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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_160_30_3_e7719999144e.json","label":"paired_column_contraction_160_30_3_e7719999144e","N":40,"d":3,"d_is_exact":true,"origin":"Wills-derived four-block Schur-orthogonal restricted-light parent (|S|=48), with searched graph punctures; 1 paired-column contraction","provenance":"gamma frontier release record paired_column_contraction_160_30_3_e7719999144e (source catalogue id paired_column_contraction_160_30_3_e7719999144e); construction: Wills-derived four-block Schur-orthogonal restricted-light parent (|S|=48), with searched graph punctures; 1 paired-column contraction; matrix e7719999144ec242...; the release states d=3 (exact), gamma=1.5237190142858297 (exact)","notes":"matrix gamma_frontier_release/matrices/e7719999144ec242fa41ec56ba41e813857c47bd5f5c504b1bdb84d9c5ebe82e.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"}]}