[JoyboyBrian]

PR6012 leaves a two-write spectator lemma open in its residual five-coordinate, ten-call two-cycle problem. This package derives the exact row-stabilizer projection while retaining the middle labels selected by e_j^T b=e_l^T and their required relabelling g b h.

For an endpoint [c]I in the two-role binary formal model, a coordinate written exactly twice has equal rank-one scalar projectors when c restores that row, and complementary projectors when c moves it. The moved-row result uses the projections of both the word and its inverse; the forward equation alone admits additional pairs. In PR6012's residual (6,4) case, these restrictions apply to both writer and reader pairs.

A standard five-call commutator gives an exact identity with a spectator written and read twice. It disproves an unrestricted three-write spectator rule; inserting it before the known twelve-call endpoint supplies a seventeen-call positive control. It is not a ten-call counterexample. The full length-ten and length-eleven exclusions remain open.

Validation passes on exact head 188cee674895aa8c1e63aafa91003e34c237e420: normal and optimized registered checks; 3,600 formal projection contexts; all 576 augmented matrix cases; six commutator identities; a separate complete-permutation group-label engine checking 288 return filters, 72 outer contexts and six seventeen-call endpoints; source pins/history and committed bytes; official export integrity; and read-only Git-free empty-PATH replays with source mutation rejection. A separate read-only agent reviewed the algebra and independently checked the matrix and group fixtures. This is not independent human or proof-kernel acceptance.

Reproduce with python3.12 -B scripts/research_package.py --package research/two-write-spectator-projection.

Credit Nick Petalas/#6012 for the projection/reduction question, Mihir Srivastava/#4939 for the formal model, James Reed/jwr404 #5005/#5379 for the cited small-dimension results, and JoyboyBrian/#4974 for the earlier single-cycle reduction. The commutator is standard. Prepared by JoyboyBrian with substantial OpenAI Codex assistance. Advance claim and canonical discussion.

No native supplier, tariff, selected-frontier change or new kappa is claimed. Hosted CI has not yet completed. The canonical base currently fails two current-status navigation tests before scientific replay; existing PR #6050 repairs those documentation mismatches. Local validation above is separate from hosted CI.

[JoyboyBrian]

CI follow-up for 188cee674895aa8c1e63aafa91003e34c237e420.

The plan failure reproduces on clean canonical main 721c03822c421b7f7fcbb2598993b947c4d88419: the two current-status navigation tests fail before this PR’s scientific replay. Existing PR #6050 (41ac3a47b91b4184e6c54af417bf576bfb429926) fixes both documentation mismatches; its exact two-file change passes all six tests locally, normally and with -O. Awaiting the shared upstream repair and a fresh CI run; this is not a successful scientific-replay claim.