Research audit: binary cover order and exact finite invoice guards

[theon199]

The selected #626 finite invoice prices routing and physical rows using the binary bilinear dot-product isometry group in dimension 73. This independent audit confirms its exact order and reproduces all nine finite invoice guards, with controls that distinguish the group definition from permissive upper-bound checks.

Status: research audit / independent finite evidence; no new κ.

• A written characteristic-vector/symplectic-basis argument is checked against exhaustive ordered orthonormal-basis enumeration in dimensions 1–7 (1,475,337 complete bases). A separate all-matrix enumeration through dimension 4 checks the enumerator.
• Exact integer arithmetic reproduces the 2,628-bit group order, 2,641-bit physical stock, and row coefficient 16,467 < 20,161. No production verifier or constructor is imported.
• Five wrong-order controls are explicitly rejected. Four smaller factors still pass every upper-bound guard; replacing the group with GL(73,2) fails the row guard (21,867 > 20,161) while the other eight pass. With other invoice quantities fixed, multiplying the cover by 2^1846 still passes; 2^1847 first fails at strict row equality. These are modified-model controls and a scoped sensitivity result, not defects alleged against the intact construction or a paid alternative cover.

Only research/orthogonal-cover-invoice-audit/ is added: proof, standalone verifier, exact certificate, tests, source pins, local sprint claim and validation receipt. The selected frontier and upstream/ are unchanged.

python3 -I -B research/orthogonal-cover-invoice-audit/verify.py
python3 -I -B research/orthogonal-cover-invoice-audit/test_verify.py

Expected: PASS_ORTHOGONAL_COVER_INVOICE_AUDIT dimensions=1..7 guards=9 controls=5 kappa=unchanged, followed by eight passing tests. Validation passed on macOS arm64 / Python 3.14.5, including -I -B -O, a minimal relocated checkout in a path with spaces, source/certificate corruption, two implementation mutations, strict row-boundary checks, make selected-record-check and staged whitespace checks.

Base: 66849e1. OS assignment seed 65, adversarial-audit track. Pins bind the selected record, source inventory, #626 assembly, invoice and owner receipts, and reviewed heads #626 660de893d27bb7abd1d5b01b1640207528a5c851, #623, #622 and #543. No pinned coordination issue exists; the claim is local. The final overlap pass covered 586 open PRs through #767. #717 explores distinct moment/invoice sensitivity and program permutations and is credited; no pending contribution supplies inputs here.

All supplier/compiler, owner geometry, common-label/mutable-basis, whole-call hosting, normalized-residual, precision/tape/exact-recovery, bit H1–H5 and analytic assumptions remain inherited. The full supplier replay, repository suite, 47 assembly inequalities, Linux CI and Lean were not rerun. Finite enumeration is not a formal proof of the full multiplication theorem.

Credits include Jeremy Kothe (#622/#623), Chafik Boukhalfa (#626), icekylinx, DreamingOfClouds, Rohan Arun (#559), eumemic (#543), the maintainer review and retained predecessors. Prepared for Sricharan Vagvala (@theon199) with substantial OpenAI Codex assistance; Apache-2.0. No independent human peer review is claimed.

[Mister-Meeseeks]

100-PR batch review at 340bedf9f0e65bb0e00ee6edb55d8fed11fcb7c7.

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

Reviewed scope: Orthogonal binary-group census and source invoice controls; characteristic-vector/symplectic classification, no new supplier.

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.