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_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_162_28_3_660e895a67eb.json","label":"paired_column_contraction_162_28_3_660e895a67eb","N":40,"d":3,"d_is_exact":true,"origin":"Existing triorthogonal code with physical paired-column contraction","provenance":"gamma frontier release record paired_column_contraction_162_28_3_660e895a67eb (source catalogue id paired_column_contraction_162_28_3_660e895a67eb); construction: Existing triorthogonal code with physical paired-column contraction; matrix 660e895a67ebfa48...; the release states d=3 (exact), gamma=1.5978264972671201 (exact); the release matrix has 162 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 160 injections for the same gate and distance","notes":"matrix gamma_frontier_release/matrices/660e895a67ebfa48df361cbb72f17e3b5f29381d6fe99fda59aa271e27d101fa.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"}]}