Audit all selected sigma charts against the binary certificate interface

[adamgall]

Result

An independently reconstructed, exact finite application audit for all 10,002 selected1094 73-dimensional helper charts, supplying the five-array auxiliary witnesses left open by the generic Lean interfaces in #1879 and #1927. Every chart satisfies A=(I+u a^T)P, a·u=0; all 69,120 helper references across 144 calls resolve to the exact content-keyed dictionary with no missing or orphan entries.

The verifier does not import the producer or any supplier/checker implementation. It checks the certificate coefficients and independently computes inverses by augmented-row Gaussian elimination. Coverage: 53,300,658 binary coefficient entries (packed exact comparison), 10,002 elimination inverses, and 1,460,292 two-sided basis compositions. All selected transvections have a=u: 6,612 weight-four and 3,390 weight-eight updates.

The address direction is explicit: A=TP, so A^-1=P^-1T, not TP^-1. An actual selected chart separates these: key 0008043bb33954fa69e0a93740f44f5a254d1bfb23f1f7b80484527f4d6bf224, input axis0, correct inverse column2128 versus wrong-order column32.

New scope and source binding

Only research/selected-sigma-chart-binding/ is added. Inputs are the selected community-frontier1094-audit/selected-replay.tar.gz and its receipt, not the inherited historical R492 dictionary. Complete source/selection pins, original chooser JSON, witness artifact, standalone recovery/verifier, meaningful controls and open next questions are included.

This is not fresh Lean kernel/interpreter acceptance. It independently checks the exact mathematical premises and serialized witness grammar of the pinned formal interface. No Lean runtime/toolchain was available locally. Logical address cancellation is not physical executor direction/allocation, complex phases, precision/tape, full paid cost, supplier admission or a multiplication theorem. No kappa or selected-profile change.

The existing native emitter/auditor already reconstructs sigmas; it is credited, not relabeled as new work. The new contribution is the complete separately recovered formal-interface-format certificate set, selected dictionary/reference binding, independent elimination and portable semantic controls. #1831's route-to-owner certificate is adjacent and distinct.

Exercised verification

On CPython3.12.12 / Clang21.1.4 / macOS27.0.1 arm64:

uv run --python 3.12 --no-project python -B research/selected-sigma-chart-binding/recover.py --output research/selected-sigma-chart-binding/WITNESSES.json.gz
uv run --python 3.12 --no-project python -I -O -B research/selected-sigma-chart-binding/verify.py --write-receipt research/selected-sigma-chart-binding/RESULT.json
uv run --python 3.12 --no-project python -B scripts/research_package.py --package research/selected-sigma-chart-binding

The first two are initial artifact-generation commands and refuse existing outputs. Ordinary replay is the last command.

Observed: PASS_SELECTED_SIGMA_CHART_BINDING charts=10002 dimension=73 helper_roles=69120 controls=19 no_new_lean_build no_new_kappa; eight focused semantic test groups pass; PASS_REGISTERED_RESEARCH_PACKAGE ... outcome=completed. Registered verifier plus tests took14.85seconds, informational only. The tests include an exhaustive independent 3D factor oracle/all matrices, inverse checks, source drift, numeric/duplicate-key boundaries, compression invariance, coefficient indexing and port bases. No full repository suite or unseen CI success is claimed.

Provenance and credit

Base 0b1cccf86e2f5132ed286a26ef0a681a495740ea; independently sampled seed e059d89919a0078380ea43f90a32a2f6; track independent-verification; refined formal-interface-lemma card. Claim: #1929 (comment).

Credit James Chang for #1879/#1927 generic formal interfaces; Rohan Arun for #1094; Jeremy Kothe for T16 chart/emitter construction; Hao Yan and the #484/#507/#514 geometry lineage; Lean/Mathlib contributors. Prepared for Adam Gall with substantial OpenAI Codex GPT-6 Astra assistance. Apache-2.0. No independent human review claimed.

[Mister-Meeseeks]

Batch review at c7d8c9febf0fcc52d2002db657165cd206ff9cec.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Independent five-array certificates bind10002 actual73-dimensional charts and all69120 helper occurrences. Exact Gauss-Jordan inverses, source/content/ordered-reference hashes,19 controls and8 test groups pass. Supplies the finite inputs for the credited Lean interface without claiming a Lean execution, physical executor direction or supplier admission.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.