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ll,"gamma_rho":1.4139186879715695,"gamma_claim":1.4139186879715695,"gamma_t_claim":null,"gamma_rho_claim":1.4139186879715695,"v_ex":44,"rate":0.21153846153846154,"t_count":null,"poly_degree":null,"effective_width":44},"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_208_44_3_3700258a70b8.json","label":"paired_column_contraction_208_44_3_3700258a70b8","N":54,"d":3,"d_is_exact":true,"origin":"Wills weighted Reed\u2013Muller parent (weights 1^6,2^2, cutoff 3), with searched graph punctures; 2 paired-column contractions","provenance":"gamma frontier release record paired_column_contraction_208_44_3_3700258a70b8 (source catalogue id paired_column_contraction_208_44_3_3700258a70b8); construction: Wills weighted Reed\u2013Muller parent (weights 1^6,2^2, cutoff 3), with searched graph punctures; 2 paired-column contractions; matrix 3700258a70b884f8...; the release states d=3 (exact), gamma=1.4139186879715695 (exact)","notes":"matrix gamma_frontier_release/matrices/3700258a70b884f8cf15432bd9b092663dc7daa72cb451670610b037e40aee1b.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"}]}