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    453,
    454,
    455,
    584,
    598,
    601
   ],
   [
    456,
    457,
    458,
    459,
    585,
    599,
    602
   ],
   [
    460,
    461,
    462,
    463,
    599,
    600,
    603
   ],
   [
    464,
    465,
    466,
    467,
    586,
    600,
    601,
    604
   ],
   [
    468,
    469,
    470,
    471,
    587,
    601,
    602,
    605
   ],
   [
    472,
    473,
    474,
    475,
    602,
    603,
    606
   ],
   [
    476,
    477,
    478,
    479,
    588,
    603,
    604,
    607
   ],
   [
    480,
    481,
    482,
    483,
    589,
    604,
    605,
    608
   ],
   [
    484,
    485,
    486,
    487,
    590,
    605,
    606,
    609
   ],
   [
    488,
    489,
    490,
    491,
    557,
    591,
    606,
    607
   ],
   [
    492,
    493,
    494,
    495,
    592,
    607,
    608
   ],
   [
    496,
    497,
    498,
    499,
    558,
    608,
    609
   ],
   [
    500,
    501,
    502,
    503,
    557,
    559,
    609
   ]
  ]
 },
 "distance": {
  "d": 22,
  "X": {
   "value": 22,
   "confidence": "upper_bound",
   "witness": [
    24,
    25,
    132,
    133,
    148,
    149,
    156,
    157,
    160,
    161,
    164,
    165,
    240,
    241,
    260,
    261,
    328,
    329,
    368,
    369,
    380,
    381
   ]
  },
  "Z": {
   "value": 22,
   "confidence": "upper_bound",
   "witness": [
    24,
    25,
    92,
    93,
    144,
    145,
    220,
    221,
    272,
    273,
    316,
    317,
    328,
    329,
    364,
    365,
    440,
    441,
    444,
    445,
    456,
    457
   ]
  }
 },
 "provenance": {
  "authors": [
   "@TimoKellerMath"
  ],
  "origin": "submission",
  "novelty": "unknown",
  "construction": "One [[4,2,2]] distance-amplification step (Liang, Gu, Chen, Eisert, Wang, arXiv:2609.37231, Eqs. (14), (15); amplifier checks G_X = G_Z = the all-one row of length 4) applied to the board entry codes/126-20-11.json ([[126,20,11]] two-block code on Z_63; d_X = d_Z = 11 certified in certs/126-20-11.json), keeping all of its checks.X except the rows [1, 8, 16, 28, 33, 36, 42, 43, 49, 51] and all of its checks.Z except the rows [0, 8, 21, 22, 29, 31, 37, 39, 50, 57] (linearly independent, 53 and 53 rows). Qubits: central (q,a) -> 4q+a (q a base qubit, 0 <= a < 4); t_j -> 504+j for the j-th kept Z-check z_j; s_i -> 557+i for the i-th kept X-check c_i. X-checks: (c_i,a) = {4q+a : q in c_i} + {s_i} (i, then a), then (q) = {4q,...,4q+3} + {t_j : q in z_j} (q = 0..125); Z-checks: (z_j,a) = {4q+a : q in z_j} + {t_j}, then (q) = {4q,...,4q+3} + {s_i : q in c_i}. n = 4*126 + 53 + 53 = 610 = 5n - k of the base, k = 2*20 = 40, check weight 9.",
  "references": [
   "arXiv:2609.37231",
   "arXiv:2306.16400",
   "arXiv:1512.07081",
   "arXiv:2611.08247"
  ],
  "date": "2026-11-10",
  "model": "Claude Opus 5.5",
  "notes": "Distance: d_X = d_Z = 22 exactly: d_P = 2 d_P(base) for P = X, Z by Lemma 4 of arXiv:2609.37231 (proof in the coordinates of this entry: Proposition 4 of amplified-and-folded-codes/README.md, github.com/TimoKellerMath/quantum-error-correction @ c203901854da), and d_X = d_Z = 11 for the base is certified in certs/126-20-11.json (tropidist b03ec2d4077f, level solver). Witnesses: u (x) (e_0 + e_1) for the witnesses u of codes/126-20-11.json. Filed as upper_bound with these witnesses: the board earns the exact tier only through certs/, and its certifiers do not reach d = 22 at k = 40. The construction and the base are published; at board commit 8042f9da no CSS entry dominates or equals this code in (n, k, d, w), and no entry has its n and k unless named here; checked, not equivalent to an existing entry. The board entry 610-40-20 has the same n, k and check weight and d <= 20 by its witness (it is the [[4,2,2]] amplification of 126-20-10, so d = 20 exactly by the same lemma and certs/126-20-10.json); 630-40-22 is the amplification of the same base with all 63 + 63 base rows, which this code shortens to n = 610 by leaving out dependent rows."
 },
 "family": "distance-amplified"
}