[davidgovea]

PR468's nine-call lower bound depends on using F101 as an exact representation of rational relation arithmetic. This standalone audit tests that obligation directly against an independent integer-determinant oracle, including the distinction between rank preservation and primitive-row parity. No new κ or construction is claimed.

The source-pinned package adds a written argument, a reproducible exact certificate, and direct probes of the existing modular kernels. It checks 319,254 small cube matrices, 6,266,880 subset pairs and 49,152 target-span decisions. The wider fixtures are a documented deterministic sample, not an exhaustive search of width-eight matrices. Four deliberately damaged implementations must fail specific mathematical comparisons. Concrete small-prime and residue-parity examples explain the failure modes.

Reproduce from the repository root:

python3 -B -S research/three-register-modular-audit/verify.py

Expected: PASS_PR468_MODULAR_ARITHMETIC_AUDIT.

Base: 66849e1475c930fd7732b1a0067ffee7e1e95f60. PR468 dependency: 07a78bf335b0b5039a1fecd7cd74a0fe1d1605ea; exact source hashes are included. Assignment seed: 66, adversarial mathematical audit.

Validation passed with standard and optimized Python, C++ address/undefined-behavior sanitizers, and an isolated-directory replay. The selected-record check and PR468's small formal controls also pass. The complete scalar-order replay and expensive repository-wide suites were not rerun; only the new audit directory changes. This does not certify all symbolic reductions, search completeness, or integer multiplication.

Credit to Ali Romman's PR468 and its predecessors eumemic's PR288 and huxint's PR203. Prepared by David Govea with substantial OpenAI Codex assistance; Apache-2.0. The refreshed PR queue contained no overlapping modular-kernel audit; PR680 treats a different complex Clifford model. No pinned sprint issue existed, so coordination was recorded locally.

[Mister-Meeseeks]

100-PR batch review at dee275599160965d77324c9ab635bc00ad5f702d.

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

Reviewed scope: Independent modular/rational three-register rank census; sampled wider controls are distinguished from exhaustive small-domain coverage.

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.