[artuskg]

Scope

This adds a computer-assisted, exact-rational lookup result for the one-line and intersection-one two-line triple complements in the original OpenAI manuscript preserved in the repository Douglas Colkitt maintains. Its motif section credits the underlying degree-one intersection construction to Alon. A paper adjacent-exterior contraction reduces every valid ordered elimination to one of 1,936 support/gap skeletons of height at most 11. The included standard-library checker enumerates those normal forms exactly and verifies a fixed table of 20 matrix values and 17 nonzero operation coefficients. The reference has h-r pivots in h row iterations, including every valid h=100 source instance.

The note derives the correct coefficient (3*1_{j in L}-1)/6 from G=I-J/9, proves the all-retained-row contraction at complete pivot blocks, and distinguishes the paper induction from the finite certificate. It credits the upstream source form and records a bounded current-source overlap check, with no priority claim. The local Tintagel audit packet is unpublished provenance; the proof and checker needed for the scoped claim are in this PR. The patch was prepared with substantial AI assistance.

Replay

python3 -I -B research/tintagel-source-lookup/replay.py --stress

Local replay of files exported from commit b6869aecced795ae6ce1ea4a0360cab6165bc8ed passed: 1,936 skeletons, 65,416 word records, 11,584 pivots, the exact 20/17 tables and digest adf555d553a11c9f2862ddf6a7206fd03428ec657763f60f9aecfc6d4850ec7d, plus 6,090 finite compression stress cases. The checker also guards the h=5 counterexample row_b=(-4,2,2,-1,0) to an invalid stronger row-state claim; the proof uses only the column invariant. The portable patch passed git apply --check against main db0e57bc7f36b5ac0fc844ad7ce1396165ee6647. A bounded Opus review did not execute the checker and suggested that false stronger claim. A subsequent independent exact-commit review caught it. Final re-review accepted the corrected invariant, attribution and exact three-file delta; it independently replayed the exported checker, including the counterexample guard. This is a bounded content review, not a formal proof.

Boundary

The all-height claim rests on a paper induction plus finite computation; the induction is not mechanically checked. This does not execute the full h=100 physical source graph, establish its arithmetic primitive implementation or charges, link the Q>11 recursive pivot child, or provide packed/phase/native/root/global composition. It is not a Lean proof, a full provider, or a new multiplication exponent. The fixed-source-W grouping scope, S0-transformed-input premise and exceptional repair terms remain open. Publication preflight rechecked upstream main and related PR descriptions; its bounded search found no matching lookup submission.

[Mister-Meeseeks]

Thank you @artuskg. This contribution at 1ba977f5b8376456dc1b2ca117195fdb4e1c39f5 is incorporated in the reviewed family through #588, published in 9594b61.

Projector coefficient Gu/2 and rank h-r follow from V^T U=I. Adjacent-exterior deletion argument concerns column-a invariants, not false unit-row assertion; all-height induction separate from finite normal-form replay. Integrate as scoped research only, no physical provider or Lean claim.

Preserved implementation and research:

• research/tintagel-source-lookup

The family review and individual disposition record the scope, evidence and attribution. Parallel and intermediate contributions remain credited even where a later composition has a stronger bound. The published multiplication bound remains conditional on the documented compiler, realization, hosting and analytic assumptions; these finite checks are not a full Lean multiplication proof.