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search: pure-T puncture caps"],"discovery":"AI search","strongest_claim":"cap witnesses, NOT records. Each ATTAINS a proved maximum puncture count for its ambient size at d=6, making that bound exact rather than an upper bound: m=8 gives [[248,8,6]] and m=9 gives [[496,16,6]], both with n/t = 31 exactly, hence gamma = log(31)/log(6) = 1.9165 independent of m. Filed as evidence that these cells are closed, not as frontier points -- the d=6 pure-T bar is gamma 1.063146.","sources":[{"regime":"AI search: pure-T puncture caps","file":"magic-states-AI/campaigns/2026-09-15_m8_m9_d6/found/n248_T8_d6_CAP_WITNESS_not_a_record.json","label":"n248_T8_d6_CAP_WITNESS_not_a_record","N":53,"d":6,"d_is_exact":true,"origin":null,"provenance":"m = 8 maximal parent class 2 (|T| = 16 intersecting triples, dim 53). Campaign 2026-09-15_m8_m9_d6 proves t <= 8 on that parent at d = 6 (and t <= 16 over ALL 15 maximal m = 8 parents, closing the [[223,33,6]] cell); this ATTAINS the cap, so the bound is tight. Pure disjoint T^8, V_ex = 8, rho = n/V_ex = 31.000, gamma = log(248/8)/log 6 = 1.916545. NOT a record and not near one: the external d=6 bar is gamma 1.086033, and this is dominated many times over by direct sums of small catalogued factories (CLAUDE.md rule 6). Filed as a tightness witness for a closure, not as an improvement."}]},"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"}]}