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3],[154,3],[157,3],[161,3],[164,3],[167,3],[171,3],[175,3],[183,3],[184,3],[185,3],[186,3],[190,3],[191,3],[193,3],[194,3],[196,3],[198,3],[202,3]]},"metrics":{"gamma":1.4649735207179269,"gamma_t":null,"gamma_rho":1.4649735207179269,"gamma_claim":1.4649735207179269,"gamma_t_claim":null,"gamma_rho_claim":1.4649735207179269,"v_ex":41,"rate":0.2,"t_count":null,"poly_degree":null,"effective_width":41},"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_207_41_3_894ef31fdffc.json","label":"paired_column_contraction_207_41_3_894ef31fdffc","N":52,"d":3,"d_is_exact":true,"origin":"Existing triorthogonal code with physical paired-column contraction","provenance":"gamma frontier release record paired_column_contraction_207_41_3_894ef31fdffc (source catalogue id paired_column_contraction_207_41_3_894ef31fdffc); construction: Existing triorthogonal code with physical paired-column contraction; matrix 894ef31fdffc8198...; the release states d=3 (exact), gamma=1.4738108641803156 (exact); the release matrix has 207 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 205 injections for the same gate and distance","notes":"matrix gamma_frontier_release/matrices/894ef31fdffc81981011bd75a566659765961a734d2bcf48b1b8871eec64f116.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"}]}