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Convention: x = S_9 tensor I_13, y = I_9 tensor S_13 (cyclic shifts), qubit index = i*m + j; A = 1 + x^6y^0, B = 1 + x^2y^2 + x^5y^2 + x^6y^0; H_X = [A|B], H_Z = [B^T|A^T]. Found by an automated evolutionary/mutation search over (l, m, A, B) exponent sets targeting the unrestricted x weight-6 (or weight-8) board cells, screened by a randomized lightest-logical surrogate and promoted through increasing trial budgets.", "origin": "submission", "date": "2026-09-16", "notes": "Internal autoresearch candidate id 6423 (canonical key 842ade0cea9868db725ecc26), search lane 'w6-gap', proposal kernel 'shared-binomial-factor'. Initial NumPy lightest-logical surrogate: trials=8000, seed=196597815. Confirmed with an accelerated bit-packed random-information-set search at rung '60k' (60000 trials, seed=196597832, pair_depth=16), tightest witness on side X at weight 3. Distance also taken through an internal exact-certification pipeline (MILP, one solve per logical-basis row per side, the same method as this repository's own verify/certify.py). Result: side_status X=exact, Z=exact (solver wall time 59.6s, CPU time 58.6s, summed over all per-row MILP solves on both sides). Per CONTRIBUTING.md's confidence-tier policy, this 'exact' claim is self-declared and will display as an upper bound on the board until a maintainer independently re-runs verify/certify.py and confirms it." } }