. A source-bound complete caller, not a +standalone packing relaxation, supplies the resulting exponent claim. + +## 4. Native maps and the caller + +The exact signed-Pauli and phase verifiers check every paid chart change, +every helper target and every main adapter. The local replay checks a strict +nested chart relation on each public move and the source's descending owned +moves. Each helper target is strictly productive. + +Cinna Davis's p16/a7 controller and Ali Romman's all-forward implementation +from PR5544 remain literal inputs. All 18 full calls use the new local word +with fresh independent helpers. Sixteen backward main interfaces use the +retained signed exchanges and central-square translations. These wrappers +act only on the main pair. They do not alter a new helper output. + +The physical caller check retains all 104 central ports, 7,488 boundary +contacts, 53,248 central-square column checks, 3,328 main Gaussian targets, +15 thin query sites and 3,120 whole idle jobs. It checks native routes, +spectators, exact phases and every whole target. The complete counts are + +```text +paid calls: 66852 +productive fields: 13084 = 18*542 + 32*104 +rank mass surplus: 760 +maximum target: 145 +maximum paid rank: 72 +``` + +The invoice is counted twice, once from literal events and once from the +controller path lengths. Input and output normalizers, added scalar basis +operations, routes, owned allocation and erasure, queries and idles are all +included. The new independent field count enters the completion-tail bound. +It is not left at the old 12,814 value. + +## 5. Strictification, compiler and outer transfer + +Two independent rational interval engines evaluate the complete moments. +The exact raw crossing is in (0.00309839352211, 0.00309839352212). +`RESULT.json` gives its rational endpoints and the strict tested margin. The claimed kappa is 0.00309839 and the tested saving is +0.0030983905. Their gap funds the finite compiler and outer parameters. An exact negative +derivative bound on [0,0.0034] makes this crossing the raw ceiling for this +fixed invoice under the retained BIT cap. It is not a global optimum. + +Power 1024, cutoff 17, target floor 18 and tail offset 1/5 are retained. +The extra independent fields require a different tail bound: both charged +tail ratios are below 39/40, and `(39/40)^128 < 1/16`. Eight such blocks still +give the retained `2^-32` remainder. The fixed reserve is `10^-10`. +The complete normalized cost is strictly less than one. The old cutoff 20 +fails and is retained as a control. + +The compiler checks its finite integer threshold, initial range, shifted +exits, complement capacity, logarithm power 1024 and predecessor integer point. The old logarithm +power 1000 does not meet the new complement-capacity inequality. +The ordinary BIT saving remains 0.0034. All 54 strict outer conditions and +four functional conditions are checked with exact rational arithmetic. +The scalar growth bound uses fewer than 26,000 local operations and the +retained per-operation bound. The native growth bound uses the actual sum +of local paid ranks. The complete ordinary-work allowance remains below +`10^9`; the local scalar and route allowance remains below `10^7` per call. + +## 6. Scope of acceptance + +The five selected framework assumptions remain: native implementation at +all widths, owned erasure, uniform compiler closure, precision and tape +cost, and analytic integer recovery. The source helper-endpoint contract +also remains. This package proves the new finite interface, the chart +identities and every new numerical condition within that framework. + +The enormous uniform word and complete rounded multiplier are not +materialized. These are author-side checks by the same AI-assisted author. +They are not independent human acceptance or a proof-kernel theorem. +Two greedy cut orders on PR5569 reached the same fifteen-split histogram. +That observation does not prove a maximum over bases, cuts, scalar programs, +frames, controllers or multiplication algorithms. diff --git a/research/p104-helper-subspace-splits/README.md b/research/p104-helper-subspace-splits/README.md new file mode 100644 index 0000000000..44f4aa9ba6 --- /dev/null +++ b/research/p104-helper-subspace-splits/README.md @@ -0,0 +1,145 @@ +# Conditional kappa 0.00309839 from independent helper splits + +This construction raises complete conditional **kappa to 0.00309839**. +The gain over [PR5580](https://github.com/CrocSwap/integer-mult-bounds/pull/5580) +(0.00308189) is **0.00001650**, about **0.5354%**. The gain over selected +0.003027288235 is **0.000071101765**. The selected record is unchanged. + +The mechanism changes the independent helper basis. At a common-frame cut, +one helper combination can finish early and a fresh independent input can +use the remaining program. Fifteen explicit splits replace 527 helper +jobs by 542 helper jobs. They add 362 scalar events and no recursive Gaussian +call. Both input and output support are checked over every field; a local +pure row alone does not earn a new target. + +Read the [proof](PROOF.md), [exact cuts](SPLITS.json), [complete word](WORD.json.gz), +[receipt](RESULT.json), [source pins](SOURCES.json), and [validation record](VALIDATION.md). +The first split is an explicit 20-ADD change from one H9 target to independent +H5 and H4 targets. The complete caller uses the new word at all 18 full sites. + +| Quantity | Result | +| --- | ---: | +| Local public inputs | 750 | +| Independent helpers per full call | 542 | +| Owned lifetimes / peak owned fields | 8 / 1 | +| Local events | 25,502 | +| Complete paid calls | 66,852, unchanged | +| Complete productive fields | 13,084 | +| Complete rank-mass surplus | 760, unchanged | +| Tested saving | 0.0030983905 | +| Complete conditional kappa | 0.00309839 | +| Raw crossing | (0.00309839352211, 0.00309839352212) | +| Exact native maps | 2,926 | + +The added helpers enter the complete completion-tail calculation. The tail +bound changes to 39/40, with `(39/40)^128 < 1/16`. The compiler logarithm +power changes from 1000 to 1024. Every native map, helper normalizer, main +adapter, scalar basis operation, route, COPY/CLEAR cost, thin query and +whole idle is included. The ordinary BIT saving remains 0.0034. Two exact +moment engines and all 54 strict plus four functional outer conditions are +checked. The receipt gives the raw crossing and the finite compiler threshold. +A negative derivative bound supplies the raw ceiling for this fixed invoice +on [0,0.0034]; it does not bound other constructions. + +## Reproduce + +Use Python 3.12 and the standard library, from the repository root: + +```sh +python3 -B scripts/research_package.py --package research/p104-helper-subspace-splits --check-only +python3 -B scripts/research_package.py --package research/p104-helper-subspace-splits +``` + +The registered hook runs normally and with `-O`. Its success markers are +`PASS_P104_HELPER_SUBSPACE_KAPPA_00309839` and +`PASS_REGISTERED_RESEARCH_PACKAGE`. Direct replay needs no Git or network: + +```sh +python3 -I -B research/p104-helper-subspace-splits/verify.py +python3 -I -O -B research/p104-helper-subspace-splits/verify.py +``` + +Normal replay is read-only. `--write` explicitly regenerates the two result +artifacts. Inputs are authenticated before imported source code executes. +Each replay uses a fresh bytecode-cache path. The checks reject contaminated +prefix and suffix vectors, missing boundary basis operations, an unearned +whole target, extra helper credit, a missing paid call, a wrong native phase, +a missing central translation, an inadequate cutoff and insufficient BIT stock. + +## Scope and coordination + +The scientific base is canonical main +`5e0052ca0aa3036a3afa8b0438927377c8d97d53`, priority revision 7. +The [canonical claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19183208) +records the changed question and local screens. The latest pre-package overlap +cache covered 329 open PRs and 4,851 Discussion records, with complete remote +pagination and incomplete sparse local coverage. Source and coverage details +are coordination evidence, not a novelty proof. + +The consumed PR5580 word is pinned to +`6efa248cf456d6101d757e9d09ba29711d18a13a`. It retains the released PR5569 +handoff and PR5561 helper endpoints. The new basis splits were first found +on PR5569. Two different greedy cut orders reached the same fifteen-split +histogram. All fifteen were then composed with PR5580 and checked again. +No new Gaussian itinerary is introduced. Active frame-extension work in +[Discussion5575](https://github.com/CrocSwap/integer-mult-bounds/discussions/5575) +is a separate investigation. + +The scope changes the scalar word, the input count and the target contract. +It therefore differs from a scalar-only simplification or a fixed-input +helper stop. The unchanged paid histogram now supports a different, +fully independent target histogram. + +The five selected framework assumptions remain: native implementation at +all widths, owned erasure, uniform compiler closure, precision and tape cost, +and analytic recovery. The helper-endpoint contract also remains. +The complete rounded multiplier and enormous uniform compiler word are not +materialized. The same AI-assisted author constructed and checked this +package. Independent human review, proof-kernel acceptance and global +optimality are not claimed. + +## Sources and credit + +- **Ali Romman**: [PR5580](https://github.com/CrocSwap/integer-mult-bounds/pull/5580) + supplies the exact source word; [PR5544](https://github.com/CrocSwap/integer-mult-bounds/pull/5544) + and [PR5545](https://github.com/CrocSwap/integer-mult-bounds/pull/5545) supply + the complete P104 caller and source replay. +- **Joel Pulikkan / GamingPuzzled**: [PR5569](https://github.com/CrocSwap/integer-mult-bounds/pull/5569) + supplies the priced helper handoff; [PR5472](https://github.com/CrocSwap/integer-mult-bounds/pull/5472) + supplies an earlier successor-handoff construction. +- **DreamingOfClouds**: [PR5561](https://github.com/CrocSwap/integer-mult-bounds/pull/5561) + supplies free helper endpoints and PR5568 supplies search tools. + **thu-nmrc** supplies the PR5551 contact improvements. +- **Gareth Davidson / bitplane**, **David Arias** and **Cinna Davis** supply + the PR2305 composition, PR2152 coalesced word and PR2219 private reuse. + Cinna Davis also supplies the controller lineage. +- **Jacob Alan Sussman** supplies productive mixed-target recursion. + **zxv** and **Cao Yifan** supply the retained interval, compiler and + native/pricing lineage. Source notices preserve earlier geometry, BIT + and analytic credit. + +The elementary rank-one basis identity is not claimed as a new general +linear-algebra theorem. The contribution is this explicit independent-target +construction and its complete conditional price. New work is by Ali Romman +with substantial OpenAI Codex assistance; no subagents. Apache-2.0. +See [NOTICE](NOTICE). + +## Open next questions + +An independent reviewer can check the first split and then replay the complete +package. Further gains could use a different compatible cut order, basis or +frame itinerary. Both prefix and suffix support must be proved before a +new target receives credit. The two greedy runs do not establish a global +maximum. [TASK.json](TASK.json) gives the first checks and remaining obligations. + +The optional continuation screen is reproducible with: + +```sh +python3 -I -B research/p104-helper-subspace-splits/search.py +``` + +It tests exact elimination-basis pairs at cuts immediately after MOVE events, +inside equal-boundary helper groups. On the final word it finds no further +candidate in 53 groups. This result covers those tested pairs. It does not +exclude different cut sequences, arbitrary basis combinations or new frames. +The complete-kappa verifier does not depend on a discovery search failure. diff --git a/research/p104-helper-subspace-splits/RESULT.json b/research/p104-helper-subspace-splits/RESULT.json new file mode 100644 index 0000000000..45eecc46a2 --- /dev/null +++ b/research/p104-helper-subspace-splits/RESULT.json @@ -0,0 +1,495 @@ +{ + "authenticated_inputs": 12, + "complete_cost": { + "compiler": { + "H": 707182000000000, + "N": "2^707182000000000", + "eta": { + "lower": "0.000000138410144483165815551326", + "upper": "0.000000138410144483165815551327" + }, + "gap": "1/14000000000", + "integer_test_exponent": 50513, + "logarithm_power": 1024, + "theta": "63/64", + "uniform_saving": "21688733/7000000000", + "word_materialized": false + }, + "full_forward_calls": 18, + "gain": "33/2000000", + "kappa": "309839/100000000", + "kappa_decimal": ".00309839", + "margin_at_previous": { + "lower": "4.021482992995643943845868968293", + "upper": "4.021482992995643943845868968294" + }, + "negative_controls": { + "old_BIT": "Rejected by outer inequalities", + "old_cutoff": "Rejected by completion-tail ratio greater than one" + }, + "nonrecursive": { + "fixed_scalar_growth_bound": "At most 2^(16*26000) before native factors; a declared constant, not an attained norm.", + "local_paid_rank_mass": 6013, + "local_routes": 5194000, + "local_scalar": 220384, + "peak_owned_fields": 1, + "raw_budget": 1000000000, + "raw_scalar_upper": 184647552, + "tensor_native_growth_bound": "Each rank-r Gaussian has row l1 norm at most 2^(rf); use local_paid_rank_mass for the whole word." + }, + "ordinary_BIT": { + "admitted": "17/5000", + "after_cover": "69/20000", + "atom": "1/250", + "before_cover": "3459/1000000", + "ordinary_saving": "8590884599/2500000000000", + "prime_rule": "odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses" + }, + "outer": { + "functional_checks": { + "actual_new_BIT_stock_sublinear": "3485999999253/3500000000000", + "fixed_halo_explicit_metadata_branch": "269500000001/3500000000", + "new_BIT_row_stock_sublinear_in_active_group": "13957999997009/14000000000000", + "new_semantic_group_guard": "3/14000000000" + }, + "margins": { + "boundary_algebraic_matrix": "607284495956622537/196000000000000000000", + "fused_gaussian": "607284495869867611/196000000000000000000", + "global_coordinate_router": "5422183/1750000000", + "group_bit_router": "75910563733733451/24500000000000000000", + "group_scans": "6999999999/7000000000", + "main_transform": "607284481956622537/196000000000000000000", + "microbox_face_corrections": "269500000001/3500000000", + "polynomial_products": "13999999999/14000000000", + "sparse_union_movement": "80232284495956622537/196000000000000000000" + }, + "parameters": { + "a": "5422183/1750000000", + "b": "8675493/2800000000", + "beta": "13999999997/14000000000", + "bit_saving": "17/5000", + "cap_xi": "178232284481956622537/196000000000000000000", + "complex_uniform_saving": "21688733/7000000000", + "d": "1/14000000000", + "epsilon": "13999999999/14000000000", + "kappa": "309839/100000000", + "lambda_": "3987606439/4000000000", + "lambda_prime": "13956622537/14000000000", + "layout": "1/14000000000", + "q": "43377463/14000000000", + "r0": "1/140000000000", + "stop": "1/14000000000", + "tested_saving": "6196781/2000000000" + }, + "strict_checks": { + "actual_bit_above_effective": "527817/1750000000", + "actual_logarithmic_gamma_guard": "1/14000000000", + "actual_logarithmic_group_guard": "17767715539043377463/98000000000000000000", + "alpha_logarithm_absorption": "1/140000000000", + "boundary_algebraic_matrix_above_kappa": "55956622537/196000000000000000000", + "cap_above_band": "80232284481956622537/196000000000000000000", + "cap_below_cell": "17767715504043377463/196000000000000000000", + "cap_below_phase_cell_power": "213767715518043377463/196000000000000000000", + "complex_above_effective": "1/14000000000", + "complex_below_one_over_32": "78824507/2800000000", + "complex_endpoint": "1/7000000000", + "epsilon_below_one": "1/14000000000", + "epsilon_positive": "13999999999/14000000000", + "fine_prime_halo_umbrella": "7/2", + "fused_gaussian_above_kappa": "55869867611/196000000000000000000", + "gaussian_above_main": "6956622537/98000000000000000000", + "global_coordinate_router_above_kappa": "1/3500000000", + "global_gamma_power_slack": "9/140000000000", + "group_below_dimension": "1/7000000000", + "group_bit_router_above_kappa": "8733733451/24500000000000000000", + "group_gauge_power_slack": "17767715538343377463/98000000000000000000", + "group_key_fits_record": "1/7000000000", + "group_positive": "13999999997/14000000000", + "group_scans_above_kappa": "6978311269/7000000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_user_baseline": "683709790400418148631/500000000000000000000000", + "lambda_above_internal": 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optimistic exact moment.", + "Design a small completed instance and independently verify its endpoint and rank bill." + ], + "acceptance_gate": "A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model. 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.", + "bottleneck_link": "Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.", + "allowed_variations": [ + "Narrow to one changed boundary or helper type with explicit counts.", + "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": [ + "Mixing only providers already inside the pinned catalogue.", + "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.", + "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": [ + "helper inventory", + "heterogeneous-owner", + "mutable leaver" + ] + }, + "scope_status": "changed", + "actual_scope": "Change the independent P104 helper basis and split 15 targets into two independent targets at common-frame cuts. Verify a complete conditional kappa gain on PR5580.", + "scope_change_reason": "The donor explicitly requested a different mechanism and a kappa gain. This changes the scalar word, independent input count and helper target contract. It is outside fixed-endpoint retiming and the historical frozen provider catalogue. The card classifies this assigned work; no task was rerolled.", + "bottleneck_link": "At unchanged recursive paid cost, 15 independent target splits strictly increase the concave target moment. Every new input has an explicit returned Gaussian target.", + "budget_minutes": null, + "stop_rule": "Require full arbitrary-input and native identities and a complete improved kappa. Stop the finite discovery scan after no further tested split remains; do not claim global optimality.", + "outcome": "completed", + "evidence": "SPLITS.json, PROOF.md and RESULT.json bind each cut, the complete word, native maps and full price. VALIDATION.md records executed checks.", + "author": "Ali Romman with OpenAI Codex assistance", + "ai_assistance": "Substantial OpenAI Codex assistance. The same assistant constructed and checked the result. No subagents or independent human review.", + "open_questions": [ + { + "question": "Can an independent reviewer accept the new helper basis, every returned independent target and the complete conditional price?", + "why_it_matters": "Author-side exact checks do not replace independent scientific review.", + "first_step": "Check the first rank-one split in PROOF.md, then replay all cuts, native maps and the complete price.", + "blocked_by": "No missing technical input; independent review is pending." + }, + { + "question": "Can a different compatible cut order or changed common frame support more independent target splits?", + "why_it_matters": "The two greedy orders found the same invoice but do not prove a global maximum.", + "first_step": "Use the new word and test both prefix and suffix support before assigning credit. Coordinate with Discussion5575 for any changed frame itinerary.", + "blocked_by": "Every added target must have a clean independent input/output contract and a complete caller bill." + } + ] +} diff --git a/research/p104-helper-subspace-splits/VALIDATION.md b/research/p104-helper-subspace-splits/VALIDATION.md new file mode 100644 index 0000000000..1ee208b2f0 --- /dev/null +++ b/research/p104-helper-subspace-splits/VALIDATION.md @@ -0,0 +1,37 @@ +# Validation record + +Environment: macOS, CPython 3.12.14, standard library only. All scientific +replays run serially in the isolated `codex/kappa-structural-20261025` worktree. +The scientific base is canonical main +`5e0052ca0aa3036a3afa8b0438927377c8d97d53`. + +## Completed checks + +The direct isolated normal replay passed with explicit artifact generation: + +```sh +python3 -I -B research/p104-helper-subspace-splits/verify.py --write +``` + +It checked all 15 prefix and suffix witnesses, every intermediate complete +interface, 574,564 final transpose coefficients, 2,926 exact native maps, +1,084 helper normalizers, 208 main adapters and the complete physical caller. +Two exact moment engines, all compiler conditions, 54 strict outer conditions +and four functional conditions passed. All eight local/controller mutation +controls rejected. The retained wrong-phase, old-cutoff and old-BIT controls +also rejected. The raw crossing is in +(0.00309839352211, 0.00309839352212). + +The first parameter trial failed the compiler complement-capacity condition +with logarithm power 1000. The final power 1024 passes that condition and the +complete compiler check. The old count and growth constants are not reused +for the changed helper inventory. + +The optional final-word discovery screen returned 53 tested boundary groups +and no further candidate. The screen restricts the cut locations and tested +basis pairs; it is not an optimality certificate. + +Optimized, registered, committed-byte and isolated export checks will be +recorded here before publication. Independent human review and hosted CI +are pending. No complete rounded multiplier or enormous uniform word was +materialized. diff --git a/research/p104-helper-subspace-splits/VERIFY.json b/research/p104-helper-subspace-splits/VERIFY.json new file mode 100644 index 0000000000..a0904d71a2 --- /dev/null +++ b/research/p104-helper-subspace-splits/VERIFY.json @@ -0,0 +1,41 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/p104-productive-controller/caller.py", + "research/p104-productive-controller/CONTROLLER.json", + "research/joint-helper-lattice/CONTROLLER.json", + "research/p104-native-channel/vendor/clifford_exact.py", + "research/p104-native-channel/vendor/native_verify.py", + "research/pr4359-p7-padding/native_inventory.py", + "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json", + "research/higher-moment-strictification/verify.py", + "research/kappa-rebuild/architecture/mixed_target_probe.py", + "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py", + "research/query-thinned-controllers/RESULT.json", + "research/p104-helper-subspace-splits/inputs/PR5580-WORD.json.gz" + ], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 600, + "checks": "Check all 15 independent cuts, every rational row and reverse column, native maps, complete caller and invoice, two moment engines, compiler and outer predicates; reject false inputs, outputs, target credit and cost." + }, + { + "argv": [ + "{python}", + "-B", + "-O", + "{package}/verify.py" + ], + "timeout_seconds": 600, + "checks": "Check all 15 independent cuts, every rational row and reverse column, native maps, complete caller and invoice, two moment engines, compiler and outer predicates; reject false inputs, outputs, target credit and cost." + } + ] +} diff --git a/research/p104-helper-subspace-splits/WORD.json.gz b/research/p104-helper-subspace-splits/WORD.json.gz 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b/research/p104-helper-subspace-splits/construct.py new file mode 100644 index 0000000000..037700ed1f --- /dev/null +++ b/research/p104-helper-subspace-splits/construct.py @@ -0,0 +1,157 @@ +"""Split independent helper jobs with three scalar basis changes. + +Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. +The source word and caller retain the credits in README.md. +""" +from copy import deepcopy +from fractions import Fraction as Q +import local as L + + +def inverse(program): + return [[e[0], *e[1:-2], + str(1/Q(e[-2]) if e[0] == 'SCALE' else -Q(e[-2])), e[-1]] + for e in reversed(program)] + + +def basis(a, b, pivot, frame): + """Return B with row pivot equal to a and B b equal to e_pivot.""" + L.need(sum(v*b.get(k, 0) for k, v in a.items()) == 1, 'Unit basis pairing') + roles = sorted(set(a) | set(b) | {pivot}) + values, program = dict(b), [] + + def emit(event): + program.append(event) + r, q = event[1], Q(event[-2]) + if event[0] == 'SCALE': + values[r] = values.get(r, 0)*q + else: + values[r] = values.get(r, 0)+q*values.get(event[2], 0) + + j = pivot if b.get(pivot) else next(r for r in roles if b.get(r)) + if j != pivot: + for event in [['ADD', pivot, j, '1', frame], + ['ADD', j, pivot, '-1', frame], + ['ADD', pivot, j, '1', frame], + ['SCALE', j, '-1', frame]]: + emit(event) + if values[pivot] != 1: + emit(['SCALE', pivot, str(1/values[pivot]), frame]) + for r in roles: + if r != pivot and values.get(r): + emit(['ADD', r, pivot, str(-values[r]), frame]) + L.need(all(values.get(r, 0) == int(r == pivot) for r in roles), 'Basis column') + inverse_rows = {r: {r: Q(1)} for r in roles} + for e in inverse(program): + if e[0] == 'SCALE': + inverse_rows[e[1]] = {k: Q(e[-2])*v for k, v in inverse_rows[e[1]].items()} + else: + L.add(inverse_rows[e[1]], inverse_rows[e[2]], Q(e[-2])) + row = {} + for r, q in a.items(): + L.add(row, inverse_rows[r], q) + L.need(row[pivot] == 1, 'Basis row coefficient') + for r in roles: + if r != pivot and row.get(r): + program.append(['ADD', pivot, r, str(row[r]), frame]) + return program + + +def check_cut(word, h): + """Check the whole prefix row and suffix column over the rationals.""" + n, cut, f, p = word['public'], h['cut_after'], h['frame'], h['pivot'] + a, b, c, d = ({int(k): Q(v) for k, v in h[s].items()} for s in ('a', 'b', 'c', 'd')) + main = set(word['live']) | {r+112 for r in word['live']} + L.need(p < n and p not in main, 'A helper supplies the retained output role') + u, v = word['initial'][p], word['final'][p] + group = {r for r in range(n) if r not in main and + (word['initial'][r], word['final'][r]) == (u, v)} + L.need(set(c) | set(d) <= group, 'Both boundary vectors use one helper group') + L.need(L.span(word['frames'][u]) < L.span(word['frames'][f]) < L.span(word['frames'][v]), + 'Two strictly productive nested targets') + L.need(h['ranks'] == [len(word['frames'][f])-len(word['frames'][u]), + len(word['frames'][v])-len(word['frames'][f])], 'Declared split ranks') + rows = [{r: Q(1)} if r < n else {} for r in range(n+8)] + current = word['initial']+[None]*8 + for e in word['program'][:cut+1]: + op, r = e[:2] + if op == 'MOVE': + current[r] = e[3] + elif op in ('INIT', 'CLEAR'): + rows[r] = {} + current[r] = e[2] if op == 'INIT' else None + elif op == 'SCALE': + rows[r] = {k: Q(e[-2])*x for k, x in rows[r].items()} + elif op == 'COPY': + rows[r] = {k: Q(e[-2])*x for k, x in rows[e[2]].items()} + else: + L.add(rows[r], rows[e[2]], Q(e[-2])) + L.need(all(current[r] == f for r in set(a) | set(b) | {p}), 'One intermediate chart') + total = {} + for r, q in a.items(): + L.add(total, rows[r], q) + L.need(total == c, 'Exact prefix functional; no other input') + column = [b.get(r, Q(0)) for r in range(n+8)] + for e in word['program'][cut+1:]: + op, r = e[:2] + if op in ('INIT', 'CLEAR'): + column[r] = Q(0) + elif op == 'SCALE': + column[r] *= Q(e[-2]) + elif op == 'COPY': + column[r] = Q(e[-2])*column[e[2]] + elif op == 'ADD': + column[r] += Q(e[-2])*column[e[2]] + L.need(column == [d.get(r, Q(0)) for r in range(n+8)], 'Exact suffix direction; no other output') + L.need(sum(x*b.get(r, 0) for r, x in a.items()) == + sum(x*d.get(r, 0) for r, x in c.items()) == 1, 'Both independent pairings') + return a, b, c, d + + +def split(word, h): + a, b, c, d = check_cut(word, h) + n, p, f, cut = word['public'], h['pivot'], h['frame'], h['cut_after'] + u, v = word['initial'][p], word['final'][p] + + def shift_owned(event): + e = event.copy() + e[1] += int(e[1] >= n) + if e[0] in ('ADD', 'COPY'): + e[2] += int(e[2] >= n) + return e + + def use_successor(event): + e = event.copy() + if e[1] == p: + e[1] = n + if e[0] in ('ADD', 'COPY') and e[2] == p: + e[2] = n + return e + + boundary, middle = basis(c, d, p, u), basis(a, b, p, f) + out = deepcopy(word) + out['public'] = n+1 + out['initial'].append(f) + out['final'].append(v) + out['final'][p] = f + out['program'] = inverse(boundary) + out['program'] += [shift_owned(e) for e in word['program'][:cut+1]] + out['program'] += middle + out['program'] += [use_successor(e) for e in inverse(middle)] + out['program'] += [use_successor(shift_owned(e)) for e in word['program'][cut+1:]] + out['program'] += [use_successor([*e[:-1], v]) for e in boundary] + return out + + +def construct(source, witnesses): + word = deepcopy(source) + baseline = L.replay(source) + receipts = [] + for h in witnesses: + word = split(word, h) + result = L.replay(word) + L.need(result['paid'] == baseline['paid'], 'Every paid Gaussian occurrence retained') + receipts.append({'cut_after': h['cut_after'], 'pivot': h['pivot'], + 'ranks': h['ranks'], 'public': word['public'], + 'events': len(word['program'])}) + return word, receipts diff --git a/research/p104-helper-subspace-splits/inputs/PR5580-WORD.json.gz b/research/p104-helper-subspace-splits/inputs/PR5580-WORD.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..9434855e7dad0d0236d23210b3e71a2b83a9ae64 GIT binary patch literal 105115 zcmZs>1z1~6*Dj2=K!BFwE!N`hw0KIP#oY<+6c12>1SwG5-GX~46e+<=ad(Oq3MF`f z;P$7_^S9KMSS~Vdw-Fq-FWJ)aILli9lW!=R$GQH+zI;lF4UDayr|x{cT#io zHC&up$ems2%98elEKbcy`Y%t-N;>^-n5jLUmULR2YLs*uikdw`IjODw11x`qdVjUW z^M3&BuQqr7zra#W^bCxK!9?-1dP}vxaMxB!>ub0=b(K4NUf*7NDw%V*?WeZ&Ht#Zb 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zIr_zhH$OkJ<>W_3eK1Cm>g6}a>g7N#iqYXE(ht7omYR!%q5dn zq*sXQ-NrQafGQBxcH)94g{fAR-v&J^%awRl$d(r4NBh$-;^ra{aov&7QcU7h@&grV zfdU$wq6XchDDfRjXt1y@g>_jo{Ao#KNW>K~bUpJvAQ9Q1Lo1T4##`P%Tw36=-KK78 zY1`5W?Gm!9srC`OghY&mogoEut4JTJ@NziGW~qupd^-}+JgU8Z(=%03l&CG+SN1QZ zLP^@X+sO%L$P&uo>dNA^Wd*C2H>qBB303n}rFL2Mt@HdQy#7MV+}!6kkA*I0>RMDu zR6)dhov3*^cE!r{1G((NvWACJGgW8VvVC1DQLUw3q9kOJNp(tbi5f;r+vIm|Dp@YI ztA5c{_4lTVvSjJy#8&iZ8B&;>5~l2BYUiJjY#KTDbvepglVf)3^^Jr~etJakjYOol zD!buQ%`Md|SvRUlm87lupbyzQWQT6D+fb9WGR|t~7en}wJ4l5%lSM@qN@QzfvoJnJ zI>;0(e2A1bOZ`>of97q{(v=o=DNUqTiO6zx-8j5AO=v55d?9D$atavMEkgs#=qrx zISB|yiPM>W(`=@>WZTFuerx(mXnOdXoX+1bV=n{m0#;2XA!0T=h5E(`oI0}ky-FlFO~uD|F8e@-~Rny|MP$T z`s3gJ;L<& ezyAHd|HuFMmw)}U{_+3)FaJNWA;@-2&= public and r not in live_owned, 'Owned initialization') + live_owned.add(r) + lifetimes += 1 + peak = max(peak, len(live_owned)) + rows[r] = {} + current[r] = e[2] + scalar += 2 + elif op == 'CLEAR': + need(r in live_owned and current[r] == e[2], 'Owned erasure at declared frame') + rows[r] = {} + current[r] = None + live_owned.remove(r) + scalar += 2 + else: + q, f = Q(e[-2]), e[-1] + need(q and current[r] == f, 'Scalar destination and coefficient') + n, d = abs(q.numerator), q.denominator + need(d & (d-1) == 0, 'Dyadic scalar coefficient') + need(abs(q)+1 < 2**16, 'Fixed scalar growth bound') + if op == 'SCALE': + need(n & (n-1) == 0, 'Dyadic unit SCALE') + rows[r] = {k:q*x for k,x in rows[r].items()} + scalar += 2*(abs(n.bit_length()-d.bit_length()) + int(q < 0)) + else: + s = e[2] + need(s != r and 0 <= s < public+8 and current[s] == f, 'Common scalar chart') + if op == 'COPY': + need(r in live_owned and not rows[r], 'COPY into cleared owned field') + rows[r] = {k:q*x for k,x in rows[s].items()} + else: + need(op == 'ADD', 'Scalar opcode') + add(rows[r], rows[s], q) + scalar += 2*(3+n.bit_length()-1+n.bit_count()+d.bit_length()-1) + need(not live_owned and peak == 1 and current[:public] == w['final'], 'All public and owned exits') + live = set(w['live']) + for r,row in enumerate(rows): + expected = {r:Q(1)} if r < public else {} + if r-112 in live: + expected[r-112] = Q(1) + need(row == expected, 'All public and owned rows') + main = live | {r+112 for r in live} + helpers = Counter(len(w['frames'][w['final'][r]])-len(w['frames'][w['initial'][r]]) for r in range(public) if r not in main) + need(len(live) == len(w['ports']) == 104 and len(main) == 208 and min(helpers) > 0, 'Independent productive inputs') + return {'paid':dict(paid), 'helpers':dict(helpers), 'public_inputs':public, 'owned_lifetimes':lifetimes, + 'peak_owned_fields':peak, 'real_scalar_allowance':scalar, 'endpoint_coefficients':(public+8)*(public+8), + 'paid_rank_mass':sum(r*count for r,count in paid.items())} + +def reverse_columns(w): + """Check the transpose with dense dyadic rows and the reverse chronology.""" + public = w['public'] + n = public+8 + rows = [[int(i == j) for j in range(n)] for i in range(n)] + exponents = [0]*n + for e in reversed(w['program']): + op,r = e[:2] + if op == 'MOVE': + continue + if op in ('INIT','CLEAR'): + rows[r] = [0]*n + exponents[r] = 0 + continue + q = Q(e[-2]) + qe = q.denominator.bit_length()-1 + if op == 'SCALE': + rows[r] = [q.numerator*x for x in rows[r]] + exponents[r] += qe + else: + s = e[2] + level = max(exponents[s], exponents[r]+qe) + a, b = 1 << (level-exponents[s]), q.numerator << (level-exponents[r]-qe) + rows[s] = [a*x+b*y for x,y in zip(rows[s],rows[r])] + exponents[s] = level + if op == 'COPY': + rows[r] = [0]*n + exponents[r] = 0 + r = s + while exponents[r] and not any(x & 1 for x in rows[r]): + rows[r] = [x//2 for x in rows[r]] + exponents[r] -= 1 + for r,row in enumerate(rows): + expected = [0]*n + if r < public: + expected[r] = 1 << exponents[r] + if r in w['live']: + expected[r+112] = 1 << exponents[r] + need(row == expected, 'Independent dense transpose columns') + return {'columns':n, 'coefficients':n*n, 'arithmetic':'Dense integer rows with binary denominators; reverse chronology'} + +def native(w): + n = w['public'] + C = load(ROOT/'research/p104-native-channel/vendor/clifford_exact.py', 'p104_productive_clifford') + V = load(ROOT/'research/p104-native-channel/vendor/native_verify.py', 'p104_productive_gaussian') + @lru_cache(None) + def chart(i): + return C.canonical_frame(9, tuple(w['frames'][i])) + recipes = {} + def check(a,b): + if (a,b) not in recipes: + recipe,_ = C.lower_child(chart(a).adjoint().then(chart(b))) + expected = V.adjoint(V.frame(w['frames'][a],9)) + V.frame(w['frames'][b],9) + V.equal(V.recipe(recipe),expected,'Native chart change and exact global phase') + need(recipe['rank'] == abs(len(w['frames'][a])-len(w['frames'][b])), 'Native boundary rank') + recipes[a,b] = recipe + return recipes[a,b] + for e in w['program']: + if e[0] == 'MOVE': + check(e[2],e[3]) + main = set(w['live']) | {r+112 for r in w['live']} + helper_profile = Counter() + for r in range(n): + if r not in main: + helper_profile[check(w['initial'][r],w['final'][r])['rank']] += 1 + adapters = [] + for r,q in zip(w['live'],w['ports']): + need(w['frames'][w['initial'][r]] == [q], 'Literal central port') + need(span(w['frames'][w['final'][r+112]]) == frozenset(x for x in range(512) if not (x&q).bit_count()%2), 'Literal output hyperplane') + tests = [ + (C.cgate(9,q,1).adjoint().then(chart(w['initial'][r])), V.adjoint((('C',q,1),))+V.frame(w['frames'][w['initial'][r]],9)), + (chart(w['final'][r+112]).adjoint().then(C.cgate(9,q,-1).then(C.fourier(9))), V.adjoint(V.frame(w['frames'][w['final'][r+112]],9))+(('C',q,-1),)+V.fourier(9))] + for actual,expected in tests: + recipe,_ = C.lower_child(actual) + need(recipe['rank'] == 0, 'Free intrinsic main adapter') + V.equal(V.recipe(recipe),expected,'Main endpoint phase') + adapters.append(recipe) + bad = json.loads(json.dumps(next(iter(recipes.values())))) + bad['left']['phase'] = (bad['left']['phase']+1)%4 + a,b = next(iter(recipes)) + try: + V.equal(V.recipe(bad),V.adjoint(V.frame(w['frames'][a],9))+V.frame(w['frames'][b],9),'Wrong phase control') + except ValueError: + pass + else: + raise ValueError('Wrong native phase accepted') + payload = [[a,b,recipes[a,b]] for a,b in sorted(recipes)] + adapters + return {'distinct_maps':len(recipes),'main_adapters':len(adapters),'helper_normalizers':2*sum(helper_profile.values()), + 'helpers':dict(helper_profile),'recipe_payload_sha256':sha256(json.dumps(payload,sort_keys=True,separators=(',',':')).encode()).hexdigest(), + 'wrong_phase_rejected':True, 'proof':'Every signed Pauli image and exact global phase; frame induction at every positive tensor width'} diff --git a/research/p104-helper-subspace-splits/pricing.py b/research/p104-helper-subspace-splits/pricing.py new file mode 100644 index 0000000000..fe03d7eebe --- /dev/null +++ b/research/p104-helper-subspace-splits/pricing.py @@ -0,0 +1,169 @@ +"""Complete mixed-target price, compiler and outer transfer. + +The interval and compiler bounds follow zxv and Cao Yifan. The productive +recursion is by Jacob Alan Sussman. The controller is by Cinna Davis. +Adapted from Ali Romman's PR5544/5545 for the two coupled contact changes. +Successor choices were prepared for thu-nmrc with OpenAI Codex assistance. +Helper-subspace targets were added by Ali Romman with OpenAI Codex assistance. +Ali Romman's complete caller/price proof and all predecessor credit are retained. +Apache-2.0. +""" +from collections import Counter +from fractions import Fraction as Q +import local as L + +KAPPA, TESTED = Q('.00309839'), Q('.0030983905') +PREVIOUS = Q('.00308189') + + +def encode(x): + if isinstance(x,Q): + return str(x) + if isinstance(x,dict): + return {str(k):encode(v) for k,v in x.items()} + if isinstance(x,(list,tuple)): + return [encode(v) for v in x] + return x + + +def assemble(local, native, word, physical): + paid, targets = Counter(), Counter() + counts = Counter() + L.need(local['helpers'] == native['helpers'], 'Every productive helper has a native target') + for e in word['physical_events']: + counts[e[0]] += 1 + if e[0] == 'LOCAL': + L.need(e[3] is False, 'Every source invocation is forward') + paid.update(local['paid']) + targets.update(local['helpers']) + elif e[0] == 'QUERY_SHEAR': + paid[1] += 104 + elif e[0] == 'IDLE': + paid[8*len(e[2])] += 208 + main = Counter() + idle = Counter({8*len(e[2]):0 for e in word['physical_events'] if e[0] == 'IDLE'}) + for e in word['physical_events']: + if e[0] == 'IDLE': + idle[8*len(e[2])] += 208 + L.need(idle == physical['whole_idle_jobs'], 'Every whole idle has a native Gaussian and full rank') + for term in word['diagonal']: + main[1+8*sum(term[1:])] += 104 + L.need(main == physical['main_targets'], 'Every main target has its full native phase') + targets.update(main) + L.need(counts['LOCAL'] == 18 and counts['QUERY_SHEAR'] == counts['IDLE'] == 15, 'Complete call census') + # Recount by the two path lengths, without using emitted main diagonals. + second_t = Counter({r:18*n for r,n in local['helpers'].items()}) + second_p = Counter({r:18*n for r,n in local['paid'].items()}) + second_t[145] += 208 + second_p[1] += 15*104 + for length in (7,8): + for j in range(1,length+1): + second_t[1+8*(j+1)] += 208 + second_p[8*(j+1)] += 208 + L.need((targets,paid) == (second_t,second_p), 'Independent full invoice') + L.need(max(targets) == 145 and max(paid) == 72, 'Maximum recursive ranks') + L.need(sum(targets.values()) == 13084 and sum(paid.values()) == 66852, 'Complete field and call counts') + L.need(sum(r*n for r,n in targets.items())-sum(r*n for r,n in paid.items()) == 760, 'Complete rank surplus') + return targets,paid,counts + + +def run(local,native,word,physical): + T,P,counts = assemble(local,native,word,physical) + E = L.load(L.ROOT/'research/higher-moment-strictification/verify.py','p104_productive_intervals') + other = L.load(L.ROOT/'research/kappa-rebuild/architecture/mixed_target_probe.py','p104_productive_second_intervals') + def margin(k): + a,b = E.moment(T,1-k), E.moment(P,1-k) + return a[0]-b[1],a[1]-b[0] + lo,hi,grid = 0,10**12,10**14 + while hi-lo > 1: + m=(lo+hi)//2 + if margin(Q(m,grid))[0] > 0: + lo=m + else: + hi=m + lower,upper = Q(lo,grid),Q(hi,grid) + signed = Counter(T) + signed.subtract(P) + cap = Q('.0034') + derivative_upper = Q(0) + for rank, count in signed.items(): + logarithm = E.log_bounds(rank) + low = E.mul(E.power(rank, 1-cap), logarithm)[0] + high = rank*logarithm[1] + derivative_upper -= count*(low if count >= 0 else high) + L.need(derivative_upper < 0, 'Unique raw crossing below the retained BIT cap') + L.need(margin(lower)[0] > 0 and margin(upper)[1] < 0, 'Strict rational crossing enclosure') + L.need(PREVIOUS < KAPPA < TESTED < lower and margin(PREVIOUS)[0] > 0, 'Changed complete bill improves selected kappa') + t,u,v,c,b = 1-TESTED,Q(1,5),1024,17,18 + target,paid = E.moment(T,t),E.moment(P,t) + tl,th = other.moment(T,TESTED) + pl,ph = other.moment(P,TESTED) + L.need(tl > ph and max(tl,target[0]) <= min(th,target[1]) and max(pl,paid[0]) <= min(ph,paid[1]), 'Two exact moment engines') + alpha = E.divide(paid,target) + gamma = E.divide(E.moment(P,t+u),E.mul(E.power(c,u),target)) + delta = E.divide((Q(sum(T.values())*b),)*2,E.mul(E.power(c,TESTED),target)) + reserve,decay = Q(1,10**10),Q(39,40) + L.need(alpha[1] < 1-reserve and gamma[1] < decay and delta[1] < decay, 'All three charged tail ratios') + L.need(decay**128 < Q(1,16), 'Both tail decay blocks') + normalized = 1/(1+v*reserve)+Q(4,2**32) + L.need(normalized < 1 and c**64 < b**63, 'Full completion, splitting and rounding charges') + theta,power = Q(63,64),1024 + eta = E.scale(E.power(145,-v*TESTED),t) + L.need(2*(c**v)**64 <= (145**v)**63 and eta[0] > theta**power, 'Shifted exits and complement capacity') + L.need(E.power(145,v*TESTED)[1] < 2**power, 'Compiler initial range') + gap = (TESTED-KAPPA)/7 + L.need(gap.numerator == 1, 'Exact compiler integer grid') + step = gap.denominator + def wins(j): + return (step*j+1)**power < 2**j + left,right=1,2 + while not wins(right): + left,right=right,2*right + while right-left > 1: + m=(left+right)//2 + if wins(m): + right=m + else: + left=m + H=step*right + L.need(H > 8*v and wins(right) and not wins(right-1), 'Finite uniform threshold with predecessor rejection') + local_routes = (sum(local['paid'].values())+native['helper_normalizers']+native['main_adapters']+4*104+4*local['owned_lifetimes'])*1000 + L.need(local['real_scalar_allowance']+local_routes < 10**7, 'Every local scalar, route and owned operation is funded') + boundary = sum(len(word['boundaries'][side+'_program']) for side in ('left','right')) + raw = 18*10**7 + 15*1664 + 32*104*(len(word['physical_events'])+boundary) + raw += 32*104*(26+1000) + L.need(raw < 10**9, 'Complete nonrecursive raw bound') + bit = L.read(L.ROOT/'research/query-thinned-controllers/RESULT.json')['ordinary_BIT'] + atom = Q(bit['atom']) + ordinary=(1-atom)*Q(bit['after_cover'])+atom*Q('.0000384599') + admitted=Q(bit['admitted']) + L.need(atom > ordinary > admitted > TESTED and atom < 1-ordinary, 'Retained BIT admission and stock') + outer_module=L.load(L.ROOT/'research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py','p104_productive_outer') + params={'kappa':KAPPA,'tested_saving':TESTED,'complex_uniform_saving':KAPPA+6*gap, + 'b':KAPPA+5*gap,'a':KAPPA+4*gap,'q':KAPPA+3*gap,'bit_saving':admitted, + 'epsilon':1-gap,'beta':1-3*gap,'r0':gap/10,'stop':gap,'layout':gap,'d':gap} + outer=outer_module.ledger(params) + outer['functional_checks']['actual_new_BIT_stock_sublinear']=params['beta']*(1-atom) + L.need(len(outer['strict_checks']) == 54 and len(outer['functional_checks']) == 4, 'Complete outer predicate inventory') + L.need(all(x > 0 for key in ('strict_checks','functional_checks') for x in outer[key].values()), 'All outer inequalities strict') + wrong_cutoff = E.divide((Q(sum(T.values())*21),)*2,E.mul(E.power(20,TESTED),target)) + L.need(wrong_cutoff[0] > 1, 'Old cutoff fails with this helper inventory') + bad=outer_module.ledger(dict(params,bit_saving=Q('.0027'))) + L.need(any(x <= 0 for x in bad['strict_checks'].values()), 'Insufficient BIT contract rejected') + return encode({'kappa':KAPPA,'kappa_decimal':'.00309839','previous_open_pr5580':PREVIOUS,'gain':KAPPA-PREVIOUS, + 'relative_gain_percent':100*(KAPPA/PREVIOUS-1),'raw_root_interval':[lower,upper], + 'raw_headroom':[lower-KAPPA,upper-KAPPA], + 'raw_ceiling':{'interval':[Q(0),cap],'derivative_upper':derivative_upper},'margin_at_previous':E.display(margin(PREVIOUS)), + 'targets':T,'paid':P,'productive_fields':sum(T.values()),'paid_calls':sum(P.values()), + 'rank_mass_surplus':760,'full_forward_calls':18,'query_shears':15,'whole_idle_jobs':3120, + 'strictification':{'tested':TESTED,'power':v,'cutoff':c,'floor':b,'tail_offset':u,'reserve':reserve,'tail_decay':decay,'tail_block':128, + 'alpha':E.display(alpha),'gamma':E.display(gamma),'delta':E.display(delta),'normalized_paid_upper':normalized}, + 'compiler':{'theta':theta,'logarithm_power':power,'eta':E.display(eta),'gap':gap,'H':H,'N':'2^'+str(H), + 'integer_test_exponent':right,'uniform_saving':params['complex_uniform_saving'],'word_materialized':False}, + 'nonrecursive':{'local_scalar':local['real_scalar_allowance'],'local_routes':local_routes, + 'raw_scalar_upper':raw,'raw_budget':10**9,'peak_owned_fields':1, + 'fixed_scalar_growth_bound':'At most 2^(16*26000) before native factors; a declared constant, not an attained norm.', + 'local_paid_rank_mass':local['paid_rank_mass'], + 'tensor_native_growth_bound':'Each rank-r Gaussian has row l1 norm at most 2^(rf); use local_paid_rank_mass for the whole word.'}, + 'ordinary_BIT':bit,'outer':outer, + 'negative_controls':{'old_cutoff':'Rejected by completion-tail ratio greater than one','old_BIT':'Rejected by outer inequalities'}}) diff --git a/research/p104-helper-subspace-splits/search.py b/research/p104-helper-subspace-splits/search.py new file mode 100644 index 0000000000..27e19ce2d2 --- /dev/null +++ b/research/p104-helper-subspace-splits/search.py @@ -0,0 +1,155 @@ +"""Screen exact helper-basis pairs after MOVE events. + +This is a finite discovery screen, not an optimality certificate. +Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. +""" +import argparse +from collections import defaultdict +from fractions import Fraction as Q +import gzip +import json +from pathlib import Path +import sys + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +from construct import basis +from local import add, span + + +def pure_combinations(rows, roles, group): + """Eliminate coordinates outside the group; retain field coefficients.""" + pivots, output = {}, [] + for role in roles: + outside = {k:v for k,v in rows[role].items() if k not in group} + inside = {k:v for k,v in rows[role].items() if k in group} + coefficients = {role:Q(1)} + while outside: + pivot = min(outside) + if pivot not in pivots: + scale = 1/outside[pivot] + pivots[pivot] = [{k:v*scale for k,v in row.items()} + for row in (outside, inside, coefficients)] + break + scale = -outside[pivot] + for target, source in zip((outside, inside, coefficients), pivots[pivot]): + add(target, source, scale) + if not outside and inside: + output.append((inside, coefficients)) + return output + + +def dyadic_program(program): + for event in program: + q = Q(event[-2]) + numerator, denominator = abs(q.numerator), q.denominator + if denominator & (denominator-1): + return False + if event[0] == 'SCALE' and numerator & (numerator-1): + return False + return True + + +def candidates(word, group, entry, exit_frame): + frames = [span(b) for b in word['frames']] + valid = {f for f,frame in enumerate(frames) if frames[entry] < frame < frames[exit_frame]} + if not valid: + return [] + public = word['public'] + snapshots, at = defaultdict(list), defaultdict(set) + rows = [{r:Q(1)} if r < public else {} for r in range(public+8)] + for r,f in enumerate(word['initial']): + at[f].add(r) + for index,event in enumerate(word['program']): + op,r = event[:2] + if op == 'MOVE': + old,new = event[2:4] + at[old].remove(r) + at[new].add(r) + for frame in (old,new): + if frame in valid and at[frame] & group: + roles = sorted(at[frame]) + combinations = pure_combinations(rows, roles, group) + if combinations: + snapshots[index].append((frame,roles,combinations)) + elif op == 'INIT': + rows[r] = {} + at[event[2]].add(r) + elif op == 'CLEAR': + rows[r] = {} + at[event[2]].remove(r) + elif op == 'COPY': + rows[r] = {k:v*Q(event[-2]) for k,v in rows[event[2]].items()} + elif op == 'SCALE': + rows[r] = {k:v*Q(event[-2]) for k,v in rows[r].items()} + else: + add(rows[r], rows[event[2]], Q(event[-2])) + columns = [{r:Q(1)} if r < public else {} for r in range(public+8)] + hits = [] + for index in range(len(word['program'])-1, -1, -1): + for frame,roles,prefix_basis in snapshots.get(index, []): + suffix_basis = pure_combinations(columns, roles, group) + for c,a in prefix_basis: + for raw_d,raw_b in suffix_basis: + pairing = sum(v*raw_d.get(k,0) for k,v in c.items()) + if not pairing: + continue + b = {k:v/pairing for k,v in raw_b.items()} + d = {k:v/pairing for k,v in raw_d.items()} + if sum(v*b.get(k,0) for k,v in a.items()) != 1: + continue + available = group & set(roles) + pivot = next((r for r in sorted(available) if b.get(r)), min(available)) + if not dyadic_program(basis(c,d,pivot,entry)+basis(a,b,pivot,frame)): + continue + ranks = [len(word['frames'][frame])-len(word['frames'][entry]), + len(word['frames'][exit_frame])-len(word['frames'][frame])] + hits.append({'cut_after':index, 'frame':frame, 'pivot':pivot, + 'a':a, 'b':b, 'c':c, 'd':d, 'ranks':ranks}) + event = word['program'][index] + op,r = event[:2] + if op == 'INIT': + columns[r] = {} + elif op == 'CLEAR': + # This screen also rejects directions lost at an owned erasure. + columns[r] = {r:Q(1)} + elif op == 'COPY': + add(columns[event[2]], columns[r], Q(event[-2])) + columns[r] = {} + elif op == 'SCALE': + columns[r] = {k:v*Q(event[-2]) for k,v in columns[r].items()} + elif op == 'ADD': + add(columns[event[2]], columns[r], Q(event[-2])) + return hits + + +def encode(value): + if isinstance(value,Q): + return str(value) + if isinstance(value,dict): + return {k:encode(v) for k,v in value.items()} + if isinstance(value,list): + return [encode(v) for v in value] + return value + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--word', type=Path, default=HERE/'WORD.json.gz') + args = parser.parse_args() + word = json.loads(gzip.decompress(args.word.read_bytes())) + mains = set(word['live']) | {r+112 for r in word['live']} + groups = defaultdict(set) + for r in range(word['public']): + if r not in mains: + groups[word['initial'][r],word['final'][r]].add(r) + hits, tested = [], 0 + for (entry,exit_frame),roles in groups.items(): + if len(word['frames'][exit_frame])-len(word['frames'][entry]) > 1: + hits.extend(candidates(word, roles, entry, exit_frame)) + tested += 1 + print(json.dumps(encode({'tested_boundary_groups':tested, 'candidates':hits}), sort_keys=True)) + + +if __name__ == '__main__': + main() diff --git a/research/p104-helper-subspace-splits/verify.py b/research/p104-helper-subspace-splits/verify.py new file mode 100644 index 0000000000..4612822077 --- /dev/null +++ b/research/p104-helper-subspace-splits/verify.py @@ -0,0 +1,130 @@ +"""Verify independent helper splits, all native maps and complete kappa. + +Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. +""" +import argparse +from collections import Counter +from copy import deepcopy +from hashlib import sha1, sha256 +import gzip +import json +from pathlib import Path +import sys +import tempfile + +sys.dont_write_bytecode = True +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] + + +def need(ok, why): + if not ok: + raise ValueError(why) + + +def authenticate(): + count = 0 + for row in json.loads((HERE/'SOURCES.json').read_bytes())['files']: + if row['usage'] == 'input': + raw = (ROOT/row['path']).read_bytes() + need(sha256(raw).hexdigest() == row['sha256'], 'Source SHA256: '+row['path']) + need(sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest() == row['git_blob'], + 'Source Git blob: '+row['path']) + count += 1 + return count + + +def rejected(action): + try: + action() + except ValueError as error: + return str(error) + raise ValueError('An invalid claim was accepted') + + +def run(): + pins = authenticate() + sys.path.insert(0, str(HERE)) + import local as L + import construct as R + import pricing as P + C = L.load(ROOT/'research/p104-productive-controller/caller.py', 'subspace_p104_caller') + source = L.read(HERE/'inputs/PR5580-WORD.json.gz') + witnesses = L.read(HERE/'SPLITS.json') + need(len(witnesses) == 15, 'Fifteen explicit independent splits') + baseline = L.replay(source) + word, cuts = R.construct(source, witnesses) + local = L.replay(word) + need((local['public_inputs'], local['owned_lifetimes'], local['peak_owned_fields']) == (750, 8, 1), + 'Complete public and owned inventory') + need(local['helpers'] == {1:4, 2:5, 4:90, 5:10, 7:5, 8:18, 9:410}, 'Exact helper histogram') + delta = Counter(local['helpers']) + delta.subtract(baseline['helpers']) + delta = {r:n for r,n in delta.items() if n} + need(delta == {1:4, 2:5, 4:7, 5:5, 7:5, 8:3, 9:-14}, 'All split credits and removed targets') + need(local['paid'] == baseline['paid'], 'Same complete local paid histogram') + columns = L.reverse_columns(word) + print('PASS 15 prefix/suffix cuts, every independent row and dense reverse columns', flush=True) + native = L.native(word) + controller = C.construct() + need(controller == L.read(ROOT/'research/p104-productive-controller/CONTROLLER.json'), 'Same complete caller') + physical = C.physical(controller, word) + print('PASS every native phase, productive target and physical caller contact', flush=True) + costs = P.run(local, native, controller, physical) + controls = C.controls(controller) + bad = deepcopy(witnesses[0]) + key = next(iter(bad['a'])) + bad['a'][key] = str(L.Q(bad['a'][key])+1) + controls['contaminated_prefix'] = rejected(lambda: R.check_cut(source, bad)) + bad = deepcopy(witnesses[0]) + key = next(iter(bad['b'])) + bad['b'][key] = str(L.Q(bad['b'][key])+1) + controls['contaminated_suffix'] = rejected(lambda: R.check_cut(source, bad)) + bad = deepcopy(word) + bad['program'].pop(0) + controls['missing_input_basis'] = rejected(lambda: L.replay(bad)) + bad = deepcopy(word) + bad['program'].pop() + controls['missing_output_basis'] = rejected(lambda: L.replay(bad)) + bad = deepcopy(word) + bad['final'][648] = 127 + controls['unearned_whole_target'] = rejected(lambda: L.replay(bad)) + bad = deepcopy(local) + bad['helpers'][1] += 1 + controls['extra_helper_credit'] = rejected(lambda: P.assemble(bad, native, controller, physical)) + bad = deepcopy(local) + bad['paid'][1] -= 1 + controls['unpaid_gaussian'] = rejected(lambda: P.assemble(bad, native, controller, physical)) + result = {'status':'PASS_P104_HELPER_SUBSPACE_KAPPA_00309839', + 'authenticated_inputs':pins, 'splits':cuts, 'local_helper_delta':delta, + 'local':local, 'separate_columns':columns, 'native':native, + 'physical_caller':physical, 'complete_cost':costs, 'negative_controls':controls, + 'limits':['The five selected framework assumptions and helper-endpoint contract remain.', + 'No complete rounded multiplier or enormous uniform compiler word is materialized.', + 'No independent human or proof-kernel acceptance or global optimality is claimed.']} + return P.encode(result), word + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--write', action='store_true') + args = parser.parse_args() + with tempfile.TemporaryDirectory(prefix='p104-subspace-bytecode-') as cache: + sys.pycache_prefix = cache + result, word = run() + for name, value in (('RESULT.json', result), ('WORD.json.gz', word)): + path = HERE/name + if args.write: + raw = (json.dumps(value, sort_keys=True, indent=None if name.endswith('.gz') else 2)+'\n').encode() + path.write_bytes(gzip.compress(raw, mtime=0) if name.endswith('.gz') else raw) + else: + raw = path.read_bytes() + need(json.loads(gzip.decompress(raw) if name.endswith('.gz') else raw) == value, + 'Exact saved artifact: '+name) + print(result['status']) + print(json.dumps({k:result['complete_cost'][k] for k in + ('kappa', 'gain', 'raw_root_interval', 'productive_fields', 'paid_calls')}, sort_keys=True)) + + +if __name__ == '__main__': + main() From b9e8f70f4843fc4e361b175cdea27402a9555ea8 Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Sun, 25 Oct 2026 16:10:52 -0500 Subject: [PATCH 2/6] Bind copied source bytes to their published Git path --- research/p104-helper-subspace-splits/SOURCES.json | 14 ++++++++++++-- research/p104-helper-subspace-splits/verify.py | 14 +++++++++++++- 2 files changed, 25 insertions(+), 3 deletions(-) diff --git a/research/p104-helper-subspace-splits/SOURCES.json b/research/p104-helper-subspace-splits/SOURCES.json index 1cdcf3e25e..71f28c1f3b 100644 --- a/research/p104-helper-subspace-splits/SOURCES.json +++ b/research/p104-helper-subspace-splits/SOURCES.json @@ -81,8 +81,8 @@ "sha256": "6ebfc8c0f09166f4834e9d7427410cb31aefff2cd4d4ce588c8e52c9c70e9a0f" }, { - "path": "research/p104-helper-subspace-splits/inputs/PR5580-WORD.json.gz", - "usage": "input", + "path": "research/p104-event-contact-step/WORD.json.gz", + "usage": "provenance", "git_blob": "9434855e7dad0d0236d23210b3e71a2b83a9ae64", "sha256": "b2a98c4bd0dbe86c09e9d15ee060dcf1aab09dbef90aa1e2127676f4039f406b", "pin": "head:6efa248cf456d6101d757e9d09ba29711d18a13a:research/p104-event-contact-step/WORD.json.gz" @@ -100,5 +100,15 @@ "sha256": "a4df92b46234bb56a966df30d9c1d43251e1346e9a1ad06cf5ee30a79c7ae591", "pin": "head:af9f091ac6f30c6eaacb9c27777bfbe2d0e5ffdf:research/p104-priced-handoff/pricing.py" } + ], + "external_inputs": [ + { + "local_path": "inputs/PR5580-WORD.json.gz", + "source_repository": "aliromman/integer-mult-bounds", + "source_commit": "6efa248cf456d6101d757e9d09ba29711d18a13a", + "source_path": "research/p104-event-contact-step/WORD.json.gz", + "sha256": "b2a98c4bd0dbe86c09e9d15ee060dcf1aab09dbef90aa1e2127676f4039f406b", + "git_blob": "9434855e7dad0d0236d23210b3e71a2b83a9ae64" + } ] } diff --git a/research/p104-helper-subspace-splits/verify.py b/research/p104-helper-subspace-splits/verify.py index 4612822077..c30227dc77 100644 --- a/research/p104-helper-subspace-splits/verify.py +++ b/research/p104-helper-subspace-splits/verify.py @@ -24,13 +24,25 @@ def need(ok, why): def authenticate(): count = 0 - for row in json.loads((HERE/'SOURCES.json').read_bytes())['files']: + manifest = json.loads((HERE/'SOURCES.json').read_bytes()) + for row in manifest['files']: if row['usage'] == 'input': raw = (ROOT/row['path']).read_bytes() need(sha256(raw).hexdigest() == row['sha256'], 'Source SHA256: '+row['path']) need(sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest() == row['git_blob'], 'Source Git blob: '+row['path']) count += 1 + for row in manifest['external_inputs']: + source, = [r for r in manifest['files'] if r['path'] == row['source_path']] + need(source['pin'] == 'head:'+row['source_commit']+':'+row['source_path'], + 'Published source path and commit') + need((source['sha256'],source['git_blob']) == (row['sha256'],row['git_blob']), + 'Copied input has the published source pins') + raw = (HERE/row['local_path']).read_bytes() + need(sha256(raw).hexdigest() == row['sha256'], 'Copied source SHA256') + need(sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest() == row['git_blob'], + 'Copied source Git blob') + count += 1 return count From 31a4de233bbdd65c04c63dc3398ecf0eed8e1375 Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Sun, 25 Oct 2026 16:19:15 -0500 Subject: [PATCH 3/6] Make source replay independent of unmerged Git objects --- .../p104-helper-subspace-splits/README.md | 6 ++++- .../p104-helper-subspace-splits/SOURCES.json | 23 +++++++++++-------- .../p104-helper-subspace-splits/construct.py | 4 ++-- .../p104-helper-subspace-splits/search.py | 3 +-- .../p104-helper-subspace-splits/verify.py | 15 ++++-------- 5 files changed, 26 insertions(+), 25 deletions(-) diff --git a/research/p104-helper-subspace-splits/README.md b/research/p104-helper-subspace-splits/README.md index 44f4aa9ba6..83cfa3114e 100644 --- a/research/p104-helper-subspace-splits/README.md +++ b/research/p104-helper-subspace-splits/README.md @@ -80,7 +80,11 @@ The consumed PR5580 word is pinned to `6efa248cf456d6101d757e9d09ba29711d18a13a`. It retains the released PR5569 handoff and PR5561 helper endpoints. The new basis splits were first found on PR5569. Two different greedy cut orders reached the same fifteen-split -histogram. All fifteen were then composed with PR5580 and checked again. +histogram. All fifteen were then composed with PR5580 and checked again. The exact +source copy is retained in this branch at commit +`29fe88ba218b5d2192d8e31f07a01d1141afdacd`. Its SHA256 and Git blob match the +recorded PR5580 source. Registered replay needs only this branch history; +it does not need cached objects from unmerged PR branches. No new Gaussian itinerary is introduced. Active frame-extension work in [Discussion5575](https://github.com/CrocSwap/integer-mult-bounds/discussions/5575) is a separate investigation. diff --git a/research/p104-helper-subspace-splits/SOURCES.json b/research/p104-helper-subspace-splits/SOURCES.json index 71f28c1f3b..1bedb207e9 100644 --- a/research/p104-helper-subspace-splits/SOURCES.json +++ b/research/p104-helper-subspace-splits/SOURCES.json @@ -81,24 +81,17 @@ "sha256": "6ebfc8c0f09166f4834e9d7427410cb31aefff2cd4d4ce588c8e52c9c70e9a0f" }, { - "path": "research/p104-event-contact-step/WORD.json.gz", - "usage": "provenance", + "path": "research/p104-helper-subspace-splits/inputs/PR5580-WORD.json.gz", + "usage": "input", "git_blob": "9434855e7dad0d0236d23210b3e71a2b83a9ae64", "sha256": "b2a98c4bd0dbe86c09e9d15ee060dcf1aab09dbef90aa1e2127676f4039f406b", - "pin": "head:6efa248cf456d6101d757e9d09ba29711d18a13a:research/p104-event-contact-step/WORD.json.gz" + "pin": "head:29fe88ba218b5d2192d8e31f07a01d1141afdacd:research/p104-helper-subspace-splits/inputs/PR5580-WORD.json.gz" }, { "path": "research/p104-productive-controller/local.py", "usage": "provenance", "git_blob": "dbb3d56a4f5b733bb0c32a91249d1f6a7e1ab5d2", "sha256": "878734dfd64c4b9d362d0ae476cc5c2a19fe93e48b7378763b23f3e0dd0a5a71" - }, - { - "path": "research/p104-priced-handoff/pricing.py", - "usage": "provenance", - "git_blob": "bb135338f1c57c48147cb214d14f542cdfe4e533", - "sha256": "a4df92b46234bb56a966df30d9c1d43251e1346e9a1ad06cf5ee30a79c7ae591", - "pin": "head:af9f091ac6f30c6eaacb9c27777bfbe2d0e5ffdf:research/p104-priced-handoff/pricing.py" } ], "external_inputs": [ @@ -110,5 +103,15 @@ "sha256": "b2a98c4bd0dbe86c09e9d15ee060dcf1aab09dbef90aa1e2127676f4039f406b", "git_blob": "9434855e7dad0d0236d23210b3e71a2b83a9ae64" } + ], + "code_derivation": [ + { + "source_repository": "GamingPuzzled/integer-mult-bounds", + "source_commit": "af9f091ac6f30c6eaacb9c27777bfbe2d0e5ffdf", + "source_path": "research/p104-priced-handoff/pricing.py", + "sha256": "a4df92b46234bb56a966df30d9c1d43251e1346e9a1ad06cf5ee30a79c7ae591", + "git_blob": "bb135338f1c57c48147cb214d14f542cdfe4e533", + "scope": "Pricing code attribution; this predecessor file is not executed." + } ] } diff --git a/research/p104-helper-subspace-splits/construct.py b/research/p104-helper-subspace-splits/construct.py index 037700ed1f..698a4cbcc0 100644 --- a/research/p104-helper-subspace-splits/construct.py +++ b/research/p104-helper-subspace-splits/construct.py @@ -136,8 +136,8 @@ def use_successor(event): out['final'][p] = f out['program'] = inverse(boundary) out['program'] += [shift_owned(e) for e in word['program'][:cut+1]] - out['program'] += middle - out['program'] += [use_successor(e) for e in inverse(middle)] + out['program'] += [shift_owned(e) for e in middle] + out['program'] += [use_successor(shift_owned(e)) for e in inverse(middle)] out['program'] += [use_successor(shift_owned(e)) for e in word['program'][cut+1:]] out['program'] += [use_successor([*e[:-1], v]) for e in boundary] return out diff --git a/research/p104-helper-subspace-splits/search.py b/research/p104-helper-subspace-splits/search.py index 27e19ce2d2..1bf5329658 100644 --- a/research/p104-helper-subspace-splits/search.py +++ b/research/p104-helper-subspace-splits/search.py @@ -111,8 +111,7 @@ def candidates(word, group, entry, exit_frame): if op == 'INIT': columns[r] = {} elif op == 'CLEAR': - # This screen also rejects directions lost at an owned erasure. - columns[r] = {r:Q(1)} + columns[r] = {} elif op == 'COPY': add(columns[event[2]], columns[r], Q(event[-2])) columns[r] = {} diff --git a/research/p104-helper-subspace-splits/verify.py b/research/p104-helper-subspace-splits/verify.py index c30227dc77..b977942a8c 100644 --- a/research/p104-helper-subspace-splits/verify.py +++ b/research/p104-helper-subspace-splits/verify.py @@ -33,16 +33,11 @@ def authenticate(): 'Source Git blob: '+row['path']) count += 1 for row in manifest['external_inputs']: - source, = [r for r in manifest['files'] if r['path'] == row['source_path']] - need(source['pin'] == 'head:'+row['source_commit']+':'+row['source_path'], - 'Published source path and commit') - need((source['sha256'],source['git_blob']) == (row['sha256'],row['git_blob']), - 'Copied input has the published source pins') - raw = (HERE/row['local_path']).read_bytes() - need(sha256(raw).hexdigest() == row['sha256'], 'Copied source SHA256') - need(sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest() == row['git_blob'], - 'Copied source Git blob') - count += 1 + retained_path = (HERE.relative_to(ROOT)/row['local_path']).as_posix() + retained, = [r for r in manifest['files'] if r['path'] == retained_path] + need(retained['usage'] == 'input', 'Copied source is a declared live input') + need((retained['sha256'],retained['git_blob']) == (row['sha256'],row['git_blob']), + 'Retained bytes equal the recorded published source') return count From 0644592d421b375c221045954fdf13932575ffa8 Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Sun, 25 Oct 2026 16:32:19 -0500 Subject: [PATCH 4/6] Record cold replay and coordinate parallel helper-basis work --- .../p104-helper-subspace-splits/README.md | 12 ++++- .../p104-helper-subspace-splits/TASK.json | 6 +++ .../p104-helper-subspace-splits/VALIDATION.md | 48 +++++++++++++++++-- 3 files changed, 60 insertions(+), 6 deletions(-) diff --git a/research/p104-helper-subspace-splits/README.md b/research/p104-helper-subspace-splits/README.md index 83cfa3114e..50d2b36104 100644 --- a/research/p104-helper-subspace-splits/README.md +++ b/research/p104-helper-subspace-splits/README.md @@ -71,8 +71,8 @@ a missing central translation, an inadequate cutoff and insufficient BIT stock. The scientific base is canonical main `5e0052ca0aa3036a3afa8b0438927377c8d97d53`, priority revision 7. The [canonical claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19183208) -records the changed question and local screens. The latest pre-package overlap -cache covered 329 open PRs and 4,851 Discussion records, with complete remote +records the changed question and local screens. The final publication overlap +cache covered 334 open PRs and 4,863 Discussion records, with complete remote pagination and incomplete sparse local coverage. Source and coverage details are coordination evidence, not a novelty proof. @@ -89,6 +89,14 @@ No new Gaussian itinerary is introduced. Active frame-extension work in [Discussion5575](https://github.com/CrocSwap/integer-mult-bounds/discussions/5575) is a separate investigation. +The final refresh also found [parallel coupled-basis and handoff work](https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19154639). +It uses the same rank-one mechanism and separately changes paid boundary +work. The [public composition handoff](https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19183908) +releases these fifteen cuts and leaves the six paid-boundary changes with +the parallel claim. No exclusive method novelty or combined gain is claimed. +The new scalar contacts and input count change the hypotheses of +[PR5590](https://github.com/CrocSwap/integer-mult-bounds/pull/5590)’s fixed-contact floor. + The scope changes the scalar word, the input count and the target contract. It therefore differs from a scalar-only simplification or a fixed-input helper stop. The unchanged paid histogram now supports a different, diff --git a/research/p104-helper-subspace-splits/TASK.json b/research/p104-helper-subspace-splits/TASK.json index 56bf3f7ac0..57449f11c7 100644 --- a/research/p104-helper-subspace-splits/TASK.json +++ b/research/p104-helper-subspace-splits/TASK.json @@ -67,6 +67,12 @@ "why_it_matters": "The two greedy orders found the same invoice but do not prove a global maximum.", "first_step": "Use the new word and test both prefix and suffix support before assigning credit. Coordinate with Discussion5575 for any changed frame itinerary.", "blocked_by": "Every added target must have a clean independent input/output contract and a complete caller bill." + }, + { + "question": "Can the fifteen released target splits compose with the six paid-boundary changes in the parallel Discussion claim?", + "why_it_matters": "The target gain and paid gain could be compatible, but the input bases and cuts must be checked together.", + "first_step": "Use the public handoff at discussioncomment-19183908. Obtain the exact other word, pin it, reconstruct the common helper groups, then replay the full combined caller and price.", + "blocked_by": "The parallel update was local-only at this publication checkpoint. No combined certificate exists here." } ] } diff --git a/research/p104-helper-subspace-splits/VALIDATION.md b/research/p104-helper-subspace-splits/VALIDATION.md index 1ee208b2f0..3505e54883 100644 --- a/research/p104-helper-subspace-splits/VALIDATION.md +++ b/research/p104-helper-subspace-splits/VALIDATION.md @@ -31,7 +31,47 @@ The optional final-word discovery screen returned 53 tested boundary groups and no further candidate. The screen restricts the cut locations and tested basis pairs; it is not an optimality certificate. -Optimized, registered, committed-byte and isolated export checks will be -recorded here before publication. Independent human review and hosted CI -are pending. No complete rounded multiplier or enormous uniform word was -materialized. +## Committed and exported replay + +The final scientific files at commit +`31a4de233bbdd65c04c63dc3398ecf0eed8e1375` passed the registered normal and +optimized replays: + +```sh +python3 -W error -B scripts/research_package.py --package research/p104-helper-subspace-splits --check-only +python3 -W error -B scripts/research_package.py --package research/p104-helper-subspace-splits +python3 -B scripts/check_research_commit.py --package research/p104-helper-subspace-splits --ref 31a4de233bbdd65c04c63dc3398ecf0eed8e1375 +``` + +The package metadata, source pins and exact committed bytes passed. +The registered hook ended with `PASS_REGISTERED_RESEARCH_PACKAGE`. +Both scientific modes ended with `PASS_P104_HELPER_SUBSPACE_KAPPA_00309839`. +Later publication edits affect only documentation and TASK metadata. + +The official exporter produced a 27-file payload plus its export manifest +from that commit. Its integrity check passed. In a fresh directory with no +Git repository, empty PATH, read-only files and read-only directories, the +isolated optimized verifier passed. Every file hash and mode stayed fixed. +A temporary one-byte source corruption was rejected at SHA256 authentication +before any imported source code ran. The original bytes and mode were then +restored and checked. The final harness marker was +`PASS_READ_ONLY_GIT_FREE_REPLAY_AND_SOURCE_FAULT` (28 files with the manifest). + +```sh +python3 -B scripts/export_research_package.py export --package research/p104-helper-subspace-splits --ref 31a4de233bbdd65c04c63dc3398ecf0eed8e1375 --output /tmp/helper-splits.tar +python3 -B scripts/export_research_package.py check /tmp/helper-splits.tar +``` + +The copied source is pinned to its retained path at ancestor commit +`29fe88ba218b5d2192d8e31f07a01d1141afdacd`. Its SHA256 and Git blob equal the +recorded PR5580 source. The original PR5580 Git object was checked before +this retention change. The final registered replay does not require cached +unmerged-branch objects. The base and retained-source commits were both +confirmed as ancestors of the contribution. Full-history preflight was not +run because this checkout is shallow. + +The final continuation screen also allows the source's owned erasures. It +still returns 53 tested boundary groups and no further candidate. + +Independent human review and hosted CI are pending. No complete rounded +multiplier or enormous uniform word was materialized. 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z9~t$*7)7d=-x!l)WJ_TRnYsmZUmvo2OgR*r{wlc~q)T>Q{UtM(Oj?m%A*y#9)6@g1 zKvdg_3!)UJT2+1<^sFpb;#DDAT8tm^uWP=W^NVXbpc>{52fy;KAx~ZjYOCz*P$gZZ^ zN9+<3F&1`)6ws|AeW=3A;Ut@-Dh~1ONJR6f_WDiFR7FvuwrpS7zmy6kY3pt$Czv5i zD2J;ni`SMFtXkfrdf6pZ&0Ce)W!1ON^PBMc3oUbVpWi$dx}2$NQ6*6Y5$|=P=H=KG zE7K3;vJ1-^9!kwron_1Rb*V(PmU@YjkVz)hDa9pf7%gp+-@U11xzw)uMOW3|n<~nZ zrI!<1(W7NZVRA~CvX`lye?qcpaZChD$ZKRI_B= zs3ujCw(5gEWbcq2y2)-sP1eddtD#>E;YaQu72-@56b_!#LRQ?T$MQrax_ zSE2uzw@FJ^TG*vDkzOSt%h`3~@ZL0`t>p2A?CA#5I=qND)(zD^6fmXHvJQr*iM$uV;tRKirdEu~~^+0u}aungs$ zcWOrVG(Jx`h-O-<0{Cz&D{aaTp#qwcwIqwl@c~|Wrw^*mKGkgQvdQEmARHx5XZlUE zndXvhBft2q=`W$_;cI#Z>3XH`oB2S`uX#kIx}1b;%AvB=u-~$&^dz$7coy*+_kaD*|M}~WfBTRB{%OC&gkAM4o)_(ol|M>6!=YRam|NO82@4x=~_y7JM|Knf& U_0Rgp|M$QA{|bmP!hO#P05iwqZ2$lO literal 0 HcmV?d00001 From 09dd0965711ca7eeb169057a420abab1c9052137 Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Sun, 25 Oct 2026 16:51:53 -0500 Subject: [PATCH 6/6] Compose independent helper splits with PR5565 for kappa 0.00310045 --- research/p104-helper-subspace-splits/NOTICE | 1 + research/p104-helper-subspace-splits/PROOF.md | 64 ++-- .../p104-helper-subspace-splits/README.md | 74 +++-- .../p104-helper-subspace-splits/RESULT.json | 290 +++++++++--------- .../p104-helper-subspace-splits/SOURCES.json | 15 + .../p104-helper-subspace-splits/SPLITS.json | 72 +---- .../p104-helper-subspace-splits/TASK.json | 10 +- .../p104-helper-subspace-splits/VALIDATION.md | 88 ++---- .../p104-helper-subspace-splits/VERIFY.json | 7 +- .../p104-helper-subspace-splits/WORD.json.gz | Bin 108157 -> 108031 bytes .../p104-helper-subspace-splits/pricing.py | 11 +- .../p104-helper-subspace-splits/verify.py | 23 +- 12 files changed, 306 insertions(+), 349 deletions(-) diff --git a/research/p104-helper-subspace-splits/NOTICE b/research/p104-helper-subspace-splits/NOTICE index a3f5136a05..f34687ff7e 100644 --- a/research/p104-helper-subspace-splits/NOTICE +++ b/research/p104-helper-subspace-splits/NOTICE @@ -3,6 +3,7 @@ Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. The same assistant performed the construction and author-side checks. Retained contributions: +Pierre-Loic Doulcet (hexapode): PR5565 commuting-contact construction, used as the exact source. Ali Romman: PR5580 contact step and PR5544/5545 complete P104 caller. Joel Pulikkan (GamingPuzzled): PR5569 priced helper handoff. DreamingOfClouds: PR5561 free helper endpoints and PR5568 search tools. diff --git a/research/p104-helper-subspace-splits/PROOF.md b/research/p104-helper-subspace-splits/PROOF.md index e479b15351..ca97998444 100644 --- a/research/p104-helper-subspace-splits/PROOF.md +++ b/research/p104-helper-subspace-splits/PROOF.md @@ -1,6 +1,6 @@ # Independent helper splits and the complete cost -This proof changes the helper input and output contract of the exact PR5580 +This proof changes the helper input and output contract of the exact PR5565 word. It retains every main endpoint, paid Gaussian call and owned lifetime. All scalar identities below are over the rationals. The native check supplies exact phases and the rule for every positive tensor width. @@ -70,61 +70,64 @@ positive width; it is not a test at width one alone. ## 2. The first explicit split -The source is PR5580 at `6efa248cf456d6101d757e9d09ba29711d18a13a`. -Use the cut after zero-based event 13778, chart 120 of dimension five, and +The source is PR5565 at `9af814164b9dfc21f19ec737959d67cb71488c95`. +Use the cut after zero-based event 13775, chart 120 of dimension five, and pivot 648. The boundary group has initial chart 3 (dimension zero) and final chart 127 (dimension nine). With e_r the coordinate at role r, the exact vectors are ```math -a=e_{651}^T+(e_{648}^T+e_{649}^T)/2,\quad -b=e_{648}+e_{649}-e_{650}-e_{652}, +a=e_{652}^T,\quad b=e_{652}-e_{648}+e_{650}-e_{649}, ``` ```math -c=(e_{648}^T+e_{649}^T)/2,\quad -d=e_{648}+e_{649}-e_{650}-e_{652}+2e_{205}. +c=e_{652}^T,\quad d=e_{652}-2e_{205}-e_{648}+e_{650}-e_{649}. ``` The complete prefix gives aP=c; the complete suffix gives Sb=d. -Both pairings are one. The first basis change uses five ADDs, the local -basis uses five ADDs, and their two inverses use ten more ADDs. The first -split therefore adds 20 scalar events and replaces H9 by H5 and H4. -A later split divides this particular H5 target further. The full sequence, -including each updated event index, is in `SPLITS.json`. +Both pairings are one. The boundary basis uses six scalar events and the +local basis uses five. With their inverses, the split adds eighteen ADDs +and four sign SCALEs. It replaces H9 by independent H5 and H4 targets. +The full sequence, including each updated event index, is in `SPLITS.json`. `check_cut` reconstructs each prefix functional and propagates each suffix column. It checks that all other input and output coefficients are zero. The verifier then checks every public and owned row after each complete -split. A separate dense-integer transpose replay checks all 574,564 entries -of the final 758 by 758 interface. +split. A separate dense-integer transpose replay checks all 571,536 entries +of the final 756 by 756 interface. ## 3. The complete target change -The fifteen splits are +The thirteen splits are - six H9 to H4 + H5; - five H9 to H2 + H7; -- three H9 to H1 + H8; -- one H5 to H1 + H4. +- two H9 to H1 + H8. -They add 15 independent helper inputs. The source's 735 public fields become -750, of which 542 are helpers and 208 are main fields. Eight owned lifetime -roles remain; only one is live at a time. The 25,140 source events become -25,502. Every source paid occurrence remains, with the same ordered pair of +They add 13 independent helper inputs. The source's 735 public fields become +748, of which 540 are helpers and 208 are main fields. Eight owned lifetime +roles remain; only one is live at a time. The 25,133 source events become +25,475. Every source paid occurrence remains, with the same ordered pair of charts, rank and ownership. Some register names change to identify the successor input. The new local helper profile is ```text -{1:4, 2:5, 4:90, 5:10, 7:5, 8:18, 9:410}. +{1:2, 2:5, 4:89, 5:11, 7:5, 8:16, 9:412}. ``` +The verifier also replays the retained PR5580 source. It checks that PR5565 +changes its local paid profile by `-8H1-H3-2H4+4H5` and its helper profile +by `-H8+H9`. These source changes are by Pierre-Loic Doulcet (hexapode). The new splits retain +that paid profile. The earlier fifteen-split component on PR5580 is frozen +at `31a4de233bbdd65c04c63dc3398ecf0eed8e1375`. Two of its cuts are absent +from the PR5565 composition, but the lower paid cost gives a larger kappa. + For every 0(a+b)^t`. Each split strictly increases the target moment and leaves the paid moment fixed. The signed local target change is ```math -4H_1+5H_2+7H_4+5H_5+5H_7+3H_8-14H_9. +2H_1+5H_2+6H_4+6H_5+5H_7+2H_8-13H_9. ``` Its rank mass is zero, as required. A source-bound complete caller, not a @@ -149,8 +152,8 @@ contacts, 53,248 central-square column checks, 3,328 main Gaussian targets, spectators, exact phases and every whole target. The complete counts are ```text -paid calls: 66852 -productive fields: 13084 = 18*542 + 32*104 +paid calls: 66726 +productive fields: 13048 = 18*540 + 32*104 rank mass surplus: 760 maximum target: 145 maximum paid rank: 72 @@ -165,9 +168,9 @@ It is not left at the old 12,814 value. ## 5. Strictification, compiler and outer transfer Two independent rational interval engines evaluate the complete moments. -The exact raw crossing is in (0.00309839352211, 0.00309839352212). -`RESULT.json` gives its rational endpoints and the strict tested margin. The claimed kappa is 0.00309839 and the tested saving is -0.0030983905. Their gap funds the finite compiler and outer parameters. An exact negative +The exact raw crossing is in (0.00310045630724, 0.00310045630725). +`RESULT.json` gives its rational endpoints and the strict tested margin. The claimed kappa is 0.00310045 and the tested saving is +0.0031004505. Their gap funds the finite compiler and outer parameters. An exact negative derivative bound on [0,0.0034] makes this crossing the raw ceiling for this fixed invoice under the retained BIT cap. It is not a global optimum. @@ -199,6 +202,7 @@ identities and every new numerical condition within that framework. The enormous uniform word and complete rounded multiplier are not materialized. These are author-side checks by the same AI-assisted author. They are not independent human acceptance or a proof-kernel theorem. -Two greedy cut orders on PR5569 reached the same fifteen-split histogram. -That observation does not prove a maximum over bases, cuts, scalar programs, +The final exact discovery screen tests 52 boundary groups and finds no +further candidate in its finite basis-pair class. It does not prove a maximum +over bases, cuts, scalar programs, frames, controllers or multiplication algorithms. diff --git a/research/p104-helper-subspace-splits/README.md b/research/p104-helper-subspace-splits/README.md index 50d2b36104..f6303a8813 100644 --- a/research/p104-helper-subspace-splits/README.md +++ b/research/p104-helper-subspace-splits/README.md @@ -1,35 +1,35 @@ -# Conditional kappa 0.00309839 from independent helper splits +# Conditional kappa 0.00310045 from independent helper splits -This construction raises complete conditional **kappa to 0.00309839**. -The gain over [PR5580](https://github.com/CrocSwap/integer-mult-bounds/pull/5580) -(0.00308189) is **0.00001650**, about **0.5354%**. The gain over selected -0.003027288235 is **0.000071101765**. The selected record is unchanged. +This construction raises complete conditional **kappa to 0.00310045**. +The gain over [PR5565](https://github.com/CrocSwap/integer-mult-bounds/pull/5565) +(0.00308520) is **0.00001525**, about **0.4943%**. The gain over selected +0.003027288235 is **0.000073161765**. The selected record is unchanged. The mechanism changes the independent helper basis. At a common-frame cut, one helper combination can finish early and a fresh independent input can -use the remaining program. Fifteen explicit splits replace 527 helper -jobs by 542 helper jobs. They add 362 scalar events and no recursive Gaussian +use the remaining program. Thirteen explicit splits replace 527 helper +jobs by 540 helper jobs. They add 342 scalar events and no recursive Gaussian call. Both input and output support are checked over every field; a local pure row alone does not earn a new target. Read the [proof](PROOF.md), [exact cuts](SPLITS.json), [complete word](WORD.json.gz), [receipt](RESULT.json), [source pins](SOURCES.json), and [validation record](VALIDATION.md). -The first split is an explicit 20-ADD change from one H9 target to independent +The first split is an explicit 22-event change from one H9 target to independent H5 and H4 targets. The complete caller uses the new word at all 18 full sites. | Quantity | Result | | --- | ---: | -| Local public inputs | 750 | -| Independent helpers per full call | 542 | +| Local public inputs | 748 | +| Independent helpers per full call | 540 | | Owned lifetimes / peak owned fields | 8 / 1 | -| Local events | 25,502 | -| Complete paid calls | 66,852, unchanged | -| Complete productive fields | 13,084 | +| Local events | 25,475 | +| Complete paid calls | 66,726, unchanged | +| Complete productive fields | 13,048 | | Complete rank-mass surplus | 760, unchanged | -| Tested saving | 0.0030983905 | -| Complete conditional kappa | 0.00309839 | -| Raw crossing | (0.00309839352211, 0.00309839352212) | -| Exact native maps | 2,926 | +| Tested saving | 0.0031004505 | +| Complete conditional kappa | 0.00310045 | +| Raw crossing | (0.00310045630724, 0.00310045630725) | +| Exact native maps | 2,923 | The added helpers enter the complete completion-tail calculation. The tail bound changes to 39/40, with `(39/40)^128 < 1/16`. The compiler logarithm @@ -51,7 +51,7 @@ python3 -B scripts/research_package.py --package research/p104-helper-subspace-s ``` The registered hook runs normally and with `-O`. Its success markers are -`PASS_P104_HELPER_SUBSPACE_KAPPA_00309839` and +`PASS_P104_HELPER_SUBSPACE_KAPPA_00310045` and `PASS_REGISTERED_RESEARCH_PACKAGE`. Direct replay needs no Git or network: ```sh @@ -76,15 +76,21 @@ cache covered 334 open PRs and 4,863 Discussion records, with complete remote pagination and incomplete sparse local coverage. Source and coverage details are coordination evidence, not a novelty proof. -The consumed PR5580 word is pinned to -`6efa248cf456d6101d757e9d09ba29711d18a13a`. It retains the released PR5569 -handoff and PR5561 helper endpoints. The new basis splits were first found -on PR5569. Two different greedy cut orders reached the same fifteen-split -histogram. All fifteen were then composed with PR5580 and checked again. The exact -source copy is retained in this branch at commit -`29fe88ba218b5d2192d8e31f07a01d1141afdacd`. Its SHA256 and Git blob match the -recorded PR5580 source. Registered replay needs only this branch history; -it does not need cached objects from unmerged PR branches. +The consumed PR5565 word is pinned to +`9af814164b9dfc21f19ec737959d67cb71488c95`. It includes Pierre-Loic Doulcet's published +commuting-contact cascade and the released PR5580/PR5569/PR5561 lineage. +The source copy is retained in this branch at commit +`bf64e66656843a64e798b8374cd9f53add3f6f46`. Its SHA256 and Git blob match +the recorded PR5565 source. The PR5580 copy remains an active comparison +input: replay checks the exact paid and helper changes supplied by PR5565. +Registered replay needs this branch history and its main base; it does not +need cached objects from unmerged PR branches. + +The earlier fifteen-split component on PR5580 remains frozen at +`31a4de233bbdd65c04c63dc3398ecf0eed8e1375`. Two cuts are absent from this +composition. PR5565's lower paid cost more than offsets that lost target +gain. The complete claim increases by 0.00000206 over that component. +This package introduces no new commuting-contact search. No new Gaussian itinerary is introduced. Active frame-extension work in [Discussion5575](https://github.com/CrocSwap/integer-mult-bounds/discussions/5575) is a separate investigation. @@ -92,8 +98,10 @@ is a separate investigation. The final refresh also found [parallel coupled-basis and handoff work](https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19154639). It uses the same rank-one mechanism and separately changes paid boundary work. The [public composition handoff](https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19183908) -releases these fifteen cuts and leaves the six paid-boundary changes with -the parallel claim. No exclusive method novelty or combined gain is claimed. +releases the earlier fifteen cuts and leaves the six paid-boundary changes +with the parallel claim. That claim is testing their composition. This +package composes only the released PR5565 source with helper splits. No +exclusive method novelty or gain from the parallel paid changes is claimed. The new scalar contacts and input count change the hypotheses of [PR5590](https://github.com/CrocSwap/integer-mult-bounds/pull/5590)’s fixed-contact floor. @@ -112,8 +120,10 @@ optimality are not claimed. ## Sources and credit +- **Pierre-Loic Doulcet / hexapode**: [PR5565](https://github.com/CrocSwap/integer-mult-bounds/pull/5565) + supplies the exact commuting-contact source word. - **Ali Romman**: [PR5580](https://github.com/CrocSwap/integer-mult-bounds/pull/5580) - supplies the exact source word; [PR5544](https://github.com/CrocSwap/integer-mult-bounds/pull/5544) + supplies its preceding contact step; [PR5544](https://github.com/CrocSwap/integer-mult-bounds/pull/5544) and [PR5545](https://github.com/CrocSwap/integer-mult-bounds/pull/5545) supply the complete P104 caller and source replay. - **Joel Pulikkan / GamingPuzzled**: [PR5569](https://github.com/CrocSwap/integer-mult-bounds/pull/5569) @@ -141,7 +151,7 @@ See [NOTICE](NOTICE). An independent reviewer can check the first split and then replay the complete package. Further gains could use a different compatible cut order, basis or frame itinerary. Both prefix and suffix support must be proved before a -new target receives credit. The two greedy runs do not establish a global +new target receives credit. The finite discovery screen does not establish a global maximum. [TASK.json](TASK.json) gives the first checks and remaining obligations. The optional continuation screen is reproducible with: @@ -152,6 +162,6 @@ python3 -I -B research/p104-helper-subspace-splits/search.py It tests exact elimination-basis pairs at cuts immediately after MOVE events, inside equal-boundary helper groups. On the final word it finds no further -candidate in 53 groups. This result covers those tested pairs. It does not +candidate in 52 groups. This result covers those tested pairs. It does not exclude different cut sequences, arbitrary basis combinations or new frames. The complete-kappa verifier does not depend on a discovery search failure. diff --git a/research/p104-helper-subspace-splits/RESULT.json b/research/p104-helper-subspace-splits/RESULT.json index 45eecc46a2..35f75c8555 100644 --- a/research/p104-helper-subspace-splits/RESULT.json +++ b/research/p104-helper-subspace-splits/RESULT.json @@ -1,27 +1,27 @@ { - "authenticated_inputs": 12, + "authenticated_inputs": 13, "complete_cost": { "compiler": { "H": 707182000000000, "N": "2^707182000000000", "eta": { - "lower": "0.000000138410144483165815551326", - "upper": "0.000000138410144483165815551327" + "lower": "0.000000136964415492079857925247", + "upper": "0.000000136964415492079857925248" }, "gap": "1/14000000000", "integer_test_exponent": 50513, "logarithm_power": 1024, "theta": "63/64", - "uniform_saving": "21688733/7000000000", + "uniform_saving": "21703153/7000000000", "word_materialized": false }, "full_forward_calls": 18, - "gain": "33/2000000", - "kappa": "309839/100000000", - "kappa_decimal": ".00309839", + "gain": "61/4000000", + "kappa": "62009/20000000", + "kappa_decimal": ".00310045", "margin_at_previous": { - "lower": "4.021482992995643943845868968293", - "upper": "4.021482992995643943845868968294" + "lower": "3.715057037515374246068780385152", + "upper": "3.715057037515374246068780385153" }, "negative_controls": { "old_BIT": "Rejected by outer inequalities", @@ -29,9 +29,9 @@ }, "nonrecursive": { "fixed_scalar_growth_bound": "At most 2^(16*26000) before native factors; a declared constant, not an attained norm.", - "local_paid_rank_mass": 6013, - "local_routes": 5194000, - "local_scalar": 220384, + "local_paid_rank_mass": 6014, + "local_routes": 5183000, + "local_scalar": 220232, "peak_owned_fields": 1, "raw_budget": 1000000000, "raw_scalar_upper": 184647552, @@ -53,82 +53,82 @@ "new_semantic_group_guard": "3/14000000000" }, "margins": { - "boundary_algebraic_matrix": "607284495956622537/196000000000000000000", - "fused_gaussian": "607284495869867611/196000000000000000000", - "global_coordinate_router": "5422183/1750000000", - "group_bit_router": "75910563733733451/24500000000000000000", + "boundary_algebraic_matrix": "607688255956593697/196000000000000000000", + "fused_gaussian": "607688255869781091/196000000000000000000", + "global_coordinate_router": "1356447/437500000", + "group_bit_router": "18990258433430659/6125000000000000000", "group_scans": "6999999999/7000000000", - "main_transform": "607284481956622537/196000000000000000000", + "main_transform": "607688241956593697/196000000000000000000", "microbox_face_corrections": "269500000001/3500000000", "polynomial_products": "13999999999/14000000000", - "sparse_union_movement": "80232284495956622537/196000000000000000000" + "sparse_union_movement": "80232688255956593697/196000000000000000000" }, "parameters": { - "a": "5422183/1750000000", - "b": "8675493/2800000000", + "a": "1356447/437500000", + "b": "8681261/2800000000", "beta": "13999999997/14000000000", "bit_saving": "17/5000", - "cap_xi": "178232284481956622537/196000000000000000000", - "complex_uniform_saving": "21688733/7000000000", + "cap_xi": "178232688241956593697/196000000000000000000", + "complex_uniform_saving": "21703153/7000000000", "d": "1/14000000000", "epsilon": "13999999999/14000000000", - "kappa": "309839/100000000", - "lambda_": "3987606439/4000000000", - "lambda_prime": "13956622537/14000000000", + "kappa": "62009/20000000", + "lambda_": "3987598199/4000000000", + "lambda_prime": "13956593697/14000000000", "layout": "1/14000000000", - "q": "43377463/14000000000", + "q": "43406303/14000000000", "r0": "1/140000000000", "stop": "1/14000000000", - "tested_saving": "6196781/2000000000" + "tested_saving": "6200901/2000000000" }, "strict_checks": { - "actual_bit_above_effective": "527817/1750000000", + "actual_bit_above_effective": "131053/437500000", "actual_logarithmic_gamma_guard": "1/14000000000", - "actual_logarithmic_group_guard": "17767715539043377463/98000000000000000000", + "actual_logarithmic_group_guard": "17767311779043406303/98000000000000000000", "alpha_logarithm_absorption": "1/140000000000", - "boundary_algebraic_matrix_above_kappa": "55956622537/196000000000000000000", - "cap_above_band": "80232284481956622537/196000000000000000000", - "cap_below_cell": "17767715504043377463/196000000000000000000", - "cap_below_phase_cell_power": "213767715518043377463/196000000000000000000", + "boundary_algebraic_matrix_above_kappa": "55956593697/196000000000000000000", + "cap_above_band": "80232688241956593697/196000000000000000000", + "cap_below_cell": "17767311744043406303/196000000000000000000", + "cap_below_phase_cell_power": "213767311758043406303/196000000000000000000", "complex_above_effective": "1/14000000000", - "complex_below_one_over_32": "78824507/2800000000", + "complex_below_one_over_32": "78818739/2800000000", "complex_endpoint": "1/7000000000", "epsilon_below_one": "1/14000000000", "epsilon_positive": "13999999999/14000000000", "fine_prime_halo_umbrella": "7/2", - "fused_gaussian_above_kappa": "55869867611/196000000000000000000", - "gaussian_above_main": "6956622537/98000000000000000000", + "fused_gaussian_above_kappa": "55869781091/196000000000000000000", + "gaussian_above_main": "6956593697/98000000000000000000", "global_coordinate_router_above_kappa": "1/3500000000", "global_gamma_power_slack": "9/140000000000", "group_below_dimension": "1/7000000000", - "group_bit_router_above_kappa": "8733733451/24500000000000000000", - "group_gauge_power_slack": "17767715538343377463/98000000000000000000", + "group_bit_router_above_kappa": "2183430659/6125000000000000000", + "group_gauge_power_slack": "17767311778343406303/98000000000000000000", "group_key_fits_record": "1/7000000000", "group_positive": "13999999997/14000000000", - "group_scans_above_kappa": "6978311269/7000000000", + "group_scans_above_kappa": "6978296849/7000000000", "halo_covers_generic_inverse_radius": "5", - "improvement_over_user_baseline": "683709790400418148631/500000000000000000000000", + "improvement_over_user_baseline": "684739790400418148631/500000000000000000000000", "lambda_above_internal": "1/28000000000", "lambda_above_sigma": "3/28000000000", "lambda_above_tau": "1/28000000000", "lambda_prime_above_lambda": "1/28000000000", - "lambda_prime_above_leaf": "5591324507/39200000000000000000", - "leaf_saving_above_effective": "2791324507/39200000000000000000", - "main_transform_above_kappa": "41956622537/196000000000000000000", + "lambda_prime_above_leaf": "5591318739/39200000000000000000", + "leaf_saving_above_effective": "2791318739/39200000000000000000", + "main_transform_above_kappa": "41956593697/196000000000000000000", "membership_arithmetic_fits_record": "1/14000000000", - "microbox_face_corrections_above_kappa": "67372288909/875000000", + "microbox_face_corrections_above_kappa": "134744574213/1750000000", "microbox_halo_volume": "1106000000003/14000000000", "new_complex_uniform_saving_above_b": "1/14000000000", "new_semantic_guard_with_C1_one": "1/14000000000", - "polynomial_products_above_kappa": "13956622539/14000000000", + "polynomial_products_above_kappa": "13956593699/14000000000", "positive_layout_slack": "1/14000000000", "q_below_effective": "1/14000000000", "q_below_internal": "1/14000000000", - "q_below_leaf": "5591324507/39200000000000000000", - "q_positive": "43377463/14000000000", - "short_record_fallback": "2791324507/2800000000", + "q_below_leaf": "5591318739/39200000000000000000", + "q_positive": "43406303/14000000000", + "short_record_fallback": "2791318739/2800000000", "source_axis_superpolynomial": "1/14000000000", - "sparse_union_movement_above_kappa": "79625000055956622537/196000000000000000000", + "sparse_union_movement_above_kappa": "79625000055956593697/196000000000000000000", "stop_below_one": "13999999999/14000000000", "stop_positive": "1/14000000000", "strassen_integer_power_gap": "1951441519231", @@ -139,57 +139,57 @@ } }, "paid": { - "1": 41358, + "1": 41214, "16": 416, "2": 8262, "24": 416, - "3": 8892, + "3": 8874, "32": 416, - "4": 1692, + "4": 1656, "40": 416, "48": 416, - "5": 2952, + "5": 3024, "56": 416, "6": 324, "64": 416, "7": 252, "72": 208 }, - "paid_calls": 66852, - "previous_open_pr5580": "308189/100000000", - "productive_fields": 13084, + "paid_calls": 66726, + "previous_open_pr5565": "7713/2500000", + "productive_fields": 13048, "query_shears": 15, "rank_mass_surplus": 760, "raw_ceiling": { - "derivative_upper": "-742178562912626993067497376712728968390111828027818261902388253/3138550867693340381917894711603833208051177722232017256448", + "derivative_upper": "-741665511346505619707405027113237790341393747177503845065075007/3138550867693340381917894711603833208051177722232017256448", "interval": [ "0", "17/5000" ] }, "raw_headroom": [ - "352211/100000000000000", - "88053/25000000000000" + "157681/25000000000000", + "25229/4000000000000" ], "raw_root_interval": [ - "309839352211/100000000000000", - "77459838053/25000000000000" + "77511407681/25000000000000", + "12401825229/4000000000000" ], - "relative_gain_percent": "165000/308189", + "relative_gain_percent": "7625/15426", "strictification": { "alpha": { - "lower": "0.999999996924671652855767269707", - "upper": "0.999999996924671652855767269708" + "lower": "0.999999994094860604597376680636", + "upper": "0.999999994094860604597376680637" }, "cutoff": 17, "delta": { - "lower": "0.974960865956418695329746822454", - "upper": "0.974960865956418695329746822455" + "lower": "0.972208404163139976829701213167", + "upper": "0.972208404163139976829701213168" }, "floor": 18, "gamma": { - "lower": "0.967384791473130552704363573836", - "upper": "0.967384791473130552704363573837" + "lower": "0.967537821927968182942254182934", + "upper": "0.967537821927968182942254182935" }, "normalized_paid_upper": "5242880004882813/5242880536870912", "power": 1024, @@ -197,25 +197,25 @@ "tail_block": 128, "tail_decay": "39/40", "tail_offset": "1/5", - "tested": "6196781/2000000000" + "tested": "6200901/2000000000" }, "targets": { - "1": 72, + "1": 36, "145": 208, "17": 416, "2": 90, "25": 416, "33": 416, - "4": 1620, + "4": 1602, "41": 416, "49": 416, - "5": 180, + "5": 198, "57": 416, "65": 416, "7": 90, "73": 208, - "8": 324, - "9": 7380 + "8": 288, + "9": 7416 }, "whole_idle_jobs": 3120 }, @@ -225,55 +225,55 @@ "No independent human or proof-kernel acceptance or global optimality is claimed." ], "local": { - "endpoint_coefficients": 574564, + "endpoint_coefficients": 571536, "helpers": { - "1": 4, + "1": 2, "2": 5, - "4": 90, - "5": 10, + "4": 89, + "5": 11, "7": 5, - "8": 18, - "9": 410 + "8": 16, + "9": 412 }, "owned_lifetimes": 8, "paid": { - "1": 2211, + "1": 2203, "2": 459, - "3": 494, - "4": 94, - "5": 164, + "3": 493, + "4": 92, + "5": 168, "6": 18, "7": 14 }, - "paid_rank_mass": 6013, + "paid_rank_mass": 6014, "peak_owned_fields": 1, - "public_inputs": 750, - "real_scalar_allowance": 220384 + "public_inputs": 748, + "real_scalar_allowance": 220232 }, "local_helper_delta": { - "1": 4, + "1": 2, "2": 5, - "4": 7, - "5": 5, + "4": 6, + "5": 6, "7": 5, - "8": 3, - "9": -14 + "8": 2, + "9": -13 }, "native": { - "distinct_maps": 2926, - "helper_normalizers": 1084, + "distinct_maps": 2923, + "helper_normalizers": 1080, "helpers": { - "1": 4, + "1": 2, "2": 5, - "4": 90, - "5": 10, + "4": 89, + "5": 11, "7": 5, - "8": 18, - "9": 410 + "8": 16, + "9": 412 }, "main_adapters": 208, "proof": "Every signed Pauli image and exact global phase; frame induction at every positive tensor width", - "recipe_payload_sha256": "7a9003650ed834a233a0f7416976e245c0df0bf93db8eab3a03a462475eb021e", + "recipe_payload_sha256": "b2e6b538f6152ccf0024ca57381e46b2fe6b75b89504d935009dade234cc3f18", "wrong_phase_rejected": true }, "negative_controls": { @@ -334,15 +334,27 @@ 31 ] }, + "published_source_delta": { + "helpers": { + "8": -1, + "9": 1 + }, + "paid": { + "1": -8, + "3": -1, + "4": -2, + "5": 4 + } + }, "separate_columns": { "arithmetic": "Dense integer rows with binary denominators; reverse chronology", - "coefficients": 574564, - "columns": 758 + "coefficients": 571536, + "columns": 756 }, "splits": [ { - "cut_after": 13778, - "events": 25162, + "cut_after": 13775, + "events": 25155, "pivot": 648, "public": 736, "ranks": [ @@ -351,8 +363,8 @@ ] }, { - "cut_after": 13768, - "events": 25184, + "cut_after": 13765, + "events": 25177, "pivot": 592, "public": 737, "ranks": [ @@ -361,8 +373,8 @@ ] }, { - "cut_after": 13709, - "events": 25202, + "cut_after": 13706, + "events": 25195, "pivot": 664, "public": 738, "ranks": [ @@ -371,8 +383,8 @@ ] }, { - "cut_after": 13676, - "events": 25224, + "cut_after": 13673, + "events": 25217, "pivot": 680, "public": 739, "ranks": [ @@ -382,7 +394,7 @@ }, { "cut_after": 12526, - "events": 25260, + "events": 25253, "pivot": 259, "public": 740, "ranks": [ @@ -392,7 +404,7 @@ }, { "cut_after": 12448, - "events": 25292, + "events": 25285, "pivot": 432, "public": 741, "ranks": [ @@ -401,8 +413,8 @@ ] }, { - "cut_after": 13967, - "events": 25306, + "cut_after": 13961, + "events": 25299, "pivot": 722, "public": 742, "ranks": [ @@ -411,8 +423,8 @@ ] }, { - "cut_after": 13642, - "events": 25324, + "cut_after": 13647, + "events": 25317, "pivot": 14, "public": 743, "ranks": [ @@ -421,8 +433,8 @@ ] }, { - "cut_after": 13643, - "events": 25342, + "cut_after": 13648, + "events": 25335, "pivot": 76, "public": 744, "ranks": [ @@ -431,8 +443,8 @@ ] }, { - "cut_after": 13643, - "events": 25376, + "cut_after": 13648, + "events": 25369, "pivot": 345, "public": 745, "ranks": [ @@ -441,8 +453,8 @@ ] }, { - "cut_after": 13632, - "events": 25426, + "cut_after": 13637, + "events": 25419, "pivot": 573, "public": 746, "ranks": [ @@ -451,45 +463,25 @@ ] }, { - "cut_after": 13779, - "events": 25434, - "pivot": 649, - "public": 747, - "ranks": [ - 1, - 8 - ] - }, - { - "cut_after": 12079, - "events": 25460, + "cut_after": 12078, + "events": 25445, "pivot": 405, - "public": 748, + "public": 747, "ranks": [ 8, 1 ] }, { - "cut_after": 12611, - "events": 25490, + "cut_after": 12610, + "events": 25475, "pivot": 225, - "public": 749, + "public": 748, "ranks": [ 8, 1 ] - }, - { - "cut_after": 13817, - "events": 25502, - "pivot": 648, - "public": 750, - "ranks": [ - 1, - 4 - ] } ], - "status": "PASS_P104_HELPER_SUBSPACE_KAPPA_00309839" + "status": "PASS_P104_HELPER_SUBSPACE_KAPPA_00310045" } diff --git a/research/p104-helper-subspace-splits/SOURCES.json b/research/p104-helper-subspace-splits/SOURCES.json index 1bedb207e9..f83bf3c818 100644 --- a/research/p104-helper-subspace-splits/SOURCES.json +++ b/research/p104-helper-subspace-splits/SOURCES.json @@ -92,6 +92,13 @@ "usage": "provenance", "git_blob": "dbb3d56a4f5b733bb0c32a91249d1f6a7e1ab5d2", "sha256": "878734dfd64c4b9d362d0ae476cc5c2a19fe93e48b7378763b23f3e0dd0a5a71" + }, + { + "path": "research/p104-helper-subspace-splits/inputs/PR5565-WORD.json.gz", + "usage": "input", + "git_blob": "4ebe6fcb7adf319bf6b247cf23d89eb1ca4cd914", + "sha256": "3d62828f53e654e3db218bf4611a47aed4a677d48043713dc004db0f8a32990d", + "pin": "head:bf64e66656843a64e798b8374cd9f53add3f6f46:research/p104-helper-subspace-splits/inputs/PR5565-WORD.json.gz" } ], "external_inputs": [ @@ -102,6 +109,14 @@ "source_path": "research/p104-event-contact-step/WORD.json.gz", "sha256": "b2a98c4bd0dbe86c09e9d15ee060dcf1aab09dbef90aa1e2127676f4039f406b", "git_blob": "9434855e7dad0d0236d23210b3e71a2b83a9ae64" + }, + { + "local_path": "inputs/PR5565-WORD.json.gz", + "source_repository": "CrocSwap/integer-mult-bounds", + "source_commit": "9af814164b9dfc21f19ec737959d67cb71488c95", + "source_path": "research/p104-commuting-contact/WORD.json.gz", + "sha256": "3d62828f53e654e3db218bf4611a47aed4a677d48043713dc004db0f8a32990d", + "git_blob": "4ebe6fcb7adf319bf6b247cf23d89eb1ca4cd914" } ], "code_derivation": [ diff --git a/research/p104-helper-subspace-splits/SPLITS.json b/research/p104-helper-subspace-splits/SPLITS.json index 81e7f0ad22..5108daabf7 100644 --- a/research/p104-helper-subspace-splits/SPLITS.json +++ b/research/p104-helper-subspace-splits/SPLITS.json @@ -1,6 +1,6 @@ [ { - "cut_after": 13778, + "cut_after": 13775, "frame": 120, "pivot": 648, "a": { @@ -28,7 +28,7 @@ ] }, { - "cut_after": 13768, + "cut_after": 13765, "frame": 1053, "pivot": 592, "a": { @@ -56,7 +56,7 @@ ] }, { - "cut_after": 13709, + "cut_after": 13706, "frame": 1051, "pivot": 664, "a": { @@ -84,7 +84,7 @@ ] }, { - "cut_after": 13676, + "cut_after": 13673, "frame": 1049, "pivot": 680, "a": { @@ -178,7 +178,7 @@ ] }, { - "cut_after": 13967, + "cut_after": 13961, "frame": 424, "pivot": 722, "a": { @@ -205,7 +205,7 @@ ] }, { - "cut_after": 13642, + "cut_after": 13647, "frame": 462, "pivot": 14, "a": { @@ -233,7 +233,7 @@ ] }, { - "cut_after": 13643, + "cut_after": 13648, "frame": 252, "pivot": 76, "a": { @@ -261,7 +261,7 @@ ] }, { - "cut_after": 13643, + "cut_after": 13648, "frame": 391, "pivot": 345, "a": { @@ -296,7 +296,7 @@ ] }, { - "cut_after": 13632, + "cut_after": 13637, "frame": 603, "pivot": 573, "a": { @@ -340,32 +340,7 @@ ] }, { - "cut_after": 13779, - "frame": 597, - "pivot": 649, - "a": { - "649": "1", - "648": "-1" - }, - "b": { - "650": "-1", - "649": "1", - "198": "-1" - }, - "c": { - "649": "1" - }, - "d": { - "650": "-1", - "649": "1" - }, - "ranks": [ - 1, - 8 - ] - }, - { - "cut_after": 12079, + "cut_after": 12078, "frame": 477, "pivot": 405, "a": { @@ -397,7 +372,7 @@ ] }, { - "cut_after": 12611, + "cut_after": 12610, "frame": 267, "pivot": 225, "a": { @@ -428,30 +403,5 @@ 8, 1 ] - }, - { - "cut_after": 13817, - "frame": 597, - "pivot": 648, - "a": { - "652": "1" - }, - "b": { - "652": "1", - "648": "-1", - "198": "-1/2", - "650": "1", - "649": "-1" - }, - "c": { - "648": "1" - }, - "d": { - "648": "1" - }, - "ranks": [ - 1, - 4 - ] } ] diff --git a/research/p104-helper-subspace-splits/TASK.json b/research/p104-helper-subspace-splits/TASK.json index 57449f11c7..a230fe5b90 100644 --- a/research/p104-helper-subspace-splits/TASK.json +++ b/research/p104-helper-subspace-splits/TASK.json @@ -46,9 +46,9 @@ ] }, "scope_status": "changed", - "actual_scope": "Change the independent P104 helper basis and split 15 targets into two independent targets at common-frame cuts. Verify a complete conditional kappa gain on PR5580.", + "actual_scope": "Change the independent P104 helper basis and split 13 targets into two independent targets at common-frame cuts. Verify a complete conditional kappa gain on the published PR5565 word.", "scope_change_reason": "The donor explicitly requested a different mechanism and a kappa gain. This changes the scalar word, independent input count and helper target contract. It is outside fixed-endpoint retiming and the historical frozen provider catalogue. The card classifies this assigned work; no task was rerolled.", - "bottleneck_link": "At unchanged recursive paid cost, 15 independent target splits strictly increase the concave target moment. Every new input has an explicit returned Gaussian target.", + "bottleneck_link": "At unchanged recursive paid cost relative to PR5565, 13 independent target splits strictly increase the concave target moment. Every new input has an explicit returned Gaussian target.", "budget_minutes": null, "stop_rule": "Require full arbitrary-input and native identities and a complete improved kappa. Stop the finite discovery scan after no further tested split remains; do not claim global optimality.", "outcome": "completed", @@ -64,15 +64,15 @@ }, { "question": "Can a different compatible cut order or changed common frame support more independent target splits?", - "why_it_matters": "The two greedy orders found the same invoice but do not prove a global maximum.", + "why_it_matters": "The finite exact screen does not prove a global maximum.", "first_step": "Use the new word and test both prefix and suffix support before assigning credit. Coordinate with Discussion5575 for any changed frame itinerary.", "blocked_by": "Every added target must have a clean independent input/output contract and a complete caller bill." }, { "question": "Can the fifteen released target splits compose with the six paid-boundary changes in the parallel Discussion claim?", "why_it_matters": "The target gain and paid gain could be compatible, but the input bases and cuts must be checked together.", - "first_step": "Use the public handoff at discussioncomment-19183908. Obtain the exact other word, pin it, reconstruct the common helper groups, then replay the full combined caller and price.", - "blocked_by": "The parallel update was local-only at this publication checkpoint. No combined certificate exists here." + "first_step": "Use the public handoff at discussioncomment-19183908. The parallel claim has released its word at 8384fb9eda5a2fd47556364b26185f3ba3cbd050 and is testing the earlier fifteen-split component. Coordinate there before testing any further composition.", + "blocked_by": "The parallel claim owns the paid-boundary synthesis. This package does not assert a combined certificate with that work." } ] } diff --git a/research/p104-helper-subspace-splits/VALIDATION.md b/research/p104-helper-subspace-splits/VALIDATION.md index 3505e54883..7f73fd1454 100644 --- a/research/p104-helper-subspace-splits/VALIDATION.md +++ b/research/p104-helper-subspace-splits/VALIDATION.md @@ -1,11 +1,11 @@ # Validation record -Environment: macOS, CPython 3.12.14, standard library only. All scientific +Environment: macOS, CPython 3.12.14, standard library only. Scientific replays run serially in the isolated `codex/kappa-structural-20261025` worktree. The scientific base is canonical main `5e0052ca0aa3036a3afa8b0438927377c8d97d53`. -## Completed checks +## Current composition The direct isolated normal replay passed with explicit artifact generation: @@ -13,65 +13,39 @@ The direct isolated normal replay passed with explicit artifact generation: python3 -I -B research/p104-helper-subspace-splits/verify.py --write ``` -It checked all 15 prefix and suffix witnesses, every intermediate complete -interface, 574,564 final transpose coefficients, 2,926 exact native maps, -1,084 helper normalizers, 208 main adapters and the complete physical caller. +It checked 13 prefix and suffix witnesses, each complete arbitrary-input +interface, 571,536 final transpose coefficients, 2,923 exact native maps, +1,080 helper normalizers, 208 main adapters and the complete physical caller. Two exact moment engines, all compiler conditions, 54 strict outer conditions and four functional conditions passed. All eight local/controller mutation controls rejected. The retained wrong-phase, old-cutoff and old-BIT controls also rejected. The raw crossing is in -(0.00309839352211, 0.00309839352212). - -The first parameter trial failed the compiler complement-capacity condition -with logarithm power 1000. The final power 1024 passes that condition and the -complete compiler check. The old count and growth constants are not reused -for the changed helper inventory. - -The optional final-word discovery screen returned 53 tested boundary groups -and no further candidate. The screen restricts the cut locations and tested -basis pairs; it is not an optimality certificate. - -## Committed and exported replay - -The final scientific files at commit -`31a4de233bbdd65c04c63dc3398ecf0eed8e1375` passed the registered normal and -optimized replays: - -```sh -python3 -W error -B scripts/research_package.py --package research/p104-helper-subspace-splits --check-only -python3 -W error -B scripts/research_package.py --package research/p104-helper-subspace-splits -python3 -B scripts/check_research_commit.py --package research/p104-helper-subspace-splits --ref 31a4de233bbdd65c04c63dc3398ecf0eed8e1375 -``` - -The package metadata, source pins and exact committed bytes passed. -The registered hook ended with `PASS_REGISTERED_RESEARCH_PACKAGE`. -Both scientific modes ended with `PASS_P104_HELPER_SUBSPACE_KAPPA_00309839`. -Later publication edits affect only documentation and TASK metadata. - -The official exporter produced a 27-file payload plus its export manifest -from that commit. Its integrity check passed. In a fresh directory with no -Git repository, empty PATH, read-only files and read-only directories, the -isolated optimized verifier passed. Every file hash and mode stayed fixed. -A temporary one-byte source corruption was rejected at SHA256 authentication -before any imported source code ran. The original bytes and mode were then -restored and checked. The final harness marker was -`PASS_READ_ONLY_GIT_FREE_REPLAY_AND_SOURCE_FAULT` (28 files with the manifest). - -```sh -python3 -B scripts/export_research_package.py export --package research/p104-helper-subspace-splits --ref 31a4de233bbdd65c04c63dc3398ecf0eed8e1375 --output /tmp/helper-splits.tar -python3 -B scripts/export_research_package.py check /tmp/helper-splits.tar -``` - -The copied source is pinned to its retained path at ancestor commit -`29fe88ba218b5d2192d8e31f07a01d1141afdacd`. Its SHA256 and Git blob equal the -recorded PR5580 source. The original PR5580 Git object was checked before -this retention change. The final registered replay does not require cached -unmerged-branch objects. The base and retained-source commits were both -confirmed as ancestors of the contribution. Full-history preflight was not -run because this checkout is shallow. - -The final continuation screen also allows the source's owned erasures. It -still returns 53 tested boundary groups and no further candidate. +(0.00310045630724, 0.00310045630725). + +The verifier authenticates 13 live inputs before importing any source code. +It replays both retained source words and checks the exact paid and helper +deltas supplied by PR5565. All new splits preserve the PR5565 paid profile. +The new local paid rank mass is 6014 and enters the native growth bound. +The exact discovery run tested 52 final boundary groups and found no further +candidate in its finite basis-pair class. This is not a global optimum. + +Registered normal/optimized replay is in progress. The committed-byte check +and fresh read-only Git-free export will follow. These checks are not yet +claimed for this composition in this revision. + +## Retained evidence + +The earlier fifteen-split component on PR5580 passed normal, optimized, +registered and read-only Git-free replay at scientific commit +`31a4de233bbdd65c04c63dc3398ecf0eed8e1375`. That evidence applies to its +0.00309839 claim. It is not substituted for the new composition checks. + +The source copies are pinned to their retained paths at ancestor commits +`29fe88ba218b5d2192d8e31f07a01d1141afdacd` (PR5580) and +`bf64e66656843a64e798b8374cd9f53add3f6f46` (PR5565). Each SHA256 and Git blob +equals the recorded published source. Registered replay needs no cached +unmerged-branch objects. Full-history preflight was not run because this +checkout is shallow. Independent human review and hosted CI are pending. No complete rounded multiplier or enormous uniform word was materialized. diff --git a/research/p104-helper-subspace-splits/VERIFY.json b/research/p104-helper-subspace-splits/VERIFY.json index a0904d71a2..f02fe9b970 100644 --- a/research/p104-helper-subspace-splits/VERIFY.json +++ b/research/p104-helper-subspace-splits/VERIFY.json @@ -15,7 +15,8 @@ "research/kappa-rebuild/architecture/mixed_target_probe.py", "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py", "research/query-thinned-controllers/RESULT.json", - "research/p104-helper-subspace-splits/inputs/PR5580-WORD.json.gz" + "research/p104-helper-subspace-splits/inputs/PR5580-WORD.json.gz", + "research/p104-helper-subspace-splits/inputs/PR5565-WORD.json.gz" ], "commands": [ { @@ -25,7 +26,7 @@ "{package}/verify.py" ], "timeout_seconds": 600, - "checks": "Check all 15 independent cuts, every rational row and reverse column, native maps, complete caller and invoice, two moment engines, compiler and outer predicates; reject false inputs, outputs, target credit and cost." + "checks": "Check all 13 independent cuts, every rational row and reverse column, native maps, complete caller and invoice, two moment engines, compiler and outer predicates; reject false inputs, outputs, target credit and cost." }, { "argv": [ @@ -35,7 +36,7 @@ "{package}/verify.py" ], "timeout_seconds": 600, - "checks": "Check all 15 independent cuts, every rational row and reverse column, native maps, complete caller and invoice, two moment engines, compiler and outer predicates; reject false inputs, outputs, target credit and cost." + "checks": "Check all 13 independent cuts, every rational row and reverse column, native maps, complete caller and invoice, two moment engines, compiler and outer predicates; reject false inputs, outputs, target credit and cost." } ] } diff --git a/research/p104-helper-subspace-splits/WORD.json.gz b/research/p104-helper-subspace-splits/WORD.json.gz index 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zUmMm*%Z>Rpt3f{Ld5m-^PG00~EW{gIC<3Du9;I6%8LbjdPA#{JQWGa5iZVeSaaE}{IY5assd}%?jDIuWxyV8tVFAuD%sVM zZP=*YHS{rJfW*ufqEa0A;F8jsO4v diff --git a/research/p104-helper-subspace-splits/pricing.py b/research/p104-helper-subspace-splits/pricing.py index fe03d7eebe..0b54ad3f16 100644 --- a/research/p104-helper-subspace-splits/pricing.py +++ b/research/p104-helper-subspace-splits/pricing.py @@ -5,6 +5,7 @@ Adapted from Ali Romman's PR5544/5545 for the two coupled contact changes. Successor choices were prepared for thu-nmrc with OpenAI Codex assistance. Helper-subspace targets were added by Ali Romman with OpenAI Codex assistance. +The source commuting-contact construction is by Pierre-Loic Doulcet (hexapode) in PR5565. Ali Romman's complete caller/price proof and all predecessor credit are retained. Apache-2.0. """ @@ -12,8 +13,8 @@ from fractions import Fraction as Q import local as L -KAPPA, TESTED = Q('.00309839'), Q('.0030983905') -PREVIOUS = Q('.00308189') +KAPPA, TESTED = Q('.00310045'), Q('.0031004505') +PREVIOUS = Q('.00308520') def encode(x): @@ -62,7 +63,7 @@ def assemble(local, native, word, physical): second_p[8*(j+1)] += 208 L.need((targets,paid) == (second_t,second_p), 'Independent full invoice') L.need(max(targets) == 145 and max(paid) == 72, 'Maximum recursive ranks') - L.need(sum(targets.values()) == 13084 and sum(paid.values()) == 66852, 'Complete field and call counts') + L.need(sum(targets.values()) == 13048 and sum(paid.values()) == 66726, 'Complete field and call counts') L.need(sum(r*n for r,n in targets.items())-sum(r*n for r,n in paid.items()) == 760, 'Complete rank surplus') return targets,paid,counts @@ -93,7 +94,7 @@ def margin(k): derivative_upper -= count*(low if count >= 0 else high) L.need(derivative_upper < 0, 'Unique raw crossing below the retained BIT cap') L.need(margin(lower)[0] > 0 and margin(upper)[1] < 0, 'Strict rational crossing enclosure') - L.need(PREVIOUS < KAPPA < TESTED < lower and margin(PREVIOUS)[0] > 0, 'Changed complete bill improves selected kappa') + L.need(PREVIOUS < KAPPA < TESTED < lower and margin(PREVIOUS)[0] > 0, 'Changed complete bill improves the source claim') t,u,v,c,b = 1-TESTED,Q(1,5),1024,17,18 target,paid = E.moment(T,t),E.moment(P,t) tl,th = other.moment(T,TESTED) @@ -150,7 +151,7 @@ def wins(j): L.need(wrong_cutoff[0] > 1, 'Old cutoff fails with this helper inventory') bad=outer_module.ledger(dict(params,bit_saving=Q('.0027'))) L.need(any(x <= 0 for x in bad['strict_checks'].values()), 'Insufficient BIT contract rejected') - return encode({'kappa':KAPPA,'kappa_decimal':'.00309839','previous_open_pr5580':PREVIOUS,'gain':KAPPA-PREVIOUS, + return encode({'kappa':KAPPA,'kappa_decimal':'.00310045','previous_open_pr5565':PREVIOUS,'gain':KAPPA-PREVIOUS, 'relative_gain_percent':100*(KAPPA/PREVIOUS-1),'raw_root_interval':[lower,upper], 'raw_headroom':[lower-KAPPA,upper-KAPPA], 'raw_ceiling':{'interval':[Q(0),cap],'derivative_upper':derivative_upper},'margin_at_previous':E.display(margin(PREVIOUS)), diff --git a/research/p104-helper-subspace-splits/verify.py b/research/p104-helper-subspace-splits/verify.py index b977942a8c..547751915a 100644 --- a/research/p104-helper-subspace-splits/verify.py +++ b/research/p104-helper-subspace-splits/verify.py @@ -56,22 +56,30 @@ def run(): import construct as R import pricing as P C = L.load(ROOT/'research/p104-productive-controller/caller.py', 'subspace_p104_caller') - source = L.read(HERE/'inputs/PR5580-WORD.json.gz') + predecessor = L.replay(L.read(HERE/'inputs/PR5580-WORD.json.gz')) + source = L.read(HERE/'inputs/PR5565-WORD.json.gz') witnesses = L.read(HERE/'SPLITS.json') - need(len(witnesses) == 15, 'Fifteen explicit independent splits') + need(len(witnesses) == 13, 'Thirteen explicit independent splits') baseline = L.replay(source) + source_delta = {} + for name, expected in (('paid', {1:-8, 3:-1, 4:-2, 5:4}), + ('helpers', {8:-1, 9:1})): + delta = Counter(baseline[name]) + delta.subtract(predecessor[name]) + source_delta[name] = {r:n for r,n in delta.items() if n} + need(source_delta[name] == expected, 'Exact published PR5565 '+name+' change') word, cuts = R.construct(source, witnesses) local = L.replay(word) - need((local['public_inputs'], local['owned_lifetimes'], local['peak_owned_fields']) == (750, 8, 1), + need((local['public_inputs'], local['owned_lifetimes'], local['peak_owned_fields']) == (748, 8, 1), 'Complete public and owned inventory') - need(local['helpers'] == {1:4, 2:5, 4:90, 5:10, 7:5, 8:18, 9:410}, 'Exact helper histogram') + need(local['helpers'] == {1:2, 2:5, 4:89, 5:11, 7:5, 8:16, 9:412}, 'Exact helper histogram') delta = Counter(local['helpers']) delta.subtract(baseline['helpers']) delta = {r:n for r,n in delta.items() if n} - need(delta == {1:4, 2:5, 4:7, 5:5, 7:5, 8:3, 9:-14}, 'All split credits and removed targets') + need(delta == {1:2, 2:5, 4:6, 5:6, 7:5, 8:2, 9:-13}, 'All split credits and removed targets') need(local['paid'] == baseline['paid'], 'Same complete local paid histogram') columns = L.reverse_columns(word) - print('PASS 15 prefix/suffix cuts, every independent row and dense reverse columns', flush=True) + print('PASS 13 prefix/suffix cuts, every independent row and dense reverse columns', flush=True) native = L.native(word) controller = C.construct() need(controller == L.read(ROOT/'research/p104-productive-controller/CONTROLLER.json'), 'Same complete caller') @@ -102,8 +110,9 @@ def run(): bad = deepcopy(local) bad['paid'][1] -= 1 controls['unpaid_gaussian'] = rejected(lambda: P.assemble(bad, native, controller, physical)) - result = {'status':'PASS_P104_HELPER_SUBSPACE_KAPPA_00309839', + result = {'status':'PASS_P104_HELPER_SUBSPACE_KAPPA_00310045', 'authenticated_inputs':pins, 'splits':cuts, 'local_helper_delta':delta, + 'published_source_delta':source_delta, 'local':local, 'separate_columns':columns, 'native':native, 'physical_caller':physical, 'complete_cost':costs, 'negative_controls':controls, 'limits':['The five selected framework assumptions and helper-endpoint contract remain.',