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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/paired_column_contraction_850_128_6_88f0ad3b3948.json","label":"paired_column_contraction_850_128_6_88f0ad3b3948","N":166,"d":6,"d_is_exact":true,"origin":"Wills weighted Reed\u2013Muller parent (weights 1^7,2^3, cutoff 4), with searched graph punctures, then 18 disjoint logical-pair checks; 5 paired-column contractions","provenance":"gamma frontier release record paired_column_contraction_850_128_6_88f0ad3b3948 (source catalogue id paired_column_contraction_850_128_6_88f0ad3b3948); construction: Wills weighted Reed\u2013Muller parent (weights 1^7,2^3, cutoff 4), with searched graph punctures, then 18 disjoint logical-pair checks; 5 paired-column contractions; matrix 88f0ad3b3948451f...; the release states d=6 (exact), gamma=1.0566184346051741 (exact)","notes":"matrix gamma_frontier_release/matrices/88f0ad3b3948451f10a735911a7c13c4bbb39b9c6493b4803e4c48c69f029aed.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"}]}