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218, 224, 255, 317, 321, 329 ], [ 137, 179, 190, 217, 223, 256, 313, 322, 325 ], [ 136, 178, 191, 216, 222, 257, 315, 323, 327 ], [ 140, 182, 192, 227, 233, 258, 266, 320, 324 ], [ 141, 183, 193, 226, 232, 259, 268, 322, 325 ], [ 138, 180, 194, 225, 231, 260, 264, 318, 326 ], [ 139, 181, 195, 224, 230, 261, 269, 323, 327 ], [ 143, 185, 196, 223, 229, 262, 265, 319, 328 ], [ 142, 184, 197, 222, 228, 263, 267, 321, 329 ] ] }, "distance": { "d": 12, "X": { "value": 12, "confidence": "upper_bound", "witness": [ 133, 146, 151, 156, 165, 174, 188, 189, 201, 207, 236, 242 ] }, "Z": { "value": 12, "confidence": "upper_bound", "witness": [ 67, 81, 84, 103, 111, 128, 224, 234, 236, 240, 242, 252 ] } }, "provenance": { "authors": [ "Bhardwaj, Aditya", "Ma, Muzhou", "Meister, Nadine", "King, Robbie", "Bluvstein, Dolev", "Preskill, John", "Cain, Madelyn", "Xu, Qian", "Huang, Hsin-Yuan", "@MathysRennela" ], "construction": "Structured-mitten code (arXiv:2607.28795 processor-code suite): rate-1/5 (k/n = 1/5) lifted-product CSS code, all checks weight 9. Check matrices taken verbatim from the authors' repository (github.com/a7b/yarn @ e1cd5452dea871efab9f3fb2e63a94f8ffd6e3b7, processor_codes/structured_mitten/[[330,66,12]]/Hx.npy and Hz.npy): Hx and Hz are 132x330 binary matrices of row weight 9 with Hx Hz^T = 0 (mod 2), n = 330 and k = 66 recomputed from matrix ranks over GF(2) at submit time; the repository's paired logical bases Lx, Lz (rows of weight 20 and 30) satisfy Lx Lz^T = I_66 (mod 2). The structured-mitten variant's parameterization in the paper is not reproduced here; the published matrices are used as-is.", "origin": "submission", "date": "2026-09-25", "references": [ "arXiv:2607.28795" ], "model": "MiMo-V2.6-Flash", "notes": "Literature reproduction of the authors' published structured_mitten matrix (github.com/a7b/yarn @ e1cd5452, processor_codes/structured_mitten). Witness-backed upper bound d <= 12 on both sides (RIS 20000 trials/side, seed 0; the gf2_fast accelerator was not loaded in this run); d >= 12 not certified here - the authors' directory labels the code [[330,66,12]]. Not equivalent to any existing entry: the board's other n = 330 codes [[330,66,10]] and [[330,66,9]] are weight-8, this one has all checks weight 9. No circuit tier: the generic sequential Z memory at 12 rounds has 204297 error mechanisms, over the 25000 circuit-tier cap (the submit CLI printed the reason)." }, "family": "lifted-product" }