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Research: sharp floors for the 216 diagonal S3 targets - #4351
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Mister-Meeseeks merged 1 commit intoOct 21, 2026
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One hundred twenty-five of the 216 targets meet the representation rank with a coordinate word, and eight of them have sharp floor 6.
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Result
Eight diagonal S3 targets, those whose three labels all lie in the two length-two elements, have representation rank 6 and a six-call coordinate word. One hundred twenty-five of the 216 diagonal targets match in the same way.
The only label whose generator length exceeds
rank(rho(g)+I)is the transposition(1 3), with length 3 and rank 1. The other 91 targets each contain it, so this comparison does not prove their generator bills sharp. The published four-call targetdiag(s, t, st)is rechecked and stays one of the 36 sharp floors of 4. The new maximum is 6.No new kappa. Claim: #4350.
Scope
Chooser seed
69b1df962b206506adae7d9b1954dd8fdrewr437-carrier-integrationfirst. That integration is already open in #4176 and #4183, so it was not repeated. This package answers the screening question in open #3893, same paid alphabet, every diagonal target. Package:research/s3-diagonal-rank-screen. Base12fa8c5c844be21bfefb38a19503fbd867a11244. Selected record SHA-256bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129is unchanged.Evidence
Expected marker:
PASS_S3_DIAGONAL_RANK_SCREEN matched=125 floor6=8 gap=91. Local Python 3.12 replay passed. The selected baseline was not run in this partial checkout.Limits
No shared-word search for
(1 3), no native bill, and no transfer to the rational-frame three-register theorem. Substantial AI assistance; no independent human review claimed. Apache-2.0.Open next question
Can a shared word shorter than length 3 write
(1 3)once a scratch register is specified? A one-register word cannot.