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    367,
    572,
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   [
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    565,
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    415,
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   [
    420,
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   [
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   [
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   [
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  ]
 },
 "distance": {
  "d": 22,
  "X": {
   "value": 22,
   "confidence": "upper_bound",
   "witness": [
    40,
    41,
    60,
    61,
    80,
    81,
    92,
    93,
    152,
    153,
    172,
    173,
    200,
    201,
    308,
    309,
    320,
    321,
    324,
    325,
    364,
    365
   ]
  },
  "Z": {
   "value": 22,
   "confidence": "upper_bound",
   "witness": [
    132,
    133,
    192,
    193,
    200,
    201,
    208,
    209,
    284,
    285,
    324,
    325,
    336,
    337,
    392,
    393,
    440,
    441,
    484,
    485,
    500,
    501
   ]
  }
 },
 "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/126-24-11.json ([[126,24,11]] two-block code over C63; d_X = d_Z = 11 certified in certs/126-24-11.json), keeping all of its checks.X except the rows [43, 49, 51, 52, 54, 56, 57, 58, 59, 60, 61, 62] and all of its checks.Z except the rows [50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62] (linearly independent, 51 and 51 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 -> 555+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 + 51 + 51 = 606 = 5n - k of the base, k = 2*24 = 48, check weight 10.",
  "references": [
   "arXiv:2609.37231",
   "arXiv:2610.13880",
   "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/126-24-11.json (tropidist b03ec2d4077f, level solver). Witnesses: u (x) (e_0 + e_1) for the witnesses u of codes/126-24-11.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 = 48. 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 630-48-22 is the amplification of the same base with all 63 + 63 base rows, which this code shortens to n = 606 by leaving out dependent rows."
 },
 "family": "distance-amplified"
}