Scoped audit: PR1417 P112 tensor rank is field-specific (no new kappa)

[1337isnot1337]

Status: scoped independent field-sensitivity audit. No new κ and no counterexample under PR #1417's stated F2 assumptions.

PR #1417's graph certificate reports that 5,824 ordered P112 edge tensors span rank 80 in an 81-dimensional matrix space. This package independently rebuilds all rows from the selected port word and distinguishes the result by field:

• rank is 80 over F2, matching the stated binary-field claim;
• rank is 81 over F1009; the package gives an explicit 81-by-81 pivot minor with determinant 548 mod 1009;
• since 1009 is prime, that minor is nonzero over the integers, so the same tensor matrix has rank 81 over Q and C.

For the identity form, port 0 has integer self-dot 3 and edge (0,1) has integer dot 2. These reduce to the required values 1 and 0 modulo 2. The pinned PR #1417 proof explicitly declares F2^9 and uses characteristic two, so the odd-characteristic result is a portability boundary, not a refutation of the theorem as written.

Pins and reproduction

• Research/source base: 410026dc5513b87db92ae98571d1d5984c69a983.
• Publication branch base after refreshing main: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc. The selected certificate and all three pinned repository inputs are byte-identical across those commits.
• Target: PR Scoped obstruction: sharp P112 endpoint dimension and complete linear-lift cost #1417 exact head c755bf393bea26d2275e1516b0560ca92de7a52e; proof and certificate snapshots and source hashes are included.

From the repository root with Python 3.12:

python3.12 scripts/research_package.py --package research/pr1417-field-sensitive-rank-seed47

Expected: PASS_REGISTERED_RESEARCH_PACKAGE research/pr1417-field-sensitive-rank-seed47 outcome=completed.

Limits and credit

This checks the finite edge-tensor ranks, their field sensitivity, and the field markers in the pinned proof. It does not audit PR #1417's dimension-18 argument, full endpoint/cost theorem, Fourier-rank invoice, controller, supplier, moments, or physical/analytic interfaces. No selected certificate or frontier value changes.

Credit Ali Romman / PR #1417 for the structural theorem, and the selected PR1094 contributors for the pinned port word. Prepared by Cinna Davis (@1337isnot1337) with substantial OpenAI Codex assistance in overlap review, exact source tracing, independent verifier design, calculation, and writing. No independent human review is claimed. New material is Apache-2.0; copied proof and certificate retain their source attribution.

[Mister-Meeseeks]

Batch review at 3695ad16e7bc4c0f6248a9e5a64fc069fa096733.

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

Reviewed scope: Independent exact rank audit distinguishes binary P112 tensor rank 80 from rational/complex rank 81 via a nonzero modular minor. The predecessor explicitly uses characteristic two, so this is a field-contract boundary, not a counterexample to its stated theorem.

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.