From c5b53a5e80372a1fae9830d8dcf21aaabce3f729 Mon Sep 17 00:00:00 2001 From: Ambassator <87917833+Ambassators@users.noreply.github.com> Date: Mon, 12 Oct 2026 23:13:13 -0500 Subject: [PATCH] Independent verification of weighted-stride closures and bilinear dual Prepared with substantial OpenAI AI assistance. Scoped exact and rounded evidence only; no new kappa. Attribution and inherited obligations in NOTICE.md and PROOF.md. --- .../cyclic-stride-independent/CHECK-LOGS.txt | 44 + research/cyclic-stride-independent/CLAIM.json | 33 + .../cyclic-stride-independent/EXPECTED.json | 19822 ++++++++++++++++ research/cyclic-stride-independent/NOTICE.md | 26 + .../cyclic-stride-independent/OVERLAP.json | 46 + research/cyclic-stride-independent/PROOF.md | 114 + research/cyclic-stride-independent/README.md | 94 + .../cyclic-stride-independent/SOURCE.json | 17 + .../cyclic-stride-independent/VALIDATION.json | 29 + .../cyclic-stride-independent/VALIDATION.md | 64 + .../cyclic-stride-independent/test_verify.py | 74 + research/cyclic-stride-independent/verify.py | 414 + 12 files changed, 20777 insertions(+) create mode 100644 research/cyclic-stride-independent/CHECK-LOGS.txt create mode 100644 research/cyclic-stride-independent/CLAIM.json create mode 100644 research/cyclic-stride-independent/EXPECTED.json create mode 100644 research/cyclic-stride-independent/NOTICE.md create mode 100644 research/cyclic-stride-independent/OVERLAP.json create mode 100644 research/cyclic-stride-independent/PROOF.md create mode 100644 research/cyclic-stride-independent/README.md create mode 100644 research/cyclic-stride-independent/SOURCE.json create mode 100644 research/cyclic-stride-independent/VALIDATION.json create mode 100644 research/cyclic-stride-independent/VALIDATION.md create mode 100644 research/cyclic-stride-independent/test_verify.py create mode 100644 research/cyclic-stride-independent/verify.py diff --git a/research/cyclic-stride-independent/CHECK-LOGS.txt b/research/cyclic-stride-independent/CHECK-LOGS.txt new file mode 100644 index 0000000000..d741073479 --- /dev/null +++ b/research/cyclic-stride-independent/CHECK-LOGS.txt @@ -0,0 +1,44 @@ +Final normal replay +PASS_STRIDE_RESOLVENT_AND_DUAL +{"all_entry_checks": 252730, "exact_cases": 266, "rejected_controls": 16, "rounded_cases": 4256, "rounded_coordinates": 53472} + +Optimized replay +PASS_STRIDE_RESOLVENT_AND_DUAL +{"all_entry_checks": 252730, "exact_cases": 266, "rejected_controls": 16, "rounded_cases": 4256, "rounded_coordinates": 53472} +real 11.61 +user 11.53 +sys 0.04 + +Focused normal tests +test_asymmetric_closure_example (__main__.FocusedTests) ... ok +test_corrupted_source_manifest_fails_before_execution (__main__.FocusedTests) ... ok +test_dual_phase_is_shifted_not_conjugated (__main__.FocusedTests) ... ok +test_missing_source_commit_fails_closed (__main__.FocusedTests) ... ok +test_one_singular_cycle_is_rejected (__main__.FocusedTests) ... ok +test_partition_and_adjacency (__main__.FocusedTests) ... ok +test_scalar_all_strides (__main__.FocusedTests) ... ok +test_zero_root_direct_inverse (__main__.FocusedTests) ... ok + +---------------------------------------------------------------------- +Ran 8 tests in 0.031s + +OK + +Focused optimized tests +test_asymmetric_closure_example (__main__.FocusedTests) ... ok +test_corrupted_source_manifest_fails_before_execution (__main__.FocusedTests) ... ok +test_dual_phase_is_shifted_not_conjugated (__main__.FocusedTests) ... ok +test_missing_source_commit_fails_closed (__main__.FocusedTests) ... ok +test_one_singular_cycle_is_rejected (__main__.FocusedTests) ... ok +test_partition_and_adjacency (__main__.FocusedTests) ... ok +test_scalar_all_strides (__main__.FocusedTests) ... ok +test_zero_root_direct_inverse (__main__.FocusedTests) ... ok + +---------------------------------------------------------------------- +Ran 8 tests in 0.030s + +OK + +Receipt tamper +exit=1 +FAIL: complete receipt mismatch diff --git a/research/cyclic-stride-independent/CLAIM.json b/research/cyclic-stride-independent/CLAIM.json new file mode 100644 index 0000000000..9d75310cc4 --- /dev/null +++ b/research/cyclic-stride-independent/CLAIM.json @@ -0,0 +1,33 @@ +{ + "track": "Independent verification", + "seed": 79, + "seed_source": "secrets.randbelow(100), OS randomness; drawn once at session start", + "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60", + "source_pr628_commit": "0768f97d06c623b8211e651543c66135796b62bf", + "coordination": "No pinned sprint coordination issue found; only open non-PR issue #650 concerns Discussions. Local claim; no reservation issue created.", + "candidates": [ + { + "task": "Independent #543 moment endpoint enclosure", + "decision": "Not selected: #678 supplies new binomial engine." + }, + { + "task": "Independent #621 prime-power resultant identity", + "decision": "Not selected: #668 supplies CRT engine and expanded radices." + }, + { + "task": "#628 weighted-scan resolvent under non-coprime strides and inverse-transpose boundary indexing", + "decision": "Selected: independent cycle-local finite geometric-sum oracle; new multi-cycle and dual obligations, not resultant or dirty-echo duplication." + } + ], + "object": "(W-rho I)^(-1), (Wx)_i=tau_i*x_(i-s mod L); distinct cycle holonomies, signed and zero stride, inner/outer roots, and bilinear inverse transpose", + "method": "Exact Fraction-pair arithmetic; cycle-local geometric resolvent checked on all columns against directly constructed dense matrices; compare rounded pinned #628 factor application after cycle permutation, both neighbor directions; explicit failing controls. No paid routing or kappa claim.", + "domain": "Lengths 1..12 plus 16,18,21; every stride residue modulo length; seed79 deterministically chooses nonconstant rational-unit phase patterns and RHS values. Inner rho=(1/4,1/8), outer rho=(2,-1/4). Fixed coverage, no search.", + "deliverable": "One standalone independent checker, exact deterministic receipt, scope/proof note, source pins and meaningful controls", + "finish": "This synchronous contribution session; no scheduled/background continuation.", + "claimed_at_utc": "2026-10-13T03:58:48.214990+00:00", + "status": "completed and locally verified; independent verification, no kappa claim", + "result": "266 exact cases; 252730 matrix-entry checks; 4256 rounded cases; 16 negative controls; 8 focused tests. Separate variable-phase closure and bilinear-dual evidence.", + "result_link": "https://github.com/Ambassators/integer-mult-bounds/tree/research/seed79-independent-verification/research/cyclic-stride-independent", + "prior_work_clarification": "PR628 already supplies scalar-gauge arbitrary-stride sorting and the direct-sum norm principle; neither is claimed new. This package independently checks varying-phase cycle closures and bilinear duals.", + "completed_at_utc": "2026-10-13T04:11:28.282482+00:00" +} diff --git a/research/cyclic-stride-independent/EXPECTED.json b/research/cyclic-stride-independent/EXPECTED.json new file mode 100644 index 0000000000..277d5f72dc --- /dev/null +++ b/research/cyclic-stride-independent/EXPECTED.json @@ -0,0 +1,19822 @@ +{ + "cases": [ + { + "cycle_count": 1, + "cycle_length": 1, + "dual_sha256": "709111102bfff5ac89098dc3a6310b7e5219eee62fd7eb639bc9dad564e46855", + "holonomies": [ + [ + "0", + "1" + ] + ], + "inverse_sha256": "709111102bfff5ac89098dc3a6310b7e5219eee62fd7eb639bc9dad564e46855", + "length": 1, + "phases": [ + [ + "0", + "1" + ] + ], + "root": 0, + "stride": 0 + }, + { + "cycle_count": 1, + "cycle_length": 1, + "dual_sha256": "aff220df345589ecd8768926116eae97b65211d6ebe5fd6786e642a905c652f1", + "holonomies": [ + [ + "0", + "1" + ] + ], + "inverse_sha256": 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"exact rational unit phases" + }, + { + "name": "empty_array", + "rejected": "nonempty phase array" + }, + { + "name": "noninteger_stride", + "rejected": "integer stride" + }, + { + "name": "source_hash_mutation", + "rejected": "source hash: control" + }, + { + "name": "pinned_wrong_inner_phase_index", + "rejected": "factor error bound" + }, + { + "name": "RHS_length", + "rejected": "RHS length" + }, + { + "name": "underprecision", + "rejected": "closure precision" + }, + { + "name": "unseparated_root", + "rejected": "factor margin beta=1/2" + } + ], + "exact_matrix_entries": 252730, + "lengths": [ + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 16, + 18, + 21 + ], + "maximum_ratio_case": [ + 18, + 9, + 0, + true, + 1, + 12, + 0 + ], + "maximum_squared_error_to_budget": "3219419765/13937745510864", + "multicycle_cases": 122, + "precisions": [ + 12, + 40 + ], + "roots": [ + [ + "1/4", + "1/8" + ], + [ + "2", + "-1/4" + ] + ], + "rounded_cases": 4256, + "rounded_coordinates": 53472, + "rounded_transcript_sha256": "7646fbf830b5c353cffb4daf41599d1fedb1eb7f759ca1d410c38ad2efb7b29b", + "schema": 1, + "seed": 79, + "signed_stride_checks": 266, + "source_commit": "0768f97d06c623b8211e651543c66135796b62bf", + "status": "PASS_STRIDE_RESOLVENT_AND_DUAL", + "stride_residues": "all, represented also by s-L", + "zero_root_edge_check": true, + "zero_stride_cases": 30 +} diff --git a/research/cyclic-stride-independent/NOTICE.md b/research/cyclic-stride-independent/NOTICE.md new file mode 100644 index 0000000000..e52c0bb584 --- /dev/null +++ b/research/cyclic-stride-independent/NOTICE.md @@ -0,0 +1,26 @@ +# Attribution and license + +New code and notes: prepared for Ryan Pinto / GitHub **Ambassators**, with +substantial OpenAI AI assistance in task selection, mathematics, coding, +verification and writing. No separate human review or delegated-worker +review is claimed. Apache-2.0, following the repository LICENSE. + +Chafik Boukhalfa / **chafreaky**, PR628 at the exact SOURCE.json head, supplies +the weighted neighboring scan, factor execution and rounding estimate. Its +NOTICE.md is hash-bound without alteration. Ali Romman's incorporated PR621 +supplies the antecedent prime-power circle bound, but that theorem is not +needed to establish this standalone single-factor identity. Preserve its +OpenAI exact-DFT, classical q-Pochhammer/Newton, Kuznetsov, Pan, Mehlhorn- +Sagraloff-Wang, Brent and Briand-Davy attribution when composing this work +with the full predecessor. No source function is presented as new work. + +Finite geometric sums, permutation cycles, weighted shifts and transpose +identities are standard algebra; no literature-priority claim is made. +The distinct contribution is the independently implemented cycle-local +oracle, the non-coprime-stride and bilinear-dual obligations, and the +source-bound exact/rounded/mutation evidence. + +Concurrent PR668 (Scott Woolsey Biggart) verifies prime-power resultants by +CRT; PR666 (Jason Willems) concerns composite seed lifting; PR663 and PR673 +concern dirty commutator/composition obligations. They are acknowledged +neighbors, not runtime or mathematical dependencies of this package. diff --git a/research/cyclic-stride-independent/OVERLAP.json b/research/cyclic-stride-independent/OVERLAP.json new file mode 100644 index 0000000000..6d029b59ad --- /dev/null +++ b/research/cyclic-stride-independent/OVERLAP.json @@ -0,0 +1,46 @@ +{ + "latest_pr_seen": 688, + "relevant_heads": [ + { + "head": "14dd937d9e2d3e51092c0c35a8c2c9cdf8ba81f4", + "number": 684, + "title": "Audit Gaussian chirp domain and exact block budgets" + }, + { + "head": "bdc9317efd6d928a0f050159670d1316ba5f4c5b", + "number": 678, + "title": "Independent verification of the #543 bit moment using binomial enclosures" + }, + { + "head": "f011d03633f0570257b653e7aa1e869b1b06d06a", + "number": 675, + "title": "Research audit: PR626 owner boundaries and bridge-omission blind spot" + }, + { + "head": "0e35f56cab3cae1eb0a99447135569d687c5695a", + "number": 673, + "title": "Research: subquadratic dirty echo composition and phase-alias repair" + }, + { + "head": "b861542035d612ff844d0a9d1deaa0713329811a", + "number": 668, + "title": "Independent verification: exact CRT resultants through radix 27" + }, + { + "head": "8df1b593cb640380a194ac8d599f2ab1cba158a3", + "number": 666, + "title": "Composite cyclic inverses: exact certificates and modular lifting" + }, + { + "head": "e0e546fd01b396478c68b6b6c5a16d87515983ba", + "number": 663, + "title": "Independent audit: nonlinear dirty restoration and exact PR628 leaf count" + }, + { + "head": "0768f97d06c623b8211e651543c66135796b62bf", + "number": 628, + "title": "Uniform rounded prime-power cyclic inversion (no \u03ba claim)" + } + ], + "distinction": "Independent finite-geometric resolvent for independently varying phases and bilinear dual, not new constant-gauge routing/direct-sum norm, CRT, composite lifting or dirty echo." +} diff --git a/research/cyclic-stride-independent/PROOF.md b/research/cyclic-stride-independent/PROOF.md new file mode 100644 index 0000000000..58fa2efdef --- /dev/null +++ b/research/cyclic-stride-independent/PROOF.md @@ -0,0 +1,114 @@ +# Cycle-local resolvents and the bilinear dual + +## Exact obligation + +Let L >= 1, s be any integer, and tau_i be complex scalars of modulus one. +Indices are modulo L. Define (W x)_i = tau_i x_(i-s). The permutation splits +into g = gcd(L,s) cycles of length m = L/g; gcd(L,0)=L. For a cycle C put +h_C = product_(i in C) tau_i. On that cycle W^m = h_C I. + +For any scalar rho such that h_C != rho^m on every cycle, define + + R_C = [sum_(j=0)^(m-1) rho^(m-1-j) W_C^j] / (h_C-rho^m). + +Multiplying the numerator by W_C-rho I on either side telescopes to +W_C^m-rho^m I. Consequently R_C is a two-sided inverse of W_C-rho I. +The direct sum of these inverses, scattered back to the original indices, +is (W-rho I)^(-1). This is a written elementary proof for all L and s, +not an inference from the finite receipt and not a proof-assistant result. + +If |rho| != 1, all denominators are nonzero because |h_C|=1. In particular, +this applies to the tested inner and outer roots. It also handles rho=0, +L=1 and s=0. At rho=0, rho^0 in the final summand means 1. +No prime-power or polynomial-kernel nonvanishing theorem is needed here. +The oracle constructs these finite sums without a Gaussian solver or the +predecessor's affine two-pass recurrence. + +## The inverse transpose is not the inverse adjoint + +For the complex bilinear pairing x^T y, direct expansion gives + + (W^T x)_i = tau_(i+s) x_(i+s). + +Thus W^T is a weighted shift of stride -s and phases +sigma_i = tau_(i+s), without complex conjugation. Substituting sigma,-s +in the preceding formula gives (W-rho I)^(-T). The checker compares this +matrix with the transpose of the independently constructed forward inverse, +then checks both matrix products against the identity. For the Hermitian +adjoint the phases AND rho would instead be conjugated. Confusing those +two interfaces is explicitly rejected, but this is not a claim that PR628 +uses the wrong pairing: its submitted neighboring forward factor is valid +on the checked inputs. + +## Reduction to the pinned rounded neighboring factor + +Enumerate each cycle as a,a+s,...,a+(m-1)s. In these coordinates its shift +is PR628's direction +1. Reversing that cycle order, while keeping its first +entry fixed, gives direction -1. Gather values and phases with the same +permutation, call the pinned factor, then scatter using the inverse map. +The execution is a direct sum, not a product, of the cycle calls. +PR628's LAYOUT.md already uses cycle decomposition and this direct-sum norm +argument for a constant scalar gauge, with two explicitly charged sorts. +They are not new claims here; the present obligations concern varying +phases, the bilinear dual and an independent exact implementation. + +Both gather and scatter preserve the infinity norm. Suppose either +|rho| <= 1-beta or |1/rho| <= 1-beta, 0 < beta <= 1, and u=2^(-w) <= beta^2/2. +The neighboring single-factor bound from PR628 WEIGHTED-PROOF.md is + + error <= 7 (B+1) u / beta^3, ||x||_infinity <= B. + +Every cycle input has norm at most B. Taking the maximum of the cycle +errors gives the SAME bound, without a factor g or L. The transpose phase +shift also preserves unit modulus, so the same argument applies to it. +This implication inherits the neighboring rounding estimate; the finite +checks corroborate that estimate but do not prove it for arbitrary inputs. +The two selected roots have beta=1/2: their stable coefficients have squared +moduli 5/64 and 16/65, both at most 1/4. + +The reference adapter invokes unchanged scan/apply definitions from the +pinned weighted.py and unchanged arithmetic from scan.py. It sets radix=1 +only to omit an initial scalar and isolate ONE factor. This is not a +radix-1 kernel certificate, a full factor cascade, or a new prime-power +construction. The parser selects complete function ASTs without rewriting +them and binds c to the same pinned scan module; unrelated kernel setup +and the predecessor's main test harness are not executed. + +## An exact counterexample to a tempting extension + +Take L=6, s=2 and phases + + [1, i, (3+4i)/5, (-5+12i)/13, -1, -i]. + +The even and odd cycles have holonomies + + h_even = (-3-4i)/5, h_odd = (-5+12i)/13. + +The global product is (63-16i)/65, which is neither local holonomy. +Replacing each cycle denominator by this global product minus rho^3, +with rho=1/4+i/8, produces a matrix that fails the exact inverse identity. +Using L instead of m in the denominator also fails. These are concrete +counterexamples to those ADAPTER MUTANTS, not counterexamples to PR628, +which explicitly restricts its submitted weighted layout to neighbors. + +## Cost and unresolved obligations + +Only algebra and numerical error transport are settled here. A complete +implementation would have cost + + C_gather(L,s) + sum_C C_neighbor(|C|) + C_scatter(L,s), + +plus every phase read/preparation, allocation and restoration required by +the target model. The Python adapter uses random indexing and clean arrays; +it does not implement or price a fixed-tape permutation, dirty reversible +storage, native-frame changes, recursive hosting or common-label access. +No routing term is assumed free. The inherited direct-sum argument prevents +a spurious cycle-count precision multiplier; no established paid expense +is reduced. The existing LAYOUT.md charge is not replaced by a free RAM +permutation. + +Kernel preparation, arbitrary growing radices, full-transform composition, +H1-H5, compiler/tape/precision/exact recovery and analytic transfer are not +verified or discharged. There is no new kappa or integer multiplication +bound. This is a scoped independent implementation and written identity +proof, not independent human review or a formal full-theorem verification. diff --git a/research/cyclic-stride-independent/README.md b/research/cyclic-stride-independent/README.md new file mode 100644 index 0000000000..c6381a15d2 --- /dev/null +++ b/research/cyclic-stride-independent/README.md @@ -0,0 +1,94 @@ +# Independent weighted-stride resolvent and dual audit + +**Status: independent verification / research note. No new kappa.** + +This contributes a finite-geometric-sum oracle, a written all-length +cycle/dual identity, and a source-bound comparison with the neighboring +weighted factor in Chafik Boukhalfa's pending PR628. It covers non-coprime +strides with separate cycle closures and the bilinear inverse transpose. +Those are different obligations from the predecessor's neighboring forward +Gaussian checks, PR668's resultant CRT, PR666's composite lifting, and +PR663/PR673's dirty composition. No defect in PR628's stated neighboring +scope was found. Incorrect extensions have exact rejecting controls. + +PR628 already supplies a charged two-sort layout for a constant scalar gauge +and the direct-sum norm argument. Neither is new here. This package instead +checks per-cycle closures with independently varying phases and the bilinear +dual through a different exact algorithm; it does not replay or improve the +predecessor's sorting implementation. + +## Pins and current state + +Base: `66849e1475c930fd7732b1a0067ffee7e1e95f60`. +PR628: `0768f97d06c623b8211e651543c66135796b62bf`. +`SOURCE.json` binds eight source/proof/layout/notice files by SHA-256. `CLAIM.json` +records OS-random seed 79, three candidates, exclusions and local scope. +No pinned sprint coordination issue was found; no reservation issue opened. + +At the base, the selected certificate is #626 with #543, conditional +kappa `51110230636731/31250000000000000 = 0.001635527380375392`. +It was followed to `research/complex-k492-owner-repair`, the retained +`research/community-k492-audit/pr626/replay/ASSEMBLY.json`, and +`docs/research/community-k492-review.md`. That frontier is not a dependency +of the algebra checked here and is not changed by this contribution. + +## Reproduce + +Python 3.9+ and Git, standard library only. Fetch the exact pending source +object once if it is absent; this does not check out or modify its files: + +```sh +git fetch --no-tags https://github.com/CrocSwap/integer-mult-bounds.git 0768f97d06c623b8211e651543c66135796b62bf +``` + +From this contribution's checkout, the complete deterministic check is: + +```sh +python3 -B -I research/cyclic-stride-independent/verify.py --check research/cyclic-stride-independent/EXPECTED.json +``` + +Expected: + +```text +PASS_STRIDE_RESOLVENT_AND_DUAL +{"all_entry_checks": 252730, "exact_cases": 266, "rejected_controls": 16, "rounded_cases": 4256, "rounded_coordinates": 53472} +``` + +The source files are extracted to an automatically removed temporary +directory and checked before execution. Only the unchanged scan/apply ASTs +and their original arithmetic are executed; no approximate-root setup or +full-kernel verifier is run. `--oracle-only` is a separately labeled partial +mode and cannot pass a full-receipt comparison. `--out PATH` writes a fresh +receipt; `--check PATH` compares every parsed field, not only status. + +Additional focused tests: `python3 -B -I research/cyclic-stride-independent/test_verify.py`. +Optimized replay: add `-O` to the complete command above. Mathematical +checks use explicit exceptions and remain enabled under optimization. + +## Fixed domain and completed coverage + +Lengths 1 through 12, plus 16,18,21; every stride residue; both roots +`1/4+i/8` and `2-i/4`; deterministic nonconstant rational-unit phase patterns +and RHS values from seed 79. There is no adaptive search or early success +stopping rule: every domain point is executed. Each exact inverse is checked +on ALL matrix entries in both orders, together with both inverse-transpose +products and its entrywise transpose identity. Signed representatives and +the zero-root edge case are checked separately. + +The receipt has 266 cases (122 with multiple cycles, 30 zero-stride), +252,730 matrix-entry obligations, and 266 signed-stride checks. Rounded +comparisons cover forward/dual, both neighboring enumeration directions, +12/40-bit grids, a dense rational RHS and a selected basis RHS: 4,256 calls +and 53,472 output coordinates. Rounded arithmetic is nonlinear; these finite +RHS tests are not an all-input proof. Exact forward/dual matrices and rounded +outputs have deterministic digest evidence, with actual phases and cycle +holonomies retained in the receipt. + +Sixteen controls reject global-product closure, global rather than local +cycle length, omitted closure, wrong dual phase indexing, conjugation, +a missing cycle, wrong scattering, a genuinely singular root, bad phases, +empty/noninteger inputs, altered source hashes, the predecessor's built-in +wrong-inner-phase mutant, wrong RHS length, underprecision and a root that +fails the admitted margin. The concrete closure example is in `PROOF.md`. + +See `VALIDATION.md` for executed commands and limits; `NOTICE.md` for credit. diff --git a/research/cyclic-stride-independent/SOURCE.json b/research/cyclic-stride-independent/SOURCE.json new file mode 100644 index 0000000000..47930d9153 --- /dev/null +++ b/research/cyclic-stride-independent/SOURCE.json @@ -0,0 +1,17 @@ +{ + "repository": "CrocSwap/integer-mult-bounds", + "pr": 628, + "commit": "0768f97d06c623b8211e651543c66135796b62bf", + "directory": "research/prime-power-cyclic-scan", + "files": { + "weighted.py": "8b0f93d131a30e64eb0ccd893779daffea79c0c00f1d2a30a91d23eb2bf0bff5", + "check.py": "a3e46b556894d71a1c83bbbac01c50c1a541285fc9422a3567d5eb1d1ee86e7d", + "scan.py": "1a9c01ca1a29a9be1e756858161202621db29d5d332a4266b4017a9502a50d7e", + "interval_kernel.py": "9b7bb24640a9a7d3f83c7951dfef483ec933db4c50de6c0130b85f450eeddfbe", + "WEIGHTED-PROOF.md": "b0643ad6ae448ca2fe11ee9a9597b5656e5e2feaaa89b16939e1d1bc7ba7437d", + "NOTICE.md": "abeacf1ad1491d5797cfcf1f3832799bbf3b24b99597229d7bc884059a51ec68", + "LAYOUT.md": "8a090a97b7be2a4e2d248bbb269157dabc05bac444cb8d84772b2980aed849e7", + "check_layout.py": "ed67efe2f418bd39b08882f4bd9f1f1908a4ceda01baa40032814bb10fdaf515" + }, + "execution_scope": "Unmodified weighted.py scan/apply AST definitions and original scan.py arithmetic only; no full-kernel certificate or existing layout replay." +} diff --git a/research/cyclic-stride-independent/VALIDATION.json b/research/cyclic-stride-independent/VALIDATION.json new file mode 100644 index 0000000000..9242323bc4 --- /dev/null +++ b/research/cyclic-stride-independent/VALIDATION.json @@ -0,0 +1,29 @@ +{ + "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60", + "source_commit": "0768f97d06c623b8211e651543c66135796b62bf", + "macos_python": "3.9.6", + "macos_platform": "macOS-27.0-arm64-arm-64bit", + "linux_oracle_python": "3.13.5", + "linux_oracle_platform": "Linux x86_64", + "exact_projection_keys": [ + "seed", + "lengths", + "roots", + "cases", + "exact_matrix_entries", + "signed_stride_checks", + "zero_stride_cases", + "multicycle_cases", + "zero_root_edge_check" + ], + "exact_projection_sha256": "391d48638394375d3255ca3c8c9377a37a67a3b4708c9a70f939a5b704063cf2", + "selected_record_sha256": "b3bf402f31a69bde0629936a9b569bed48281568d7b16d5fba120b5311ea1f53", + "selected_certificate_sha256": "6127732e2fcdd470dab349c1c51d03cd9f0787ad0309b1b4a7c811a908028f4e", + "latest_pr_seen": 688, + "full_repository_suite": "not run: no selected construction or generator changed", + "frontier626_cold_replay": "not run: no selected construction changed", + "remote_ci": "not claimed", + "prepared_at_utc": "2026-10-13T04:11:28.281838+00:00", + "overlap_file": "OVERLAP.json", + "overlap_sha256": "3f952a22878294040a762ea89d3fa956d26f278e3d341b06b5d01f4d985662aa" +} diff --git a/research/cyclic-stride-independent/VALIDATION.md b/research/cyclic-stride-independent/VALIDATION.md new file mode 100644 index 0000000000..de6f558e6f --- /dev/null +++ b/research/cyclic-stride-independent/VALIDATION.md @@ -0,0 +1,64 @@ +# Validation and limitations + +## Executed checks + +The complete source-bound checker passed on macOS arm64 / CPython 3.9.6 +under isolated normal execution and isolated optimized execution. The full +parsed EXPECTED.json receipt matched, including all exact cases, phases, +holonomies, matrix digests, rounded-output digest, maximum rational error +ratio, counts and controls. The first full run took 11.71 seconds; this is +an environment observation, not a before/after performance claim. + +Commands from the repository root: + +```sh +python3 -B -I research/cyclic-stride-independent/verify.py --check research/cyclic-stride-independent/EXPECTED.json +python3 -B -I -O research/cyclic-stride-independent/verify.py --check research/cyclic-stride-independent/EXPECTED.json +python3 -B -I research/cyclic-stride-independent/test_verify.py +python3 -B -I -O research/cyclic-stride-independent/test_verify.py +``` + +Both modes retain 266 exact cases, 252,730 matrix-entry obligations, +4,256 rounded cases / 53,472 coordinates, and 16 rejected controls. +All eight focused tests pass in both modes. These additionally exercise +actual corrupt-manifest and missing-Git-object paths, exact scalar and +zero-root formulas, the asymmetric closure witness, one singular cycle, +and cycle partitions for every stride from -L through L, L=1..31. + +A separate CLI test decremented only `rounded_cases` in a temporary copy of +EXPECTED.json. Optimized full execution exited 1 with +`FAIL: complete receipt mismatch`. The checked-in receipt was not modified. +This is in addition to the 16 controls, not counted as a seventeenth member +of the deterministic receipt. + +An oracle-only run on Linux x86_64 / CPython 3.13.5 passed the same 266 +exact cases. Its complete exact-evidence projection matched the macOS +full run, SHA-256: + + 391d48638394375d3255ca3c8c9377a37a67a3b4708c9a70f939a5b704063cf2 + +The projection keys are listed in VALIDATION.json. Canonicalize that +subdictionary with `json.dumps(..., sort_keys=True, separators=(',', ':'))` +and hash its UTF-8 bytes. This verifies agreement of all retained exact +case data, not merely a count. A full Linux predecessor replay is NOT +claimed; only the independent oracle was executed there. + +## Scope integrity and review status + +The selected record was compared byte-for-byte to the base. Its referenced +ASSEMBLY.json SHA-256 matched the selected certificate's declared hash. +The construction proof note and maintainer review were also compared to +the base. No existing tracked file, including upstream/, was changed. +Staged whitespace and isolated-base-index patch applicability were checked +when packaging. These are source-integrity checks, not a fresh cold rebuild. + +`make verify` and `make frontier626-verify` were not run: the change adds a +standalone research package, not a generator, supplier, selected record, +root build rule or imported certificate. No root-wide regeneration or +full-kernel/cascade/layout replay is claimed. No remote CI pass, formal +proof-assistant run, independent human review or new kappa is claimed. + +The PR queue was refreshed before publication. OVERLAP.json records the +relevant exact heads and the distinction from scalar-gauge stride routing, +CRT resultants, composite lifting and dirty restoration. Newer supplier +headlines were not treated as the selected frontier. diff --git a/research/cyclic-stride-independent/test_verify.py b/research/cyclic-stride-independent/test_verify.py new file mode 100644 index 0000000000..b9357bca58 --- /dev/null +++ b/research/cyclic-stride-independent/test_verify.py @@ -0,0 +1,74 @@ +#!/usr/bin/env python3 +"""Focused edge, arithmetic, source-binding and cycle tests (Apache-2.0).""" +import importlib.util +import json +from pathlib import Path +import tempfile +import unittest + +P = Path(__file__).resolve().parent +spec = importlib.util.spec_from_file_location('stride_check', P / 'verify.py') +v = importlib.util.module_from_spec(spec) +spec.loader.exec_module(v) + + +class FocusedTests(unittest.TestCase): + def test_scalar_all_strides(self): + tau = v.UNITS[2] + for s in (-17, 0, 1, 9): + for rho in v.ROOTS: + self.assertEqual(v.resolvent([tau], s, rho), + [[v.quotient(v.ONE, v.minus(tau, rho))]]) + + def test_zero_root_direct_inverse(self): + phases = list(v.UNITS[:6]) + inverse = v.resolvent(phases, 2, v.ZERO) + for i, row in enumerate(inverse): + for j, value in enumerate(row): + expected = v.quotient(v.ONE, phases[(i+2) % 6]) if j == (i+2) % 6 else v.ZERO + self.assertEqual(value, expected) + + def test_partition_and_adjacency(self): + for n in range(1, 32): + for s in range(-n, n+1): + cc = v.cycles(n, s) + self.assertEqual(sorted(i for c in cc for i in c), list(range(n))) + for c in cc: + for j, i in enumerate(c): + self.assertEqual(c[(j+1) % len(c)], (i+s) % n) + + def test_asymmetric_closure_example(self): + phases = list(v.UNITS[:6]) + h = [v.product([phases[i] for i in c]) for c in v.cycles(6, 2)] + self.assertEqual(h, [(v.F(-3, 5), v.F(-4, 5)), (v.F(-5, 13), v.F(12, 13))]) + self.assertEqual(v.product(phases), (v.F(63, 65), v.F(-16, 65))) + with self.assertRaisesRegex(ValueError, 'inverse identity'): + v.check_inverse(v.operator(phases, 2, v.ROOTS[0]), + v.resolvent(phases, 2, v.ROOTS[0], 'global_holonomy')) + + def test_one_singular_cycle_is_rejected(self): + with self.assertRaisesRegex(ValueError, 'singular cycle closure'): + v.resolvent([v.ONE, v.UNITS[1], v.ONE, v.UNITS[1]], 2, v.ONE) + + def test_dual_phase_is_shifted_not_conjugated(self): + phases = list(v.UNITS[:6]) + a = v.operator(phases, 2, v.ROOTS[0]) + self.assertEqual(v.operator(v.dual_phases(phases, 2), -2, v.ROOTS[0]), v.transpose(a)) + + def test_corrupted_source_manifest_fails_before_execution(self): + source = json.loads((P / 'SOURCE.json').read_text()) + source['files']['weighted.py'] = '0' * 64 + with tempfile.TemporaryDirectory() as tmp: + with self.assertRaisesRegex(ValueError, 'source hash: weighted.py'): + v.load_source(P.parents[1], source, Path(tmp)) + + def test_missing_source_commit_fails_closed(self): + source = json.loads((P / 'SOURCE.json').read_text()) + source['commit'] = '0' * 40 + with tempfile.TemporaryDirectory() as tmp: + with self.assertRaisesRegex(ValueError, 'Missing pinned PR628 git object'): + v.load_source(P.parents[1], source, Path(tmp)) + + +if __name__ == '__main__': + unittest.main(verbosity=2) diff --git a/research/cyclic-stride-independent/verify.py b/research/cyclic-stride-independent/verify.py new file mode 100644 index 0000000000..bbd820daee --- /dev/null +++ b/research/cyclic-stride-independent/verify.py @@ -0,0 +1,414 @@ +#!/usr/bin/env python3 +"""Independent finite-geometric resolvent audit of PR628's weighted factor. + +Apache-2.0. Prepared for Ryan Pinto / Ambassators with substantial OpenAI +assistance. The oracle does not call the predecessor's arithmetic, recurrence, +Gaussian solve, matrix expansion, kernel preparation, or factor certificates. +""" +from __future__ import annotations + +import argparse +import ast +from fractions import Fraction as F +import hashlib +import importlib.util +import json +from math import gcd +from pathlib import Path +import random +import subprocess +import sys +import tempfile +import types + +Z = tuple[F, F] +Matrix = list[list[Z]] +ZERO: Z = (F(0), F(0)) +ONE: Z = (F(1), F(0)) +HERE = Path(__file__).resolve().parent +LENGTHS = tuple(range(1, 13)) + (16, 18, 21) +ROOTS: tuple[Z, ...] = ((F(1, 4), F(1, 8)), (F(2), F(-1, 4))) +UNITS: tuple[Z, ...] = ( + ONE, (F(0), F(1)), (F(3, 5), F(4, 5)), (F(-5, 13), F(12, 13)), + (F(-1), F(0)), (F(0), F(-1)), (F(5, 13), F(-12, 13)), +) +SEED = 79 + + +def require(ok: bool, message: str) -> None: + if not ok: + raise ValueError(message) + + +def plus(a: Z, b: Z) -> Z: + return a[0] + b[0], a[1] + b[1] + + +def minus(a: Z, b: Z) -> Z: + return a[0] - b[0], a[1] - b[1] + + +def times(a: Z, b: Z) -> Z: + return a[0]*b[0] - a[1]*b[1], a[0]*b[1] + a[1]*b[0] + + +def quotient(a: Z, b: Z) -> Z: + norm = b[0]**2 + b[1]**2 + require(norm != 0, 'singular cycle closure') + return ((a[0]*b[0] + a[1]*b[1])/norm, + (a[1]*b[0] - a[0]*b[1])/norm) + + +def power(a: Z, n: int) -> Z: + require(type(n) is int and n >= 0, 'nonnegative integer exponent') + out = ONE + while n: + if n & 1: + out = times(out, a) + a = times(a, a) + n >>= 1 + return out + + +def norm2(a: Z) -> F: + return a[0]**2 + a[1]**2 + + +def product(values: list[Z]) -> Z: + out = ONE + for value in values: + out = times(out, value) + return out + + +def pair_text(a: Z) -> list[str]: + return [str(a[0]), str(a[1])] + + +def matrix_digest(a: Matrix) -> str: + raw = json.dumps([[pair_text(z) for z in row] for row in a], + separators=(',', ':')).encode() + return hashlib.sha256(raw).hexdigest() + + +def phase_check(phases: list[Z], stride: int) -> None: + require(bool(phases), 'nonempty phase array') + require(type(stride) is int, 'integer stride') + require(all(len(z) == 2 and all(isinstance(v, F) for v in z) + and norm2(z) == 1 for z in phases), 'exact rational unit phases') + + +def cycles(length: int, stride: int) -> list[list[int]]: + """Permutation orbits, with +stride order; supports zero/negative stride.""" + require(type(length) is int and length > 0, 'positive length') + require(type(stride) is int, 'integer stride') + unused = set(range(length)) + result = [] + while unused: + start = min(unused) + orbit, i = [], start + while i in unused: + unused.remove(i) + orbit.append(i) + i = (i + stride) % length + require(i == start, 'cycle closes at its start') + result.append(orbit) + require(len(result) == gcd(length, stride), 'gcd cycle census') + require(all(len(c) == length // gcd(length, stride) for c in result), + 'cycle length census') + return result + + +def resolvent(phases: list[Z], stride: int, rho: Z, + mutation: str | None = None) -> Matrix: + """Sum rho^(m-1-j) W^j / (h_C-rho^m), independently of scan order.""" + phase_check(phases, stride) + n = len(phases) + out = [[ZERO for _ in range(n)] for _ in range(n)] + for orbit in cycles(n, stride): + m = len(orbit) + holonomy = product([phases[i] for i in orbit]) + if mutation == 'global_holonomy': + holonomy = product(phases) + exponent = n if mutation == 'global_length' else m + denominator = minus(holonomy, power(rho, exponent)) + if mutation == 'omit_closure': + denominator = ONE + coefficients = [quotient(power(rho, m-1-j), denominator) + for j in range(m)] + for i in orbit: + weight, column = ONE, i + for coefficient in coefficients: + out[i][column] = plus(out[i][column], times(coefficient, weight)) + weight = times(weight, phases[column]) + column = (column - stride) % n + return out + + +def operator(phases: list[Z], stride: int, rho: Z) -> Matrix: + """Construct W-rho I directly, not from the oracle's cycle decomposition.""" + n = len(phases) + a = [[ZERO for _ in range(n)] for _ in range(n)] + for i, tau in enumerate(phases): + a[i][i] = minus(ZERO, rho) + j = (i - stride) % n + a[i][j] = plus(a[i][j], tau) # Addition matters when stride == 0. + return a + + +def transpose(a: Matrix) -> Matrix: + return [list(row) for row in zip(*a)] + + +def matmul(a: Matrix, b: Matrix) -> Matrix: + """Generic exact matrix product; skipping zero terms changes no coverage.""" + n = len(a) + out = [[ZERO for _ in range(n)] for _ in range(n)] + for i, row in enumerate(a): + for k, value in enumerate(row): + if value != ZERO: + for j, other in enumerate(b[k]): + if other != ZERO: + out[i][j] = plus(out[i][j], times(value, other)) + return out + + +def matvec(a: Matrix, x: list[Z]) -> list[Z]: + out = [] + for row in a: + value = ZERO + for entry, component in zip(row, x): + value = plus(value, times(entry, component)) + out.append(value) + return out + + +def check_inverse(a: Matrix, inv: Matrix) -> None: + identity = [[ONE if i == j else ZERO for j in range(len(a))] + for i in range(len(a))] + require(matmul(a, inv) == identity, 'left inverse identity') + require(matmul(inv, a) == identity, 'right inverse identity') + + +def dual_phases(phases: list[Z], stride: int) -> list[Z]: + return [phases[(i + stride) % len(phases)] for i in range(len(phases))] + + +def rounded_adapter(module, phases: list[Z], stride: int, rho: Z, + x: list[Z], bits: int, direction: int, + wrong_phase: bool = False) -> list[Z]: + """Gather / call exact pinned predecessor / scatter, not a paid tape schedule.""" + phase_check(phases, stride) + require(len(x) == len(phases), 'RHS length') + require(direction in (-1, 1), 'neighbor direction') + require(type(bits) is int and bits >= 3, 'closure precision') + inside = norm2(rho) < 1 + b = rho if inside else quotient(ONE, rho) + require(norm2(b) <= F(1, 4), 'factor margin beta=1/2') + # radix=1 suppresses initial scalar scaling to isolate a single factor; + # this is NOT a certificate of a radix-1 prime-power polynomial. + state = dict(radix=1, factors=[(inside, b)], beta=F(1, 2), bits=bits) + result = [ZERO for _ in x] + for orbit in cycles(len(x), stride): + order = orbit if direction == 1 else orbit[:1] + orbit[:0:-1] + local_x = [x[i] for i in order] + local_phases = [phases[i] for i in order] + values = module.apply(local_x, state, local_phases, direction, + wrong_phase=wrong_phase) + for i, value in zip(order, values): + result[i] = value + return result + + +def error_ratio_squared(y: list[Z], exact: list[Z], x: list[Z], bits: int) -> F: + # WEIGHTED-PROOF's single-factor bound, with B an exact modulus upper bound. + B = max(abs(z[0]) + abs(z[1]) for z in x) + bound = 7 * (B + 1) * F(1, 1 << bits) / F(1, 2)**3 + return max(norm2(minus(a, b)) for a, b in zip(y, exact)) / bound**2 + + +def hash_check(raw: bytes, expected: str, name: str) -> None: + require(hashlib.sha256(raw).hexdigest() == expected, 'source hash: ' + name) + + +def load_source(repo: Path, source: dict, directory: Path): + for name, expected in source['files'].items(): + reference = source['commit'] + ':' + source['directory'] + '/' + name + try: + raw = subprocess.check_output(['git', '-C', str(repo), 'show', reference], + stderr=subprocess.PIPE) + except subprocess.CalledProcessError as exc: + raise ValueError('Missing pinned PR628 git object; run the README fetch command') from exc + hash_check(raw, expected, name) + (directory / name).write_bytes(raw) + # Execute the pinned arithmetic module. Only scan/apply definitions are + # selected from weighted.py; their ASTs are not rewritten. This omits the + # unrelated kernel-certification import (and its Python 3.11 requirement). + spec = importlib.util.spec_from_file_location('pinned_scan_s79', directory / 'scan.py') + require(spec is not None and spec.loader is not None, 'module loader') + arithmetic = importlib.util.module_from_spec(spec) + spec.loader.exec_module(arithmetic) + tree = ast.parse((directory / 'weighted.py').read_text()) + functions = [node for node in tree.body + if isinstance(node, ast.FunctionDef) and node.name in ('scan', 'apply')] + require([node.name for node in functions] == ['scan', 'apply'], 'exact source function slice') + module = types.ModuleType('pinned_weighted_s79') + module.c = arithmetic + module.F = F + exec(compile(ast.Module(body=functions, type_ignores=[]), str(directory / 'weighted.py'), 'exec'), + module.__dict__) + return module + + +def controls(module) -> list[dict]: + # Deliberately asymmetric phases: two different holonomies for L=6,s=2. + phases = list(UNITS[:6]) + stride, rho = 2, ROOTS[0] + a = operator(phases, stride, rho) + correct = resolvent(phases, stride, rho) + results = [] + + def reject(name, operation): + try: + operation() + except ValueError as exc: + results.append(dict(name=name, rejected=str(exc))) + else: + raise ValueError('Negative control accepted: ' + name) + + for name in ('global_holonomy', 'global_length', 'omit_closure'): + reject(name, lambda name=name: check_inverse(a, resolvent(phases, stride, rho, name))) + reject('reverse_stride_without_phase_shift', + lambda: check_inverse(transpose(a), resolvent(phases, -stride, rho))) + wrong_dual = [(z[0], -z[1]) for z in dual_phases(phases, stride)] + reject('conjugation_in_bilinear_transpose', + lambda: check_inverse(transpose(a), resolvent(wrong_dual, -stride, (rho[0], -rho[1])))) + missing = [row[:] for row in correct] + for i in cycles(6, stride)[1]: + missing[i] = [ZERO] * 6 + reject('missing_second_cycle', lambda: check_inverse(a, missing)) + shifted = correct[1:] + correct[:1] + reject('incorrect_scatter', lambda: check_inverse(a, shifted)) + reject('singular_unit_root', lambda: resolvent([ONE, ONE], 1, ONE)) + reject('nonunit_phase', lambda: resolvent([ONE, (F(1), F(1))], 1, rho)) + reject('empty_array', lambda: resolvent([], 1, rho)) + reject('noninteger_stride', lambda: resolvent(phases, F(1, 2), rho)) + reject('source_hash_mutation', lambda: hash_check(b'bad', hashlib.sha256(b'good').hexdigest(), 'control')) + if module is not None: + x = [ONE, ZERO, (F(1, 2), F(1, 4)), ZERO, ONE, (F(-1, 3), F(1, 5))] + exact = matvec(correct, x) + wrong = rounded_adapter(module, phases, stride, rho, x, 40, 1, True) + reject('pinned_wrong_inner_phase_index', + lambda: require(error_ratio_squared(wrong, exact, x, 40) <= 1, 'factor error bound')) + reject('RHS_length', lambda: rounded_adapter(module, phases, stride, rho, [], 40, 1)) + reject('underprecision', lambda: rounded_adapter(module, phases, stride, rho, x, 2, 1)) + reject('unseparated_root', lambda: rounded_adapter(module, phases, stride, (F(3, 4), F(0)), x, 40, 1)) + return results + + +def run(module, source: dict | None) -> dict: + rng = random.Random(SEED) + receipt = dict(schema=1, status='PASS_STRIDE_RESOLVENT_AND_DUAL', seed=SEED, + source_commit=source['commit'] if source else None, + lengths=list(LENGTHS), stride_residues='all, represented also by s-L', + roots=[pair_text(r) for r in ROOTS], precisions=[12, 40], cases=[]) + exact_entries = rounded_cases = rounded_coordinates = 0 + signed_checks = zero_cases = multicycle_cases = 0 + max_ratio = F(0) + max_ratio_case = None + transcript = hashlib.sha256() + for n in LENGTHS: + for stride in range(n): + phases = [UNITS[rng.randrange(len(UNITS))] for _ in range(n)] + # Alternating deterministic inputs include denominators not dividing 2^bits. + dense_x = [(F(rng.randrange(-7, 8), 17), F(rng.randrange(-8, 9), 19)) + for _ in range(n)] + basis = [ONE if i == (SEED + stride) % n else ZERO for i in range(n)] + orbit_data = cycles(n, stride) + for ri, rho in enumerate(ROOTS): + a = operator(phases, stride, rho) + inv = resolvent(phases, stride, rho) + check_inverse(a, inv) + dp = dual_phases(phases, stride) + inv_t = resolvent(dp, -stride, rho) + require(inv_t == transpose(inv), 'inverse transpose phase/index identity') + check_inverse(transpose(a), inv_t) + require(resolvent(phases, stride-n, rho) == inv, 'signed-stride representative') + signed_checks += 1 + # Four products and one matrix equality are checked entry-by-entry. + exact_entries += 5*n*n + zero_cases += int(stride == 0) + multicycle_cases += int(len(orbit_data) > 1) + case = dict(length=n, stride=stride, root=ri, + phases=[pair_text(z) for z in phases], + cycle_count=len(orbit_data), cycle_length=len(orbit_data[0]), + holonomies=[pair_text(product([phases[i] for i in c])) for c in orbit_data], + inverse_sha256=matrix_digest(inv), dual_sha256=matrix_digest(inv_t)) + receipt['cases'].append(case) + if module is not None: + for dual, pp, ss, oracle in ((False, phases, stride, inv), (True, dp, -stride, inv_t)): + for direction in (-1, 1): + for bits in (12, 40): + for xi, x in enumerate((dense_x, basis)): + exact = matvec(oracle, x) + # Inputs to the adapter are never mutated by gathering. + saved = (pp[:], x[:]) + y = rounded_adapter(module, pp, ss, rho, x, bits, direction) + require((pp, x) == saved, 'read-only input preservation') + ratio = error_ratio_squared(y, exact, x, bits) + require(ratio <= 1, 'rounded factor error bound') + rounded_cases += 1 + rounded_coordinates += n + tag = [n, stride, ri, dual, direction, bits, xi] + transcript.update(json.dumps([tag, [pair_text(z) for z in y]], separators=(',', ':')).encode()) + if ratio > max_ratio: + max_ratio, max_ratio_case = ratio, tag + # rho=0 is exact W^-1; isolate this degenerate polynomial case explicitly. + edge_phases = list(UNITS[:6]) + zero_root = resolvent(edge_phases, 2, ZERO) + check_inverse(operator(edge_phases, 2, ZERO), zero_root) + receipt.update(exact_matrix_entries=exact_entries, signed_stride_checks=signed_checks, + zero_stride_cases=zero_cases, multicycle_cases=multicycle_cases, + zero_root_edge_check=True, rounded_cases=rounded_cases, + rounded_coordinates=rounded_coordinates, + rounded_transcript_sha256=transcript.hexdigest(), + maximum_squared_error_to_budget=str(max_ratio), + maximum_ratio_case=max_ratio_case, controls=controls(module)) + return receipt + + +def main() -> None: + ap = argparse.ArgumentParser(description=__doc__) + ap.add_argument('--repo', type=Path, default=HERE.parents[1]) + ap.add_argument('--out', type=Path) + ap.add_argument('--check', type=Path) + ap.add_argument('--oracle-only', action='store_true', help='development mode; NOT the full audit') + args = ap.parse_args() + require(sys.version_info >= (3, 9), 'Python 3.9+ required') + if args.oracle_only: + result = run(None, None) + result['status'] = 'PASS_ORACLE_ONLY_NOT_PREDECESSOR_REPLAY' + else: + source = json.loads((HERE / 'SOURCE.json').read_text()) + with tempfile.TemporaryDirectory(prefix='stride-independent-') as tmp: + module = load_source(args.repo, source, Path(tmp)) + result = run(module, source) + raw = json.dumps(result, indent=2, sort_keys=True) + '\n' + if args.check: + require(json.loads(args.check.read_text()) == result, 'complete receipt mismatch') + if args.out: + args.out.write_text(raw) + print(result['status']) + print(json.dumps(dict(exact_cases=len(result['cases']), + all_entry_checks=result['exact_matrix_entries'], + rounded_cases=result['rounded_cases'], + rounded_coordinates=result['rounded_coordinates'], + rejected_controls=len(result['controls'])), sort_keys=True)) + + +if __name__ == '__main__': + try: + main() + except (ValueError, OSError) as error: + print('FAIL: ' + str(error), file=sys.stderr) + sys.exit(1)