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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_409_101_3_27ab58f50806.json","label":"paired_column_contraction_409_101_3_27ab58f50806","N":114,"d":3,"d_is_exact":true,"origin":"Existing triorthogonal code with physical paired-column contraction","provenance":"gamma frontier release record paired_column_contraction_409_101_3_27ab58f50806 (source catalogue id paired_column_contraction_409_101_3_27ab58f50806); construction: Existing triorthogonal code with physical paired-column contraction; matrix 27ab58f50806c670...; the release states d=3 (exact), gamma=1.2730557027512523 (exact)","notes":"matrix gamma_frontier_release/matrices/27ab58f50806c670bd302cd7488d386ec1fb7fdb3f4fc00f033e80d3ff766cc1.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"}]}