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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_427_81_4_2eb1d1c3a580.json","label":"paired_column_contraction_427_81_4_2eb1d1c3a580","N":100,"d":4,"d_is_exact":true,"origin":"Wills weighted Reed\u2013Muller parent (weights 1^8,2^1, cutoff 3), with searched graph punctures; 2 paired-column contractions","provenance":"gamma frontier release record paired_column_contraction_427_81_4_2eb1d1c3a580 (source catalogue id paired_column_contraction_427_81_4_2eb1d1c3a580); construction: Wills weighted Reed\u2013Muller parent (weights 1^8,2^1, cutoff 3), with searched graph punctures; 2 paired-column contractions; matrix 2eb1d1c3a5800d38...; the release states d=4 (exact), gamma=1.199121128367933 (exact)","notes":"matrix gamma_frontier_release/matrices/2eb1d1c3a5800d38175cd2a97685763142fac1651fa3555a944e5e2c25fd9dd5.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"}]}