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,[67,3],[68,3],[69,3],[73,3],[76,3],[78,3],[80,3],[82,3],[83,3],[84,3],[85,3],[86,3],[88,3],[89,3],[90,3],[93,3],[94,3],[98,3],[103,7],[104,7],[105,3],[106,3],[108,3],[109,3],[111,3],[112,3],[118,3],[122,3],[125,3],[126,3],[127,7],[130,3],[132,3],[133,3],[134,3],[135,3],[136,3],[137,3],[138,3],[140,3],[144,3],[147,3],[149,3],[150,3],[151,3],[154,3],[155,3],[157,3],[158,3],[160,3],[161,3],[163,3],[169,3],[171,3],[172,3],[176,3],[178,3],[180,3],[181,3],[185,3],[187,3],[188,3],[192,3],[195,3],[196,3],[197,3],[200,3],[201,3],[203,3]]},"metrics":{"gamma":1.4216206022402027,"gamma_t":null,"gamma_rho":1.4216206022402027,"gamma_claim":1.4216206022402027,"gamma_t_claim":null,"gamma_rho_claim":1.4216206022402027,"v_ex":43,"rate":0.2097560975609756,"t_count":null,"poly_degree":null,"effective_width":43},"provenance":{"regimes":["AI 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/paired_column_contraction_207_43_3_51a333ca691e.json","label":"paired_column_contraction_207_43_3_51a333ca691e","N":53,"d":3,"d_is_exact":true,"origin":"Wills weighted Reed\u2013Muller parent (weights 1^6,2^2, cutoff 3), with searched graph punctures; 3 paired-column contractions","provenance":"gamma frontier release record paired_column_contraction_207_43_3_51a333ca691e (source catalogue id paired_column_contraction_207_43_3_51a333ca691e); construction: Wills weighted Reed\u2013Muller parent (weights 1^6,2^2, cutoff 3), with searched graph punctures; 3 paired-column contractions; matrix 51a333ca691e0f18...; the release states d=3 (exact), gamma=1.4304579457025914 (exact); the release matrix has 207 columns of which 2 are a repeated pair -- equal columns cancel to a diagonal Clifford and deposit nothing, so they are deleted here and this circuit is the reduced one, with 205 injections for the same gate and distance","notes":"matrix gamma_frontier_release/matrices/51a333ca691e0f18ea8241c824a97f829288f7205265fd464a186c8967af9523.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"}]}