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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_160_28_3_87c0fa5a4aaa.json","label":"paired_column_contraction_160_28_3_87c0fa5a4aaa","N":39,"d":3,"d_is_exact":true,"origin":"Existing triorthogonal code with physical paired-column contraction","provenance":"gamma frontier release record paired_column_contraction_160_28_3_87c0fa5a4aaa (source catalogue id paired_column_contraction_160_28_3_87c0fa5a4aaa); construction: Existing triorthogonal code with physical paired-column contraction; matrix 87c0fa5a4aaafb7c...; the release states d=3 (exact), gamma=1.586519032270877 (exact); the release matrix has 160 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 158 injections for the same gate and distance","notes":"matrix gamma_frontier_release/matrices/87c0fa5a4aaafb7c5e9bb4916a8840ae709c85a13374a9fec69eb336923a9f14.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"}]}