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245, 306, 496, 503 ], "witness_provenance": { "found_by": [ "@mathysrennela" ], "date": "2026-10-10", "found_at_samples": 3000, "survived_samples": 3000, "tool": "research/kit/surrogate.lightest_logical", "seeds": [ 1 ] } }, "Z": { "value": 4, "confidence": "upper_bound", "witness": [ 193, 251, 344, 405 ], "witness_provenance": { "found_by": [ "@mathysrennela" ], "date": "2026-10-10", "found_at_samples": 3000, "survived_samples": 3000, "tool": "research/kit/surrogate.lightest_logical", "seeds": [ 2 ] } } }, "provenance": { "authors": [ "@mathysrennela" ], "construction": "Regular {7,7} hyperbolic surface code on a closed orientable surface. Quotient Q = Delta_7/Gamma with Q = PSL(2,13); the face-vertex swap is a projective involution J in PGL(2,13) imposing y = J x J^-1, with ord(x) = ord(y) = 7 and ord(xy) = 2. Data qubits on edges = left cosets of the order-2 subgroup ; Z checks on face boundaries = left cosets of ; X checks on vertex stars = left cosets of . Checks commute because each face boundary meets each vertex an even number of times. n = |Q|/2 and k/n = (7-4)/7 + 2/n by Euler, giving k=236 at n=546. Regenerated from the algebra of arXiv:2610.10948 Sec. II by research/hyperbolic_psl.py; the matrices are recomputed, not copied, since that paper publishes its matrices on request only.", "references": [ "arXiv:2610.10948" ], "date": "2026-10-10", "notes": "Distance is a homological systole on each side, carried as explicit weight-4 witnesses, so d<=4 is witness-backed rather than certified exact. The paper's d=5 for this member is not reproduced here and is not claimed.", "model": "human", "origin": "submission", "search_budget": { "candidates_screened": 1500, "ris_trials_per_side": 1000000 } }, "family": "topological" }