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307, 333, 416, 740, 752 ], [ 29, 137, 223, 308, 334, 417, 741, 753 ] ] }, "distance": { "d": 36, "X": { "value": 36, "confidence": "upper_bound", "witness": [ 8, 19, 21, 27, 31, 38, 127, 134, 135, 144, 146, 162, 166, 203, 249, 322, 348, 353, 360, 397, 409, 414, 419, 424, 436, 441, 442, 479, 523, 529, 534, 581, 586, 597, 653, 658 ], "witness_provenance": { "found_by": [ "@jacksongquera" ], "date": "2026-10-23", "found_at_samples": 4627935, "survived_samples": 55118061, "tool": "own Stern ISD (C++, p=2, l=16); method in notes/996-166-36.md" } }, "Z": { "value": 36, "confidence": "upper_bound", "witness": [ 5, 9, 22, 36, 52, 69, 113, 122, 130, 140, 149, 160, 171, 183, 188, 193, 199, 245, 278, 283, 291, 295, 300, 328, 347, 384, 439, 466, 530, 535, 552, 599, 604, 616, 621, 626 ], "witness_provenance": { "found_by": [ "@jacksongquera" ], "date": "2026-10-23", "found_at_samples": 4731131, "survived_samples": 55067099, "tool": "own Stern ISD (C++, p=2, l=16); method in notes/996-166-36.md" } } }, "provenance": { "authors": [ "@jacksongquera" ], "construction": "Irregular pair-partition CPM CSS code: the pair-partition commutation rule of Okada-Kasai (arXiv:2607.14091) on an irregular base template, cyclic lift P=83 (Z_83), n=996, k=166. Template (PR #4045's 5x12 'pair-complement-2', same on both sides): 12 block columns in 6 pairs; each block row contains all pairs but two, the left-out pairs forming a triangle on pairs 0,1,2 and a path 4-3-5; block columns per row [[4..11],[2,3,6..11],[0,1,6..11],[0..5,10,11],[0..5,8,9]]. Pairing of the X-row/Z-row overlaps: the pairing filed with PR #4045 (codes/996-166-32.json there, provenance.construction), unchanged. H[i*P + r, c*P + ((r + s_ic) mod P)] = 1 with exponents ('-' = empty cell): S_X = [[-, -, -, -, 13, 12, 47, 33, 4, 17, 23, 82], [-, -, 70, 33, -, -, 36, 5, 51, 19, 34, 65], [16, 46, -, -, -, -, 1, 34, 69, 76, 69, 75], [57, 45, 48, 77, 20, 30, -, -, -, -, 55, 20], [49, 74, 57, 59, 76, 76, -, -, 18, 30, -, -]], S_Z = [[-, -, -, -, 68, 67, 77, 63, 9, 22, 9, 68], [-, -, 38, 1, -, -, 58, 27, 43, 11, 62, 10], [58, 5, -, -, -, -, 75, 25, 32, 39, 15, 21], [73, 61, 54, 0, 63, 73, -, -, -, -, 1, 49], [30, 55, 58, 60, 3, 3, -, -, 78, 7, -, -]]. The exponent draw was selected so that the block-level Tanner graph has no 4-cycles and only the 6-cycles the pairing forces (12 block hexagons per side), then screened with a Stern ISD.", "references": [ "arXiv:2607.14091", "arXiv:2609.30069", "arXiv:1301.1493", "https://github.com/unitaryfoundation/qldpc-challenge/pull/4035", "https://github.com/unitaryfoundation/qldpc-challenge/pull/4045", "https://github.com/unitaryfoundation/qldpc-challenge/pull/4055" ], "date": "2026-10-23", "notes": "The gate flags a shared Weisfeiler-Leman signature with codes/996-166-32.json; the board's other lift of this template, codes/996-166-34.json, shares it too (every lift of the 5x12 template at P = 83 has the same colour refinement). This code is equivalent to neither under any qubit permutation, with or without an X/Z swap. The board's decider, research/audits/permutation_audit.py, returns inequivalent for both pairs (and for the two board entries against each other) once its light-vector enumeration budget is raised from the default 1e9 to 2e9 row sums (each row space needs 1,241,929,417; about 140 s per pair): its Brouwer-Zimmermann enumeration finds that the row-space vectors of weight <= 8 are exactly the 415 checks on every side, and their hypergraphs are not isomorphic in either orientation. An independent run of the same argument agrees: (1) a Brouwer-Zimmermann enumeration (K.-H. Zimmermann, Tech. Rep. 3-96, TU Hamburg-Harburg, 1996, after A. E. Brouwer) over two disjoint information sets, all sums of at most 4 systematic rows on each, lists every vector of weight <= 9 in each of the six row spaces, and each list is exactly that side's 415 weight-8 checks; (2) a weight-preserving permutation therefore carries checks onto checks (J. S. Leon, IEEE Trans. Inf. Theory 28 (1982) 496-511), so equivalence is isomorphism of the typed Tanner graphs; (3) their nauty canonical forms (B. D. McKay and A. Piperno, J. Symbolic Comput. 60 (2014) 94-112, arXiv:1301.1493), computed as in research/provenance/iso_common.py, differ in both orientations, and their 6-cycle counts differ: 996 per side here, 1826 in codes/996-166-32.json and 1992 in codes/996-166-34.json (83 times the 12, 22 and 24 zero-sum block hexagons). The method is the one in notes/996-166-34.md.", "model": "Claude Opus 5.5 (Claude Code)", "origin": "submission", "search_budget": { "tool": "own Stern ISD (C++, p=2) + research/kit/coordination.py gate", "notes": "ris_trials_per_side is the deepest single rung, one round of two Stern runs per side; the code's full-length Stern runs total 55,118,061 (X) and 55,067,099 (Z) iterations.", "ris_trials_per_side": 10830006 } }, "family": "pair-partition-cpm" }