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_claim":null,"gamma_rho_claim":1.5517285850726805,"v_ex":28,"rate":0.18181818181818182,"t_count":null,"poly_degree":null,"effective_width":28},"provenance":{"regimes":["AI search (gamma frontier): contraction of an existing code"],"discovery":"AI search","strongest_claim":"a paired-column contraction of an existing triorthogonal code, 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): contraction of an existing code","file":"gamma_frontier_release/protocols/paired_column_contraction_156_28_3_6b999f3a09d8.json","label":"paired_column_contraction_156_28_3_6b999f3a09d8","N":37,"d":3,"d_is_exact":true,"origin":"Existing triorthogonal code with physical paired-column contraction","provenance":"gamma frontier release record paired_column_contraction_156_28_3_6b999f3a09d8 (source catalogue id paired_column_contraction_156_28_3_6b999f3a09d8); construction: Existing triorthogonal code with physical paired-column contraction; matrix 6b999f3a09d8922f...; the release states d=3 (exact), gamma=1.5634737703113704 (exact); the release matrix has 156 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 154 injections for the same gate and distance","notes":"matrix gamma_frontier_release/matrices/6b999f3a09d8922f0215076f84e45a2214dee5b7945b54669c5dc81151e4e81a.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"}]}