{"index_version":"2.0","counts":{"factories":2114,"parameter_sets":1846,"with_t_count":1187},"ranges":{"n":[8,262142],"k":[1,373],"N":[4,818],"d":[2,3,4,5,6,7,8,9,11,13,15,17,19,21,23,25,27,29,31]},"source":{"commit":"0493f52","date":"2026-10-30"},"dedup_key":"(n, k, d, gate up to GL(k,2)) -- circuits at different distances are always different classes; at one distance two gates are one class when an invertible change of the output basis (a CNOT frame) and diagonal Clifford corrections carry one to the other, the CNOT+S output equivalence; decided for every same-(n,k,d) pair by glcanon.gl_isomorphic. The stored circuit is one representative, shown in its S_k-canonical frame where that was proved","regimes":{"exhaustive classification n<=54 (Pareto point)":"a Pareto point of the exhaustive classification of generalised triorthogonal protocols through length 54 (classification/length54/): no protocol with n <= 54, the same CNOT+S output class and the same exact distance has n and S both no larger and one of them smaller, where S counts every matrix row -- the N of this table","exhaustive classification n<=54":"found within the exhaustive classification through length 54 but not one of its Pareto points: a Pareto point with the same output class (after removing spectator outputs) and the same exact distance strictly dominates it, which tests/test_master_catalog.py checks -- a verified witness, not an optimum","symmetry-SAT search":"found by the symmetry-slot or ansatz-free SAT search (symmetry_sat_search/); a verified witness, not a maximum","AI search":"found by an AI search campaign; a verified witness, not a maximum","AI search: punctured r=7 simplex parents":"found by the 48 < n < 128 AI campaigns, from punctured r=7 simplex parents with free-row appending; a verified witness, not a maximum","AI search: multi-agent campaign 39<=n<=127":"found by the 39 <= n <= 127 multi-actor AI campaign (three Opus 5 actors, two conferring Fable 5 reviewers, three rounds, 2026-09-01); a verified witness, not a maximum","AI search (gamma frontier): from Wills parent codes":"built from one of Wills's parent codes (weighted Reed-Muller, restricted-light or one-heavy) by searched punctures, paired-column contractions or logical-pair checks, 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","AI search (gamma frontier): contraction of an existing code":"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","AI search (gamma frontier): logical restriction of a length-54 Pareto point":"a restriction to fewer logical rows of a Pareto point of the length-54 classification, 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","AI search (gamma frontier): punctured Reed-Muller code":"a punctured Reed-Muller code found by the gamma sub-1000 AI campaign (RM(3,10) punctured at 123 points), filed with the pure-T distillation-exponent frontier (gamma = log(n/k)/log d, n < 1000); a verified witness, not a maximum","AI search: Wills downset framework":"verified witness from the 2026-09-14 wills_downset_theory campaign in magic-states-AI, which solved the arXiv:2608.24000 downset framework EXACTLY at every n <= 1000; the d=7 and d=8 rows are proved optima of that framework, not merely best-found, but the framework is one family and they are not maxima over all factories","AI search: pure-T width campaign n=255, 511":"new [[n,k,d]] classes at n=255 and n=511 (the n=511 one the first at d=3 there) -- pure disjoint T^k, verified from columns. NOT rate records: both are strictly dominated by direct sums of the catalogued [[127,23,3]] (rho 5.5217) -- 2 copies give [[254,46,3]] and 4 give [[508,92,3]], each with FEWER inputs and MORE outputs than the row here. Beating the derived baseline needs k>=47 at n=255 and k>=93 at n=511.","AI search: generalised triorthogonal search 55<=n<=64":"found by the AI-assisted public search for generalised triorthogonal protocols at lengths 55-64; a verified witness, not a maximum","AI search: pure-T puncture caps":"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.","AI search: full-simplex pure-T frames":"widest pure-T frames held at n=511. DOMINATED on rate by the derived direct-sum baseline [[508,92,3]] = 4 x [[127,23,3]], rho = 508/92 = 5.5217. These are WIDTH points, explicitly NOT rate records: beating the baseline at n=511 needs k >= 93.","AI search: graph gluing":"found by an AI search that glues catalogued small factories along a graph of paired-column contractions; exact distance verified from columns; a verified witness, not a maximum","borrowed-identity search: two-group":"found by the two-group borrowed-identity search of Singh, Gidney and Jones (arXiv:2606.28518; borrowed_identities/): an identity circuit symmetric within its output and check blocks, with its output-only gates removed; a verified witness, not a maximum","borrowed-identity search: symmetry-free":"found by the symmetry-free, targeted-output borrowed-identity search of Singh, Gidney and Jones (arXiv:2606.28518; borrowed_identities/), which solves for the check couplings of a chosen output; a verified witness, not a maximum","Jain-Albert doubling: weak triply even family":"a code of the weak triply even family of Jain and Albert (arXiv:2408.12752, Table II; transversal_t_codes/): quadratic-residue CSS codes doubled onto [[95,1,7]], rebuilt here from the paper's construction, where T on some qubits and T-dagger on the rest is a logical T; a verified witness, not a maximum","Jain-Albert doubling: triorthogonal family":"a code of the triorthogonal family of Jain and Albert (arXiv:2408.12752, Table I; transversal_t_codes/), self-dual CSS codes doubled onto [[95,1,7]], rebuilt here from the paper's construction; a verified witness, not a maximum","borrowed-identity search: SAT recovery":"found by the SAT stage of the unified borrowed-identity search of Singh, Gidney and Jones (arXiv:2606.28518; borrowed_identities/), asked for a factory below the circuit size the other stages reach; a verified witness, not a maximum","Gong et al.: F8 codes concatenated with 8T->CCZ":"a concatenated protocol of Gong, Pattison, Rall and Wills (arXiv:2608.09727): an F8 code fed by copies of the 8T->CCZ protocol, rebuilt from the paper's construction and written as one circuit on 18 wires; a verified witness, not a maximum","Gong doubling: triply even family":"a code of the triply even family of A. Gong (note in github.com/gongaa/RM127, triply-even/; transversal_t_codes/): her doubly even self-dual [[41,1,9]] and [[65,1,13]] codes and quantum QR codes doubled onto [[95,1,7]], rebuilt here from her self-dual codes, where T on every qubit is a logical T or T-dagger; a verified witness, not a maximum","Jain-Albert doubling of Gong's codes":"a code built here by the doubling method of Jain and Albert (arXiv:2408.12752) from the codes in A. Gong's repository (github.com/gongaa/RM127, triply-even/): her [[559,1,15]] doubled with the self-dual CSS codes of the paper's Table I from distance 17 on (transversal_t_codes/); a verified witness, not a maximum"},"discovery":{"pre-existing":"not an AI discovery of this project: a classification stage this repository ran, the symmetry-SAT search catalogue, the borrowed-identity searches, the codes of Jain and Albert and of A. Gong rebuilt in transversal_t_codes/ and the codes built there by doubling hers with theirs, the exhaustive length-54 classification alone, or a community contribution has this class","AI search":"found only by AI search campaigns: no classification stage this repository ran, no symmetry-SAT search, no borrowed-identity search and no community contribution is recorded among its sources (the length-54 classification may have it too); whether it was new to the literature is what citations says"},"references":{"bombin2007exact":{"short":"Bomb\u00edn & Martin-Delgado (2007)","full":"H. Bomb\u00edn and M. A. Martin-Delgado, \"Exact topological quantum order in D=3 and beyond: Branyons and brane-net condensates,\" Phys. Rev. B 75, 075103 (2007).","url":"https://doi.org/10.1103/PhysRevB.75.075103","date":"2007-02"},"bravyi2005universal":{"short":"Bravyi & Kitaev (2005)","full":"S. Bravyi and A. Kitaev, \"Universal quantum computation with ideal Clifford gates and noisy ancillas,\" Phys. Rev. A 71, 022316 (2005).","url":"https://doi.org/10.1103/PhysRevA.71.022316","date":"2005-02-22"},"bravyi2012magic":{"short":"Bravyi & Haah (2012)","full":"S. Bravyi and J. Haah, \"Magic-state distillation with low overhead,\" Phys. Rev. A 86, 052329 (2012).","url":"https://doi.org/10.1103/PhysRevA.86.052329","date":"2012-11-27"},"campbell2017unified":{"short":"Campbell & Howard (2017)","full":"E. T. Campbell and M. Howard, \"Unified framework for magic state distillation and multiqubit gate synthesis with reduced resource cost,\" Phys. Rev. A 95, 022316 (2017).","url":"https://doi.org/10.1103/PhysRevA.95.022316","date":"2017-02-09"},"gong2024computation":{"short":"Gong & Renes (2024)","full":"A. Gong and J. M. Renes, \"Computation with quantum Reed-Muller codes and their mapping onto 2D atom arrays,\" arXiv:2410.23263 (2024).","url":"https://arxiv.org/abs/2410.23263","date":"2024-10-30"},"gong2025triply":{"short":"Gong (2025)","full":"A. Gong, \"On some K=1 codes admitting strongly transversal T,\" note in the RM127 repository, triply-even/ (2025).","url":"https://github.com/gongaa/RM127/tree/main/triply-even","date":"2025-04-10"},"gong2026magic":{"short":"Gong et al. (2026)","full":"A. Gong, C. A. Pattison, P. Rall, and A. Wills, \"Magic State Distillation via Codes over Binary Extension Fields,\" arXiv:2608.09727 (2026).","url":"https://arxiv.org/abs/2608.09727","date":"2026-08-10"},"haah2018codes":{"short":"Haah & Hastings (2018)","full":"J. Haah and M. B. Hastings, \"Codes and Protocols for Distilling T, controlled-S, and Toffoli Gates,\" Quantum 2, 71 (2018).","url":"https://doi.org/10.22331/q-2018-06-07-71","date":"2018-06-07"},"jacinto2026exploring":{"short":"Jacinto et al. (2026)","full":"H. Jacinto, X. Valcarce, V. Barizien, \u00c9. Gouzien, and N. Sangouard, \"Exploring the landscape of compact magic-state distillation factories,\" arXiv:2606.07734 (2026).","url":"https://arxiv.org/abs/2606.07734","date":"2026-06-05"},"jain2025transversal":{"short":"Jain & Albert (2025)","full":"S. P. Jain and V. V. Albert, \"Transversal Clifford and T-gate codes of short length and high distance,\" IEEE J. Sel. Areas Inf. Theory 6, 127-137 (2025); arXiv:2408.12752.","url":"https://doi.org/10.1109/JSAIT.2025.3570832","date":"2025-05-16"},"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"},"litinski2019magic":{"short":"Litinski (2019)","full":"D. Litinski, \"Magic state distillation: not as costly as you think,\" Quantum 3, 205 (2019).","url":"https://doi.org/10.22331/q-2019-12-02-205","date":"2019-12-02"},"nezami2022classification":{"short":"Nezami & Haah (2022)","full":"S. Nezami and J. Haah, \"Classification of small triorthogonal codes,\" Phys. Rev. A 106, 012437 (2022).","url":"https://doi.org/10.1103/PhysRevA.106.012437","date":"2022-07-28"},"rengaswamy2020optimality":{"short":"Rengaswamy et al. (2020)","full":"N. Rengaswamy, R. Calderbank, M. Newman, and H. D. Pfister, \"On Optimality of CSS Codes for Transversal T,\" IEEE J. Sel. Areas Inf. Theory 1, 499 (2020).","url":"https://doi.org/10.1109/JSAIT.2020.3012914","date":"2020-08"},"shi2024triorthogonal":{"short":"Shi et al. (2024)","full":"M. Shi, H. Lu, J.-L. Kim, and P. Sol\u00e9, \"Triorthogonal codes and self-dual codes,\" Quantum Inf. Process. 23, 280 (2024).","url":"https://doi.org/10.1007/s11128-024-04485-9","date":"2024-07-20"},"singh2026borrowed":{"short":"Singh et al. (2026)","full":"S. Singh, C. Gidney, and C. Jones, \"Borrowed Identities: Malleable Distillation Factories and a Unified Numerical Search,\" arXiv:2606.28518 (2026).","url":"https://arxiv.org/abs/2606.28518","date":"2026-06-26"},"sullivan2024code":{"short":"Sullivan (2024)","full":"M. Sullivan, \"Code conversion with the quantum Golay code for a universal transversal gate set,\" Phys. Rev. A 109, 042416 (2024).","url":"https://doi.org/10.1103/PhysRevA.109.042416","date":"2024-04-18"},"vuillot2022quantum":{"short":"Vuillot & Breuckmann (2022)","full":"C. Vuillot and N. P. Breuckmann, \"Quantum Pin Codes,\" IEEE Trans. Inf. Theory 68, 5955 (2022).","url":"https://doi.org/10.1109/TIT.2022.3170846","date":"2022-09"},"webster2023transversal":{"short":"Webster et al. (2023)","full":"M. A. Webster, A. O. Quintavalle, and S. D. Bartlett, \"Transversal diagonal logical operators for stabiliser codes,\" New J. Phys. 25, 103018 (2023).","url":"https://doi.org/10.1088/1367-2630/acfc5f","date":"2023-10-01"},"wills2026classification":{"short":"Wills et al. (2026)","full":"A. Wills, S. P. Jain, and S. 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