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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_312_70_3_d96036de1dc4.json","label":"paired_column_contraction_312_70_3_d96036de1dc4","N":83,"d":3,"d_is_exact":true,"origin":"Existing triorthogonal code with physical paired-column contraction","provenance":"gamma frontier release record paired_column_contraction_312_70_3_d96036de1dc4 (source catalogue id paired_column_contraction_312_70_3_d96036de1dc4); construction: Existing triorthogonal code with physical paired-column contraction; matrix d96036de1dc4d4cc...; the release states d=3 (exact), gamma=1.3603597567363581 (exact)","notes":"matrix gamma_frontier_release/matrices/d96036de1dc4d4cc62dad5d3eaae70da727fdf4f96d50a7e9dd2b770a530d6f3.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"}]}