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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_205_41_3_e9df5bc28e07.json","label":"paired_column_contraction_205_41_3_e9df5bc28e07","N":51,"d":3,"d_is_exact":true,"origin":"Wills weighted Reed\u2013Muller parent (weights 1^6,2^2, cutoff 3), with searched graph punctures; 5 paired-column contractions","provenance":"gamma frontier release record paired_column_contraction_205_41_3_e9df5bc28e07 (source catalogue id paired_column_contraction_205_41_3_e9df5bc28e07); construction: Wills weighted Reed\u2013Muller parent (weights 1^6,2^2, cutoff 3), with searched graph punctures; 5 paired-column contractions; matrix e9df5bc28e07d55b...; the release states d=3 (exact), gamma=1.4649735207179269 (exact); the release matrix has 205 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 203 injections for the same gate and distance","notes":"matrix gamma_frontier_release/matrices/e9df5bc28e07d55b578960ffd6627afe95804edd9610e41e60a862328f7532df.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"}]}