From eb92cbdf211f0c3717ff6fa71af47ec38f8e412d Mon Sep 17 00:00:00 2001 From: ToikY <27568617+ToikY@users.noreply.github.com> Date: Mon, 26 Oct 2026 14:27:51 -0700 Subject: [PATCH] research: construct dyadic words for all111 G20 port normalizers Emit exact RIGHT words with unit-only scales, source-bound port data, independent matrix/address checks and positive named P2 coefficient counts. Retain Ali Romman, JoyboyBrian and all predecessor credit. New work by ToikY with substantial OpenAI Codex assistance and separate implementation/oracle/review contexts. No physical ROW/tape or kappa admission. --- research/g20-normalizer-dyadic-words/NOTICE | 16 + .../g20-normalizer-dyadic-words/ORACLE.json | 3248 ++ research/g20-normalizer-dyadic-words/PROOF.md | 141 + .../g20-normalizer-dyadic-words/README.md | 100 + .../g20-normalizer-dyadic-words/RESULT.json | 48152 ++++++++++++++++ .../g20-normalizer-dyadic-words/SOURCES.json | 69 + .../g20-normalizer-dyadic-words/TASK.json | 100 + .../g20-normalizer-dyadic-words/VERIFY.json | 47 + .../inputs/CALLS.json | 1262 + .../inputs/CONTROLLER.json | 2175 + .../inputs/PORTS.json | 18875 ++++++ .../g20-normalizer-dyadic-words/oracle.py | 258 + .../g20-normalizer-dyadic-words/verify.py | 308 + 13 files changed, 74751 insertions(+) create mode 100644 research/g20-normalizer-dyadic-words/NOTICE create mode 100644 research/g20-normalizer-dyadic-words/ORACLE.json create mode 100644 research/g20-normalizer-dyadic-words/PROOF.md create mode 100644 research/g20-normalizer-dyadic-words/README.md create mode 100644 research/g20-normalizer-dyadic-words/RESULT.json create mode 100644 research/g20-normalizer-dyadic-words/SOURCES.json create mode 100644 research/g20-normalizer-dyadic-words/TASK.json create mode 100644 research/g20-normalizer-dyadic-words/VERIFY.json create mode 100644 research/g20-normalizer-dyadic-words/inputs/CALLS.json create mode 100644 research/g20-normalizer-dyadic-words/inputs/CONTROLLER.json create mode 100644 research/g20-normalizer-dyadic-words/inputs/PORTS.json create mode 100644 research/g20-normalizer-dyadic-words/oracle.py create mode 100644 research/g20-normalizer-dyadic-words/verify.py diff --git a/research/g20-normalizer-dyadic-words/NOTICE b/research/g20-normalizer-dyadic-words/NOTICE new file mode 100644 index 0000000000..88e90cfa4a --- /dev/null +++ b/research/g20-normalizer-dyadic-words/NOTICE @@ -0,0 +1,16 @@ +Retained source notice from PR #5798 (the following credits describe predecessor work): + +New G20 global boundary checker, rational port certificates and proof: +Ali Romman with substantial OpenAI Codex assistance. No subagents. Apache-2.0. + +The construction is PR5708, building on PR5679, Dugongue PR5657/5665 and +ai-nanachi PR5512. The local all-address proof is PR5782. Their complete source +attribution and limitations remain in source/PROOF.md, source/NATIVE-README.md, +source/NATIVE-PROOF.md and source/NOTICE-*.md. The controller, native involution, +helper retirement/split, query accounting and positive finite-fee schema are +source contributions. This package claims the separate global boundary audit +and explicit port/interface witnesses, not those constructions. + +Named ROW/P2 contract and earlier schedule: JoyboyBrian with substantial OpenAI Codex assistance. Retain ai-nanachi, Chris R/Clear1nsight, rohanarun, Maxime Fleury, Cinna Davis, zxv, Jacob Alan Sussman, Mark/Matarener and the native/E8/ordinary/ROW/routing/precision/tape lineage in the pinned ROW-generator README. + +New finite dyadic words and certificate: ToikY with substantial OpenAI Codex assistance, using separate primary, independent-oracle and read-only proof/review contexts. Apache-2.0. No predecessor construction, physical ABI implementation or complete supplier admission is claimed. diff --git a/research/g20-normalizer-dyadic-words/ORACLE.json b/research/g20-normalizer-dyadic-words/ORACLE.json new file mode 100644 index 0000000000..2eefbf7e4a --- /dev/null +++ b/research/g20-normalizer-dyadic-words/ORACLE.json @@ -0,0 +1,3248 @@ +{ + "convention": "I E1 ... Em = W; ADD[i,j,q] has matrix entry (i,j)=q and updates row coordinate j from i; no word reversal.", + "cross_product_catalogue_count": [ + { + "N": 127, + "all_matrix_rows_times_lanes_times_calls_times_halves": 4572, + "both_directions_in_base_histogram": true, + "coefficient_counts": [ + { + "coefficient": "-1", + "count": 10561320, + "primitive": "ordered_shift" + }, + { + "coefficient": "-1/2", + "count": 1673352, + "primitive": "ordered_shift" + }, + { + "coefficient": "-2", + "count": 859536, + "primitive": "ordered_shift" + }, + { + "coefficient": "-3", + "count": 452628, + "primitive": "ordered_shift" + }, + { + "coefficient": "-3/2", + "count": 64008, + "primitive": "ordered_shift" + }, + { + "coefficient": "-4", + "count": 13716, + "primitive": "ordered_shift" + }, + { + "coefficient": "1", + "count": 10561320, + "primitive": "ordered_shift" + }, + { + "coefficient": "1/2", + "count": 1673352, + "primitive": "ordered_shift" + }, + { + "coefficient": "2", + "count": 859536, + "primitive": "ordered_shift" + }, + { + "coefficient": "3", + "count": 452628, + "primitive": "ordered_shift" + }, + { + "coefficient": "3/2", + "count": 64008, + "primitive": "ordered_shift" + }, + { + "coefficient": "4", + "count": 13716, + "primitive": "ordered_shift" + }, + { + "coefficient": "-1", + "count": 4407408, + "primitive": "unit_scale" + }, + { + "coefficient": "-1/2", + "count": 68580, + "primitive": "unit_scale" + }, + { + "coefficient": "-1/4", + "count": 210312, + "primitive": "unit_scale" + }, + { + "coefficient": "-2", + "count": 68580, + "primitive": "unit_scale" + }, + { + "coefficient": "-4", + "count": 210312, + "primitive": "unit_scale" + }, + { + "coefficient": "1/2", + "count": 2235708, + "primitive": "unit_scale" + }, + { + "coefficient": "1/4", + "count": 251460, + "primitive": "unit_scale" + }, + { + "coefficient": "2", + "count": 2235708, + "primitive": "unit_scale" + }, + { + "coefficient": "4", + "count": 251460, + "primitive": "unit_scale" + } + ], + "f": 1, + "full_calls": 18, + "paired_halves": 2, + "primitive_counts": { + "ordered_shift": 27249120, + "unit_scale": 9939528 + } + }, + { + "N": 254, + "all_matrix_rows_times_lanes_times_calls_times_halves": 18288, + "both_directions_in_base_histogram": true, + "coefficient_counts": [ + { + "coefficient": "-1", + "count": 42245280, + "primitive": "ordered_shift" + }, + { + "coefficient": "-1/2", + "count": 6693408, + "primitive": "ordered_shift" + }, + { + "coefficient": "-2", + "count": 3438144, + "primitive": "ordered_shift" + }, + { + "coefficient": "-3", + "count": 1810512, + "primitive": "ordered_shift" + }, + { + "coefficient": "-3/2", + "count": 256032, + "primitive": "ordered_shift" + }, + { + "coefficient": "-4", + "count": 54864, + "primitive": "ordered_shift" + }, + { + "coefficient": "1", + "count": 42245280, + "primitive": "ordered_shift" + }, + { + "coefficient": "1/2", + "count": 6693408, + "primitive": "ordered_shift" + }, + { + "coefficient": "2", + "count": 3438144, + "primitive": "ordered_shift" + }, + { + "coefficient": "3", + "count": 1810512, + "primitive": "ordered_shift" + }, + { + "coefficient": "3/2", + "count": 256032, + "primitive": "ordered_shift" + }, + { + "coefficient": "4", + "count": 54864, + "primitive": "ordered_shift" + }, + { + "coefficient": "-1", + "count": 17629632, + "primitive": "unit_scale" + }, + { + "coefficient": "-1/2", + "count": 274320, + "primitive": "unit_scale" + }, + { + "coefficient": "-1/4", + "count": 841248, + "primitive": "unit_scale" + }, + { + "coefficient": "-2", + "count": 274320, + "primitive": "unit_scale" + }, + { + "coefficient": "-4", + "count": 841248, + "primitive": "unit_scale" + }, + { + "coefficient": "1/2", + "count": 8942832, + "primitive": "unit_scale" + }, + { + "coefficient": "1/4", + "count": 1005840, + "primitive": "unit_scale" + }, + { + "coefficient": "2", + "count": 8942832, + "primitive": "unit_scale" + }, + { + "coefficient": "4", + "count": 1005840, + "primitive": "unit_scale" + } + ], + "f": 2, + "full_calls": 18, + "paired_halves": 2, + "primitive_counts": { + "ordered_shift": 108996480, + "unit_scale": 39758112 + } + } + ], + "flat_address_templates_checked": 731520, + "incidence_limit": "7992 is the declared Cartesian catalogue count, not an actual source paid-route count. 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These are not actual source route-use counts or a physical head map. Full ROW borrow/cache/carry/return, coefficient preparation, tape tariffs, native admission and compiler closure remain open.", + "source_sha256": { + "CALLS.json": "30dcc37cdade6b2dc05478837eca28b696894d1c4782bac6a1caab5e7f56c9e8", + "CONTROLLER.json": "39ac84fb848b908f7ba051fae4556d507900c421dc5d23501a9c0cb1d61fd08d", + "PORTS.json": "a53a49c938a46c5a9da8c05ffdec4c2ef2dd906dd94c009d6fa451af4ed350e9" + }, + "spectator_argument": "Every emitted address lies in one active column and the same matrix row/lane; all119f inactive columns remain fixed for every port word.", + "status": "PASS_G20_NORMALIZER_DYADIC_WORD_ORACLE", + "word_lengths": [ + { + "forward": 8, + "inverse": 8, + "port": 0 + }, + { + "forward": 12, + "inverse": 12, + "port": 1 + }, + { + "forward": 16, + "inverse": 16, + "port": 2 + }, + { + "forward": 20, + "inverse": 20, + "port": 3 + }, + { + "forward": 24, + "inverse": 24, + "port": 4 + }, + { + "forward": 28, + "inverse": 28, + "port": 5 + }, + { + "forward": 32, + 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file mode 100644 index 0000000000..72804fb402 --- /dev/null +++ b/research/g20-normalizer-dyadic-words/PROOF.md @@ -0,0 +1,141 @@ +# Dyadic normalizer words and a declared address kernel + +The source is the 111 port interfaces in PR #5798 at +`eaa9cc8c15d8e994d7b81b0cda3f6dd63b0db826`. Frozen PORTS, CONTROLLER and CALLS +data bind the matrices and the ordered list of 18 thick stages. This package +constructs finite elementary words and a chosen address layout. It does not +identify that layout with the complete retained physical ROW route. + +## Exact matrix and operator conventions + +For distinct indices i,j define `E(i,j,a) = I + a e_i e_j^T`, and let D(i,u) +scale coordinate i by u. A published word is a **right product**: + +``` +I E1 E2 ... Em = W. +``` + +Consequently a row value v is updated chronologically by `v <- v E1`, then +`v <- v E2`, and so on. An ADD factor E(i,j,a) means +`v[j] <- v[j] + a*v[i]`; its destination is j and its source is i. A SCALE +D(i,u) means `v[i] <- u*v[i]`. The inverse word reverses the factor list and +inverts each factor: `E(i,j,a)^-1 = E(i,j,-a)` and `D(i,u)^-1 = D(i,1/u)`. + +The source W has a different, column-vector interpretation: `x -> W x` maps +axis data to line data, and `x -> W^-1 x` maps line data to axis data. The +address kernel here computes `v -> v W` on row values. On columnized row data +that is `v^T -> W^T v^T`, not `v^T -> W v^T`. Equality of the matrix products +does not make these two operator conventions interchangeable. Binding this +row kernel to the final physical head-map convention remains an obligation. + +## Existence using only dyadic ADDs and unit SCALEs + +Let `D = Z[1/2]`. For every n and every matrix A whose entries and inverse +entries lie in D, there is a finite factorization into E(i,j,a), a in D, and +D(i,u), where `u = +/- 2^k`, k an integer. This is classical elementary +elimination over the dyadic ring; no new general theorem is claimed. + +Indeed `det(A)*det(A^-1)=1` in D, so det(A) is a unit of D, hence a signed +power of two. At an elimination stage the remaining nonsingular block has +unit determinant. Clear its row denominators by multiplying rows by suitable +powers of two, which are permitted unit scalings. The resulting integer block +still has determinant a signed power of two. The gcd g of its first column +divides that determinant, by expansion along the column, so g is a power of +two. Integer Euclidean row additions and row swaps reduce that column to a +single nonzero pivot +/-g. They terminate by the usual decreasing nonnegative +integer remainder. Scale the pivot to one using a signed power of two. +The remaining block again has unit determinant; repeat. Clear the entries +above pivots by dyadic row additions. Every operation and its inverse stays +in the permitted class, and the reduction ends at I. + +If the chronological left row operations are R1,...,Rm, then + +``` +Rm ... R2 R1 A = I, hence A = R1^-1 R2^-1 ... Rm^-1. +``` + +Thus the forward **right** word consists of the inverses in the same order +as the recorded left reduction operations. Reversing that order would in +general be wrong. Only construction of the inverse word reverses the +already-correct right factor list. + +A swap is lowered to three ADDs and one negation SCALE. With the conventions +above its right-factor identity is + +``` +S(i,j) = E(i,j,1) E(j,i,-1) E(i,j,1) D(i,-1). +``` + +On row values (a,b), the successive pairs are `(a,a+b)`, `(-b,a+b)`, +`(-b,a)`, `(b,a)`. No SWAP primitive is silently left uncharged. For every +admitted odd q, dyadic coefficients reduce modulo the required power of q, +and each signed power-of-two SCALE is a unit. This algebra does not supply +the physical implementation or time tariff of a named P2 primitive. + +## Chosen stage layout and all-row address lift + +Number the retained 18 thick stages by their **ordinal** j=0,...,17 in the +authenticated CALLS order. Their controller stage identifiers need not equal +j. For that ordinal choose the eight active coordinates + +``` +active_j = [0, 1+7*j, 2+7*j, ..., 7+7*j] +``` + +inside ambient dimension 127. The other 119 coordinates are spectators for +this stage kernel. Different stages share coordinate zero; this construction +does not assert that their kernels commute or can run concurrently. + +For every integer f>=1 put N=127*f. For every row r=0,...,N-1 and lane +l=0,...,f-1, the local active coordinate i has flattened address + +``` +address(r,i,l) = r*N + active_j[i]*f + l. +``` + +Within the two-half namespace, half b=0 or 1 adds the disjoint offset +`b*N^2` to this address. Thus no factor crosses the paired-half boundary. + +Lower E(i,j,a) to +`ordered_shift(dst=address(r,j,l), src=address(r,i,l), coefficient=a)` and +D(i,u) to `unit_scale(address(r,i,l), coefficient=u)`. These are precisely +the destination/source conventions of JoyboyBrian's retained +`bit-row-route-generator` ABI. No predecessor generator is imported. + +For a fixed row and lane, induction on the chronological factors proves the +row action vW on the eight active coordinates. Addresses for distinct rows +or lanes are disjoint, so the same induction proves the lift on all N rows +and all f lanes. Every spectator address is untouched, including arbitrary +dirty spectator values. The inverse word restores every active address as +well. This is a claim about this explicit logical address kernel under its +named primitive semantics, not a claim that an arbitrary physical ROW can +be accessed or borrowed at no cost. + +## Positive counts and remaining obligations + +Each coefficient-specific ADD or SCALE occurrence in one local word produces +exactly `N*f = 127*f^2` addressed primitive calls. Keep ADD and SCALE histograms +separate, including negative coefficients and all lowered swap factors. +The declared cross product of 111 ports, both words, 18 stages and two paired +halves contains `111*2*18*2 = 7,992` catalogue kernels. It is not the source's +physical paid-route incidence list or a complete caller allowance. An exact +incidence map is required before assigning those counts to the full source +schedule. + +The operation counts are positive named counts. Their physical P2 unit prices +and movement/precision tariffs remain unknown; unknown costs are not zero. +Summing symbolic tariffs over the emitted address calls is legitimate, but +assuming a common unit tariff or absorbing these kernels into a retained +fee near `9.5*10^11` is not established here. + +The complete ROW borrow/cache schedule, N-squared low-cache COPYs and CLEARs, +carry corrections, low-type commit, padding, return/restoration, physical +head-map correspondence, compiler and admission remain open. No new kappa +or selected-frontier change follows from this finite certificate. + +Credit: Ali Romman with substantial OpenAI Codex assistance for the G20 source +port interfaces and controller/caller data; JoyboyBrian with OpenAI Codex +assistance for the retained row-route address ABI and ROW obligations. +This scoped construction/proof/audit was prepared by ToikY with substantial +OpenAI Codex assistance in separate primary, oracle and review contexts. +All retained predecessor credit is in NOTICE. Apache-2.0. diff --git a/research/g20-normalizer-dyadic-words/README.md b/research/g20-normalizer-dyadic-words/README.md new file mode 100644 index 0000000000..d2b500468b --- /dev/null +++ b/research/g20-normalizer-dyadic-words/README.md @@ -0,0 +1,100 @@ +# Constructive dyadic words for G20 port normalizers + +This supplies explicit operation words for all 111 exact port normalizers +`W` and `W^-1` retained by Ali Romman's PR #5798 at +`eaa9cc8c15d8e994d7b81b0cda3f6dd63b0db826`. The source audit already +checks the matrices. This contribution constructs finite words and a declared +address-kernel embedding; it does not claim the native construction or a new +conditional bound. [Canonical claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/5777#discussioncomment-19204776). + +Both directions together contain **5,960 ADDs and 2,174 SCALEs**. Every scale +is a signed power of two; all ADD coefficients are dyadic. The largest +absolute numerator or denominator is 4. Swaps are explicitly lowered to +three ADDs and one sign scale. The unit-preserving Euclidean construction +never divides by an odd nonunit. Classical elimination is not claimed as a +new general theorem. + +The serialized convention is **RIGHT**: `I E1 ... Em = W`, where +`ADD[i,j,a] = I+a e_i e_j^T` updates row coordinate `j` from `i`. The +inverse word reverses the word and inverts each factor. The source's column +identity is separate: `W` maps the central coordinate axis to the local line, +and `W^-1` maps that line to the central axis. No automatic entry/exit +choice is inferred from the word names. + +The chosen compatible 127-coordinate layout uses central coordinate 0 and +one seven-coordinate block for each of the exact 18 thick-stage positions. +A stage uses its **position** in the retained list, not its raw stage ID. +Each placement fixes 119 spectator coordinates. For `N=127f`, a right +factor uses addresses `half*N^2 + row*N + column*f + lane`, across every +one of the N matrix rows and f lanes, on two disjoint address halves. +This is a declared layout, not the retained literal physical head map. + +## Exact evidence and conditional cost + +[RESULT.json](RESULT.json) retains every forward/inverse word, source +port/line/complement binding, coefficient histogram, layout, positive named +call counts and six targeted rejection controls. [ORACLE.json](ORACLE.json) +records independent dense elementary-matrix products, separate basis-row +execution and both round trips: 222 checks of each kind. Its flattened +address checks cover all 18 layouts at f=1 and f=2. + +A catalogue cross-product over all ports, stages, halves and both words has +7,992 kernel instances. **This is not an actual paid-event incidence count** +and no event is presumed to equal one word. Both directions are already in +the word histogram. Per coefficient, lifting it to the full catalogue +multiplies its count by `18*2*N*f = 4572*f^2`. At f=1 this gives 27,249,120 +`ordered_shift` and 9,939,528 `unit_scale` calls. Each coefficient retains +its own positive named primitive tariff; none is assigned zero or a universal +unit price. Each symbolic tariff may depend on the radix, width and tape parameters; no uniform implementation bound is supplied. This is not absorption into the source's finite fee. + +The named P2 ABI is pinned to the current-main +[ROW generator](https://github.com/CrocSwap/integer-mult-bounds/blob/de5ec2e7a6074068452f45b1a191b5c72832df4a/research/bit-row-route-generator/generator.py). +Its implementations, coefficient preparation and physical tape tariffs remain +contracts. Full ROW borrowing, old-low cache COPY/CLEAR, carries, low-type +commit, padding, return, ownership and caller integration are outside this +kernel certificate. The full supplier and five inherited framework +assumptions are not admitted here. + +## Reproduction + +Python 3.12 and the standard library suffice. Neither checker imports the +other or any predecessor implementation. Frozen source data authenticate +by SHA256; the independent oracle also checks their Git blob identities. + +```sh +python3.12 -B scripts/research_package.py --package research/g20-normalizer-dyadic-words +``` + +The primary generator/replayer uses unit-only elimination; the oracle +consumes the retained words and independently checks RIGHT products, +basis-row semantics, address isolation and positive per-coefficient counts. +Default runs compare complete canonical JSON receipts, including numeric +type distinctions. `--emit` is an explicit candidate-generation mode and +never writes files. The six controls remove an operation, reverse word +order, insert a forbidden odd scale in the chosen unit alphabet, corrupt +source bytes, write a spectator and confuse raw stage ID with position. +They are injected faults, not defects alleged in predecessor code. + +[SOURCES.json](SOURCES.json) pins the exact data and main-context ABI; +[TASK.json](TASK.json) records the changed finite constructive scope and +source-bound budget. No Lean build ran. The selected baseline passed source +bindings/metadata only; no selected native replay or frontier change. + +## Open next questions + +Bind one exact kernel direction and paired owner to the complete retained +ROW route, including all old-low cache, carry, type-commit, padding and +restoration costs. Prove the literal physical head-map correspondence and +actual route incidence before treating the catalogue counts as a caller +invoice. Physical P2 preparation/tariffs and compiler/stock/precision/tape +obligations remain blockers. The structured next question is in TASK.json. + +## Credit + +Ali Romman with OpenAI Codex assistance supplied the G20 source audit and +normalizer witnesses. Retain Dugongue, ai-nanachi, the PR #5679/#5708 +construction, PR #5782 native audit and all predecessor credit in NOTICE. +Joyboy Brian with Codex assistance supplied the retained ROW generator and +P2 schedule; its predecessors retain their credit. New finite words and +certificate: ToikY with substantial OpenAI Codex assistance, using separate +primary, independent-oracle and read-only proof/review contexts. 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"source_binding_scope": "Exact retained source data only; no source head ancestry, physical ROW/tape implementation or full caller replay follows." +} diff --git a/research/g20-normalizer-dyadic-words/TASK.json b/research/g20-normalizer-dyadic-words/TASK.json new file mode 100644 index 0000000000..105d1a688f --- /dev/null +++ b/research/g20-normalizer-dyadic-words/TASK.json @@ -0,0 +1,100 @@ +{ + "schema_version": 1, + "task_id": "formal-interface-lemma", + "priority_revision": 8, + "base_commit": "de5ec2e7a6074068452f45b1a191b5c72832df4a", + "original_card": { + "id": "formal-interface-lemma", + "question": "Can one uncovered interface implication be formalized with exact caller and certificate bindings?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/gate-operand-parity-lean/README.md", + "research/staged544-certified-endpoint/README.md", + "research/unconditional-batched-crt/README.md" + ], + "methods": [ + "Formalize a missing boundary lemma identified by the selected review.", + "Audit a formal theorem-to-certificate binding independently." + ], + "acceptance_gate": "State the exact formalized proposition and remaining assumptions; avoid duplicate arithmetic formalizations already present.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_selected_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Resolve the current selected review, separate complex/ordinary BIT/admitted BIT/outer budgets, and compare the card against live handoffs before starting. Historical ceilings require exact source/model equivalence.", + "scope": "Source-binding orientation only; not a scientific replay or all-size proof. Materialize selected inputs if this checkout is sparse." + }, + "first_experiment": "Write one missing statement with quantified hypotheses, actual caller and existing coverage. A compact-switch lemma is a candidate only after its mathematical contract is reviewed. Establish a bounded proof plan before a separately budgeted proof-assistant build; do not rerun large Lean jobs as orientation.", + "bottleneck_link": "A missing interface proof can reduce the conditional gap even if it does not change kappa.", + "allowed_variations": [ + "Narrow to one formal lemma or one theorem-to-certificate binding." + ], + "scope_change_triggers": [ + "Formalizing already-covered arithmetic and claiming the full multiplication theorem." + ], + "overlap_terms": [ + "hyperplane end", + "formal interface", + "Lean binding", + "3807", + "3857", + "4100", + "gate-operand-parity-lean", + "staged544-certified-endpoint", + "unconditional-batched-crt" + ], + "existing_checks": [ + { + "scope": "PR #3807: scoped gate-operand parity formalization.", + "evidence": "research/gate-operand-parity-lean/README.md", + "remaining": "Exact theorem-to-caller binding and genuinely uncovered interface lemmas.", + "status": "author-checked", + "source_commit": "4c3530f42a6abcc48e7a6bcffd6c901911dc8269", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #3857: certified real-power moment/endpoint arithmetic.", + "evidence": "research/staged544-certified-endpoint/README.md", + "remaining": "Uniform algorithmic implications, not another endpoint digit.", + "status": "author-checked", + "source_commit": "ef4315b8caa605e47a2515004845eb2d2ed71a86", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4100: compact-switch formalization proposed as future validation.", + "evidence": "research/unconditional-batched-crt/README.md", + "remaining": "Audit the statement and assumptions before a formal proof campaign.", + "status": "author-checked", + "source_commit": "337d04939571a637aeab54a0f58f54fde811663a", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + "scope_status": "changed", + "actual_scope": "Construct exact dyadic elementary operation words for all111 G20 W/W^-1 port normalizers from PR5798, with conditional P2 address-kernel embedding in chosen127-coordinate thick-stage layout and positive named-operation counts.", + "scope_change_reason": "Follow the explicit unresolved ROW/spectator realizability clause in the released5798 handoff. This is a finite exact constructive kernel certificate, not Lean, native/P2 implementation or full ROW borrow/carry/tape admission.", + "bottleneck_link": "Supplies constructive words for matrices already audited at the actual G20 port interface, separating finite algebra/address work from still-open physical ROW/tape costs.", + "budget_minutes": 60, + "stop_rule": "Freeze by21:48UTC. Stop/narrow on non-dyadic source data, nonunit scale, failed exact matrix/inverse/spectator identity or inability to bind the declared layout. No broader search or kappa/frontier claim.", + "outcome": "completed", + "evidence": "RESULT.json:111 exact RIGHT forward/inverse words;5960 ADD/2174 unit SCALE, coefficient height<=4,6 meaningful controls. ORACLE.json:222 dense products,222 independent row-basis products,222 roundtrips,18layouts and731520address checks. Counts apply to declared Cartesian catalogue, not actual paid-event incidence or a full ROW invoice.", + "author": "ToikY", + "ai_assistance": "Substantial OpenAI Codex assistance, separate primary/oracle/proof-review contexts.", + "open_questions": [ + { + "question": "Can these exact finite kernels be integrated with the complete current ROW borrow/cache/carry/return schedule and physical tape tariffs?", + "why_it_matters": "P2 operation words and positive counts do not establish an ordinary compiler or full caller cost.", + "first_step": "Bind one chosen kernel direction and paired owner to the retained full route, charging N-squared low-cache COPY/CLEAR, carries, type commit and all padding/restoration.", + "blocked_by": "Physical P2 implementation/tariffs and retained literal head-map correspondence are outside this finite kernel certificate." + } + ], + "started_at": "2026-10-26T21:03:53.408369+00:00", + "science_cutoff": "2026-10-26T21:48:53.408369+00:00", + "finish_by": "2026-10-26T22:03:53.408369+00:00", + "source_head": "eaa9cc8c15d8e994d7b81b0cda3f6dd63b0db826", + "claim_expires": "2026-10-26T23:10:00Z" +} diff --git a/research/g20-normalizer-dyadic-words/VERIFY.json b/research/g20-normalizer-dyadic-words/VERIFY.json new file mode 100644 index 0000000000..a3efa48a91 --- /dev/null +++ b/research/g20-normalizer-dyadic-words/VERIFY.json @@ -0,0 +1,47 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 120, + "checks": "All111 source normalizers/inverses, unit-only RIGHT words, six controls, chosen address/spectator law, positive named coefficient bill and exact canonical RESULT receipt." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-W", + "error", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 120, + "checks": "Optimized full primary replay with explicit guards and strict canonical receipt." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-W", + "error", + "-B", + "{package}/oracle.py" + ], + "timeout_seconds": 120, + "checks": "Independent elementary products/basis-row execution/roundtrips, all18 layouts, flat addresses and counts, complete canonical ORACLE receipt." + } + ] +} diff --git a/research/g20-normalizer-dyadic-words/inputs/CALLS.json b/research/g20-normalizer-dyadic-words/inputs/CALLS.json new file mode 100644 index 0000000000..9ee8c26f32 --- /dev/null +++ b/research/g20-normalizer-dyadic-words/inputs/CALLS.json @@ -0,0 +1,1262 @@ +[ + { + "stage": 0, + "pair": 0, + "source_bank": 0, + "target_bank": 1, + "old_direction_inverse": false, + "new_direction_inverse": true, + "helper_old_owner_begin": 3552, + "core_begin": 6597, + "core_end": 21391, + "owned_global_indices": [ + 11022, + 11023, + 11024, + 11025, + 11026, + 11027, + 11028, + 11029, + 11030, + 11031, + 11032, + 11033, + 11034, + 11035, + 11036, + 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index 0000000000..33d4c07b98 --- /dev/null +++ b/research/g20-normalizer-dyadic-words/oracle.py @@ -0,0 +1,258 @@ +#!/usr/bin/env python3 +"""Check canonical RIGHT-factor certificates independently of their generator. + +ToikY with substantial OpenAI Codex assistance in a separate implementation +context. Ali Romman supplied the frozen G20 port matrices and caller data. +JoyboyBrian supplied the retained addressed P2 route interface. Apache-2.0; +NOTICE and PROOF retain the source and primitive authors' credit. +""" +import argparse +from collections import Counter +from fractions import Fraction +from hashlib import sha1, sha256 +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +PINS = { + "PORTS.json": (311085, + "a53a49c938a46c5a9da8c05ffdec4c2ef2dd906dd94c009d6fa451af4ed350e9", + "aeffcdb444f564d247aff2265f9aebc424bce14f"), + "CONTROLLER.json": (23753, + "39ac84fb848b908f7ba051fae4556d507900c421dc5d23501a9c0cb1d61fd08d", + "89c400d5970024b3debe870c36ce43889beed001"), + "CALLS.json": (18903, + "30dcc37cdade6b2dc05478837eca28b696894d1c4782bac6a1caab5e7f56c9e8", + "9ee8c26f321ee3d420976fab69075c0c05db12ce"), +} +STAGES = [0, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 32] + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def authenticated(name): + raw = (HERE / "inputs" / name).read_bytes() + size, digest, blob = PINS[name] + require(len(raw) == size and sha256(raw).hexdigest() == digest, + "Oracle exact source bytes: " + name) + require(sha1(b"blob " + str(len(raw)).encode() + b"\0" + raw).hexdigest() == blob, + "Oracle exact Git blob: " + name) + return json.loads(raw) + + +def identity(): + return [[Fraction(i == j) for j in range(8)] for i in range(8)] + + +def product(left, right): + # General matrix products, unlike the generator's elementary row updates. + return [[sum((left[i][k] * right[k][j] for k in range(8) + if left[i][k] and right[k][j]), Fraction(0)) + for j in range(8)] for i in range(8)] + + +def power_of_two(value): + return type(value) is int and value > 0 and value & (value - 1) == 0 + + +def parse(event): + require(type(event) is list and event and event[0] in ("ADD", "SCALE"), + "Oracle only explicit ADD/SCALE operations") + kind = event[0] + require(len(event) == (4 if kind == "ADD" else 3), "Oracle opcode arity") + indices = event[1:3] if kind == "ADD" else event[1:2] + require(all(type(i) is int and 0 <= i < 8 for i in indices), + "Oracle active coordinate range") + require(type(event[-1]) is str, "Oracle exact coefficient string") + q = Fraction(event[-1]) + require(q and str(q) == event[-1] and power_of_two(q.denominator), + "Oracle nonzero canonical dyadic coefficient") + if kind == "SCALE": + require(power_of_two(abs(q.numerator)), "Oracle dyadic unit SCALE") + return kind, indices[0], indices[0], q + require(indices[0] != indices[1], "Oracle distinct ADD coordinates") + return kind, indices[0], indices[1], q + + +def matrix_from_word(word): + require(type(word) is list and len(word) <= 10000, "Oracle finite word") + result = identity() + for event in word: + kind, i, j, q = parse(event) + elementary = identity() + elementary[i][j] = q + result = product(result, elementary) + return result + + +def row_basis_from_word(word): + # A second interpretation: eight independent row vectors execute the + # canonical RIGHT list directly. ADD[i,j,q] updates coordinate j from i. + output = [] + for basis in range(8): + row = [Fraction(basis == j) for j in range(8)] + for event in word: + kind, i, j, q = parse(event) + if kind == "ADD": + row[j] += q * row[i] + else: + row[i] *= q + output.append(row) + return output + + +def source_matrix(table): + require(type(table) is list and len(table) == 8 + and all(type(row) is list and len(row) == 8 for row in table), + "Oracle source matrix dimensions") + return [[Fraction(value) for value in row] for row in table] + + +def inverse_word(word): + result = [] + for event in reversed(word): + kind, i, j, q = parse(event) + result.append(["ADD", i, j, str(-q)] if kind == "ADD" + else ["SCALE", i, str(1 / q)]) + return result + + +def address_layouts(pairs): + layouts = [] + templates = 0 + for ordinal, stage in enumerate(STAGES): + active = [0] + list(range(1 + 7 * ordinal, 8 + 7 * ordinal)) + spectators = sorted(set(range(127)) - set(active)) + require(len(active) == len(set(active)) == 8 and len(spectators) == 119, + "Oracle exact active/spectator split") + for f in (1, 2): + dimension = 127 * f + touched = {coordinate * f + lane for coordinate in active + for lane in range(f)} + require(len(touched) == 8 * f + and len(set(range(dimension)) - touched) == 119 * f, + "Oracle tensor spectators") + for i, j in sorted(pairs): + for row in range(dimension): + for lane in range(f): + src = row * dimension + active[i] * f + lane + dst = row * dimension + active[j] * f + lane + require(0 <= src < dimension**2 and 0 <= dst < dimension**2, + "Oracle flat address range") + require(src // dimension == dst // dimension == row + and src % dimension in touched + and dst % dimension in touched, + "Oracle same-row active-address law") + require(src % f == dst % f == lane, + "Oracle exact spectator-lane preservation") + templates += 1 + layouts.append({"stage": stage, "ordinal": ordinal, + "active": active, "spectators": spectators}) + return layouts, templates + + +def run(): + source = authenticated("PORTS.json") + controller = authenticated("CONTROLLER.json") + calls = authenticated("CALLS.json") + require(controller["ambient_rank"] == 127 + and controller["invoice"]["thick_stages"] == STAGES, + "Oracle exact caller stage inventory") + require(len(calls) == 18 and [row["stage"] for row in calls] == STAGES, + "Oracle every actual full call") + raw = (HERE / "RESULT.json").read_bytes() + candidate = json.loads(raw) + records = candidate["ports"] + ports = source["port_interfaces"]["ports"] + require(len(records) == len(ports) == 111 + and [row["port"] for row in records] == list(range(111)) + and [row["port"] for row in ports] == list(range(111)), + "Oracle exact 111-port inventory") + histogram = Counter() + pairs = set() + lengths = [] + for record, original in zip(records, ports): + forward, backward = record["forward_word"], record["inverse_word"] + require(backward == inverse_word(forward), "Oracle literal inverse word") + matrices = [] + for word, table in ((forward, original["normalizer"]), + (backward, original["inverse"])): + expected = source_matrix(table) + found = matrix_from_word(word) + require(found == expected == row_basis_from_word(word), + "Oracle RIGHT product and eight basis rows") + matrices.append(found) + for event in word: + kind, i, j, q = parse(event) + histogram[(kind, str(q))] += 1 + pairs.add((i, j)) + require(product(matrices[0], matrices[1]) == identity() + == product(matrices[1], matrices[0]), "Oracle both round trips") + lengths.append({"port": record["port"], "forward": len(forward), + "inverse": len(backward)}) + layouts, templates = address_layouts(pairs) + counts = [] + for f in (1, 2): + dimension = 127 * f + multiplier = 18 * 2 * dimension * f + leaves = {"ordered_shift" if kind == "ADD" else "unit_scale": 0 + for kind, coefficient in histogram} + coefficients = [] + for (kind, coefficient), count in sorted(histogram.items()): + leaf = "ordered_shift" if kind == "ADD" else "unit_scale" + leaves[leaf] += count * multiplier + coefficients.append({"primitive": leaf, "coefficient": coefficient, + "count": count * multiplier}) + counts.append({"f": f, "N": dimension, "full_calls": 18, + "paired_halves": 2, "both_directions_in_base_histogram": True, + "all_matrix_rows_times_lanes_times_calls_times_halves": multiplier, + "coefficient_counts": coefficients, "primitive_counts": leaves}) + return { + "status": "PASS_G20_NORMALIZER_DYADIC_WORD_ORACLE", + "result_sha256": sha256(raw).hexdigest(), + "source_sha256": {name: pin[1] for name, pin in PINS.items()}, + "convention": "I E1 ... Em = W; ADD[i,j,q] has matrix entry (i,j)=q " + "and updates row coordinate j from i; no word reversal.", + "ports": 111, "right_products": 222, "row_basis_products": 222, + "round_trips": 222, "layouts": layouts, + "flat_address_templates_checked": templates, + "word_lengths": lengths, + "cross_product_catalogue_count": counts, + "nominal_kernel_instances": 111 * 18 * 2 * 2, + "incidence_limit": "7992 is the declared Cartesian catalogue count, not an " + "actual source paid-route count. A per-event mapping " + "is open; no event is presumed to equal one word.", + "spectator_argument": "Every emitted address lies in one active column " + "and the same matrix row/lane; all119f inactive " + "columns remain fixed for every port word.", + "scope": "Finite RIGHT-factor semantics and positive named P2 call counts. " + "These are not actual source route-use counts or a physical head " + "map. Full ROW borrow/cache/carry/return, coefficient preparation, " + "tape tariffs, native admission and compiler closure remain open.", + } + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--emit", action="store_true", + help="Print a candidate receipt without writing any file") + args = parser.parse_args() + receipt = run() + if args.emit: + print(json.dumps(receipt, indent=2, sort_keys=True)) + else: + expected = json.loads((HERE / "ORACLE.json").read_bytes()) + require(json.dumps(expected, sort_keys=True, separators=(",", ":"), allow_nan=False) + == json.dumps(receipt, sort_keys=True, separators=(",", ":"), allow_nan=False), + "Oracle complete retained receipt") + print(json.dumps({"status": receipt["status"], "right_products": 222, + "row_basis_products": 222, "round_trips": 222}, + sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/g20-normalizer-dyadic-words/verify.py b/research/g20-normalizer-dyadic-words/verify.py new file mode 100644 index 0000000000..f468a490bc --- /dev/null +++ b/research/g20-normalizer-dyadic-words/verify.py @@ -0,0 +1,308 @@ +#!/usr/bin/env python3 +"""Construct exact dyadic words for the retained G20 port matrices. + +ToikY with substantial OpenAI Codex assistance. Apache-2.0. +Ali Romman's frozen port/controller data retain the credit in NOTICE. +RIGHT convention: ADD[i,j,a] is I+a e_i e_j^T, so row[j] += a*row[i]. +""" +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path +import argparse +import json + + +HERE = Path(__file__).resolve().parent +SOURCE_HASHES = { + "PORTS.json": "a53a49c938a46c5a9da8c05ffdec4c2ef2dd906dd94c009d6fa451af4ed350e9", + "CONTROLLER.json": "39ac84fb848b908f7ba051fae4556d507900c421dc5d23501a9c0cb1d61fd08d", + "CALLS.json": "30dcc37cdade6b2dc05478837eca28b696894d1c4782bac6a1caab5e7f56c9e8", +} + + +def need(condition, reason): + if not condition: + raise ValueError(reason) + + +def canonical(value): + return json.dumps(value, sort_keys=True, separators=(",", ":"), allow_nan=False).encode() + + +def power_two(integer): + return integer > 0 and integer & (integer - 1) == 0 + + +def dyadic(value): + return power_two(value.denominator) + + +def unit(value): + return dyadic(value) and power_two(abs(value.numerator)) + + +def identity(size): + return [[Q(i == j) for j in range(size)] for i in range(size)] + + +def inverse_operation(operation): + if operation[0] == "ADD": + return ["ADD", operation[1], operation[2], str(-Q(operation[3]))] + return ["SCALE", operation[1], str(1 / Q(operation[2]))] + + +def validate_operation(operation, size): + opcode, i = operation[:2] + need(type(i) is int and 0 <= i < size, "word coordinate") + if opcode == "ADD": + need(len(operation) == 4, "ADD arity") + j, value = operation[2], Q(operation[3]) + need(type(j) is int and 0 <= j < size and i != j and value and dyadic(value), + "nonzero dyadic ADD") + else: + need(opcode == "SCALE" and len(operation) == 3 and unit(Q(operation[2])), + "SCALE is a dyadic unit") + + +def right_product(word, size): + result = identity(size) + for operation in word: + validate_operation(operation, size) + i = operation[1] + if operation[0] == "ADD": + j, coefficient = operation[2], Q(operation[3]) + for row in result: + row[j] += coefficient * row[i] + else: + coefficient = Q(operation[2]) + for row in result: + row[i] *= coefficient + return result + + +def checked_product(word, expected): + need(right_product(word, len(expected)) == expected, "exact RIGHT matrix product") + + +def factor(matrix): + """Unit-only row reduction, with Euclidean pivots over dyadic integers. + + At each column, unit row scales first clear powers-of-two denominators. + Euclidean ADDs and explicitly lowered swaps produce its integer gcd. A + nonunit gcd is a strict stop, never an invitation to divide by an odd part. + """ + size = len(matrix) + current = [row[:] for row in matrix] + reduction = [] + + def emit(operation): + validate_operation(operation, size) + reduction.append(operation) + i = operation[1] + if operation[0] == "ADD": + j, coefficient = operation[2], Q(operation[3]) + current[i] = [a + coefficient * b for a, b in zip(current[i], current[j])] + else: + current[i] = [Q(operation[2]) * a for a in current[i]] + + def swap(i, j): + if i != j: + emit(["ADD", i, j, "1"]) + emit(["ADD", j, i, "-1"]) + emit(["ADD", i, j, "1"]) + emit(["SCALE", j, "-1"]) + + for column in range(size): + for row in range(column, size): + denominator = max(value.denominator for value in current[row]) + need(power_two(denominator), "dyadic source matrix") + if denominator != 1: + emit(["SCALE", row, str(denominator)]) + candidates = [row for row in range(column, size) if current[row][column]] + need(candidates, "invertible source matrix") + swap(column, min(candidates, key=lambda row: abs(current[row][column]))) + for row in range(column + 1, size): + while current[row][column]: + need(current[row][column].denominator == current[column][column].denominator == 1, + "integer Euclidean pivot") + quotient = current[row][column] // current[column][column] + if quotient: + emit(["ADD", row, column, str(-quotient)]) + if current[row][column]: + swap(column, row) + pivot = current[column][column] + need(unit(pivot), "Euclidean pivot must be a dyadic unit") + if pivot != 1: + emit(["SCALE", column, str(1 / pivot)]) + for row in range(size): + if row != column and current[row][column]: + emit(["ADD", row, column, str(-current[row][column])]) + need(current == identity(size), "complete unit row reduction") + # R_m ... R_1 W = I implies W = R_1^-1 ... R_m^-1. + forward = [inverse_operation(operation) for operation in reduction] + inverse = [inverse_operation(operation) for operation in reversed(forward)] + checked_product(forward, matrix) + return forward, inverse + + +def authenticated(name, raw): + need(sha256(raw).hexdigest() == SOURCE_HASHES[name], "source bytes: " + name) + return json.loads(raw) + + +def placement(stage, ordinal, stages): + need(type(ordinal) is int and 0 <= ordinal < len(stages) and stages[ordinal] == stage, + "stage ordinal binding") + active = [0] + list(range(1 + 7 * ordinal, 8 + 7 * ordinal)) + need(len(active) == len(set(active)) == 8 and max(active) < 127, "compatible active layout") + return active + + +def address(half, row, slot, lane, f): + size = 127 * f + return half * size * size + row * size + slot * f + lane + + +def route_guard(source, destination, active, half, row, lane, f): + size = 127 * f + base = half * size * size + row * size + need(0 <= row < size and 0 <= lane < f and half in (0, 1), "address domain") + need(source in {base + slot * f + lane for slot in active} + and destination in {base + slot * f + lane for slot in active}, + "spectator write or wrong row/lane") + need(half * size * size <= source < (half + 1) * size * size + and half * size * size <= destination < (half + 1) * size * size, + "address half boundary") + + +def layout_checks(stages): + samples = [] + for f in (1, 2): + checks = 0 + size = 127 * f + for ordinal, stage in enumerate(stages): + active = placement(stage, ordinal, stages) + spectators = set(range(127)) - set(active) + need(len(spectators) == 119 and not spectators & set(active), "119 untouched spectators") + for half in (0, 1): + for row in range(size): + for lane in range(f): + addresses = [address(half, row, slot, lane, f) for slot in active] + need(len(set(addresses)) == 8, "injective active addresses") + for source in addresses: + # Every possible target is in the same validated set; + # this checks all ADD pairs without allocating a tape. + route_guard(source, source, active, half, row, lane, f) + checks += 1 + samples.append({"f": f, "N": size, "active_address_checks": checks, + "stages": len(stages), "spectator_slots_per_row_lane": 119}) + return samples + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--emit", action="store_true", help="emit candidate only; never write files") + args = parser.parse_args() + raw = {name: (HERE / "inputs" / name).read_bytes() for name in SOURCE_HASHES} + data = {name: authenticated(name, content) for name, content in raw.items()} + records = data["PORTS.json"]["port_interfaces"]["ports"] + controller, calls = data["CONTROLLER.json"], data["CALLS.json"] + stages = controller["invoice"]["thick_stages"] + need(stages == [call["stage"] for call in calls] == [0, 1, *range(3, 32, 2), 32], + "exact retained thick-stage schedule") + need(controller["ambient_rank"] == 127 and len(stages) == 18, "ambient and stage counts") + need([record["port"] for record in records] == list(range(111)), "all exact port IDs") + ports, histograms = [], {"ADD": Counter(), "SCALE": Counter()} + max_height = max_numerator_bits = max_denominator_bits = 0 + for record in records: + matrix = [[Q(value) for value in row] for row in record["normalizer"]] + inverse_matrix = [[Q(value) for value in row] for row in record["inverse"]] + need(len(matrix) == len(inverse_matrix) == 8 + and all(len(row) == 8 for row in matrix + inverse_matrix), "eight-coordinate source matrices") + forward, inverse = factor(matrix) + checked_product(inverse, inverse_matrix) + checked_product(forward + inverse, identity(8)) + for operation in forward + inverse: + value = Q(operation[-1]) + histograms[operation[0]][str(value)] += 1 + max_height = max(max_height, abs(value.numerator), value.denominator) + max_numerator_bits = max(max_numerator_bits, abs(value.numerator).bit_length()) + max_denominator_bits = max(max_denominator_bits, value.denominator.bit_length()) + ports.append({"port": record["port"], "line": record["line"], + "complement": record["complement"], + "forward_word": forward, "inverse_word": inverse}) + synthetic = [[Q(3), Q(1)], [Q(2), Q(1)]] + synthetic_word, synthetic_inverse = factor(synthetic) + checked_product(synthetic_word + synthetic_inverse, identity(2)) + samples = layout_checks(stages) + controls = [] + + def reject(name, expected, operation): + try: + operation() + except ValueError as error: + need(str(error) == expected, "control wrong failure: " + name) + controls.append({"name": name, "reason": str(error), "rejected": True}) + else: + raise ValueError("control accepted: " + name) + + first_matrix = [[Q(value) for value in row] for row in records[0]["normalizer"]] + reject("omitted_operation", "exact RIGHT matrix product", + lambda: checked_product(ports[0]["forward_word"][1:], first_matrix)) + witness = next(index for index, port in enumerate(ports) + if right_product(list(reversed(port["forward_word"])), 8) + != [[Q(value) for value in row] for row in records[index]["normalizer"]]) + reject("wrong_direction", "exact RIGHT matrix product", + lambda: checked_product(list(reversed(ports[witness]["forward_word"])), + [[Q(value) for value in row] for row in records[witness]["normalizer"]])) + reject("odd_SCALE", "SCALE is a dyadic unit", lambda: right_product([["SCALE", 0, "3"]], 8)) + reject("source_drift", "source bytes: PORTS.json", + lambda: authenticated("PORTS.json", raw["PORTS.json"] + b" ")) + active = placement(stages[0], 0, stages) + spectator = min(set(range(127)) - set(active)) + reject("spectator_write", "spectator write or wrong row/lane", + lambda: route_guard(address(0, 0, active[0], 0, 1), address(0, 0, spectator, 0, 1), + active, 0, 0, 0, 1)) + reject("raw_stage_used_as_ordinal", "stage ordinal binding", lambda: placement(3, 3, stages)) + histogram = {kind: dict(sorted(counts.items(), key=lambda item: Q(item[0]))) + for kind, counts in histograms.items()} + # Each coefficient receives its own named primitive cost. Both directions + # are already included in histogram; two halves and 18 stage placements + # multiply by 2*18*(127*f)*f. No unit-price replacement is made. + bill = {kind: {coefficient: 4572 * count for coefficient, count in counts.items()} + for kind, counts in histogram.items()} + result = { + "schema": "g20-normalizer-dyadic-words/1", "ports": ports, + "source_raw_sha256": SOURCE_HASHES, + "word_convention": "RIGHT product E1...Em=W; ADD[i,j,a]=I+a*e_i*e_j^T; row[j]+=a*row[i]", + "ordered_shift": "source=half*N^2+row*N+active[i]*f+lane; target=half*N^2+row*N+active[j]*f+lane", + "scale": "SCALE[i,u] scales the corresponding active[i] coordinate; u is a dyadic unit", + "placements": [{"stage": stage, "ordinal": ordinal, + "active_indices": placement(stage, ordinal, stages)} + for ordinal, stage in enumerate(stages)], + "layout_scope": "Chosen compatible 127-slot layout; not the retained literal physical head map", + "sample_layout_checks": samples, "operation_histogram_both_directions": histogram, + "operation_counts_both_directions": {kind: sum(counts.values()) for kind, counts in histogram.items()}, + "coefficient_height": {"maximum": max_height, "numerator_bits": max_numerator_bits, + "denominator_bits": max_denominator_bits}, + "named_primitive_counts_times_f_squared": bill, + "parametric_bill": "sum over ADD/SCALE coefficients a of counts[a]*f^2*C_kind(a), with positive named primitive costs", + "bill_scope": "Cartesian catalogue cross-product; not a bijection to retained paid route events or a full caller invoice", + "call_cross_product_catalogue_count": 111 * 18 * 2 * 2, + "multiplicity": {"address_halves": 2, "stages": 18, "row_count": "N=127*f", + "lanes": "f", "directions": "forward and inverse already counted"}, + "synthetic_nonunit_pivot": {"matrix": [["3", "1"], ["2", "1"]], + "forward_word": synthetic_word, "inverse_word": synthetic_inverse}, + "failure_controls": controls, "wrong_direction_witness_port": witness, + "remaining": "Full borrow/cache/carry/type commitments, padding, tape and physical ROW ABI implementation; no unit-price bound or supplier/native admission", + } + if not args.emit: + need(canonical(result) == canonical(json.loads((HERE / "RESULT.json").read_text(encoding="utf-8"))), + "frozen RESULT.json comparison") + print(json.dumps(result, sort_keys=True, indent=2)) + print("PASS_G20_NORMALIZER_DYADIC_WORDS") + + +if __name__ == "__main__": + main()