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search (gamma frontier): from Wills parent codes"],"discovery":"AI search","strongest_claim":"built from one of Wills's parent codes (weighted Reed-Muller, restricted-light or one-heavy) by searched punctures, paired-column contractions or logical-pair checks, in the pure-T distillation-exponent release (gamma = log(n/k)/log d, n < 1000); a verified witness, not a maximum -- only the release's own frontier points are the lowest gamma it knows","sources":[{"regime":"AI search (gamma frontier): from Wills parent codes","file":"gamma_frontier_release/protocols/simultaneous_physical_contraction_logical_repair_1715_287_6.json","label":"simultaneous_physical_contraction_logical_repair_1715_287_6","N":329,"d":3,"d_is_exact":false,"origin":"Wills weighted Reed\u2013Muller parent (weights 1^9,2^2, cutoff 4), with searched graph punctures, then 8 disjoint logical-pair checks; delete 9 physical pairs under simultaneous equality restrictions, then add 6 logical-pair checks","provenance":"gamma frontier release record simultaneous_physical_contraction_logical_repair_1715_287_6 (source catalogue id simultaneous_physical_contraction_logical_repair_1715_287_6); construction: Wills weighted Reed\u2013Muller parent (weights 1^9,2^2, cutoff 4), with searched graph punctures, then 8 disjoint logical-pair checks; delete 9 physical pairs under simultaneous equality restrictions, then add 6 logical-pair checks; matrix f10cd7072e5220bc...; the release states d=6 (exact), gamma=0.9977266338157595 (exact)","notes":"matrix gamma_frontier_release/matrices/f10cd7072e5220bcf849ec6e2df8da9eb3124be79f3acd73e8f0c1c0608e0ab5.matrix"}]},"references":[{"key":"jain2026symmetry","short":"Jain et al. (2026)","full":"S. P. Jain, A. Wills, and S. Singh, \"Symmetry and AI-assisted discovery of magic-state factories,\" arXiv:2610.06535 (2026).","url":"https://arxiv.org/abs/2610.06535","date":"2026-10-05"}]}