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     717
    ]
   },
   {
    "X": [
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    "Z": [
     679,
     718
    ]
   },
   {
    "X": [
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    ],
    "Z": [
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     719
    ]
   },
   {
    "X": [
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     701
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    "Z": [
     681,
     720
    ]
   },
   {
    "X": [
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     702
    ],
    "Z": [
     682,
     721
    ]
   },
   {
    "X": [
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     703
    ],
    "Z": [
     683,
     722
    ]
   },
   {
    "X": [
     703,
     704
    ],
    "Z": [
     684,
     723
    ]
   },
   {
    "X": [
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     705
    ],
    "Z": [
     685,
     724
    ]
   },
   {
    "X": [
     705,
     706
    ],
    "Z": [
     686,
     725
    ]
   },
   {
    "X": [
     706,
     707
    ],
    "Z": [
     687,
     726
    ]
   },
   {
    "X": [
     707,
     708
    ],
    "Z": [
     688,
     727
    ]
   },
   {
    "X": [
     708,
     709
    ],
    "Z": [
     689,
     728
    ]
   },
   {
    "X": [
     709,
     710
    ],
    "Z": [
     690,
     729
    ]
   },
   {
    "X": [
     710,
     711
    ],
    "Z": [
     691,
     730
    ]
   },
   {
    "X": [
     711,
     712
    ],
    "Z": [
     692,
     731
    ]
   },
   {
    "X": [
     712,
     713
    ],
    "Z": [
     693,
     732
    ]
   },
   {
    "X": [
     713,
     714
    ],
    "Z": [
     694,
     733
    ]
   },
   {
    "X": [
     714,
     715
    ],
    "Z": [
     695,
     734
    ]
   },
   {
    "X": [
     715,
     716
    ],
    "Z": [
     696,
     735
    ]
   },
   {
    "X": [
     716,
     717
    ],
    "Z": [
     697,
     736
    ]
   },
   {
    "X": [
     717,
     718
    ],
    "Z": [
     698,
     737
    ]
   },
   {
    "X": [
     718,
     719
    ],
    "Z": [
     699,
     738
    ]
   },
   {
    "X": [
     719,
     720
    ],
    "Z": [
     700,
     739
    ]
   },
   {
    "X": [
     720,
     721
    ],
    "Z": [
     701,
     740
    ]
   },
   {
    "X": [
     721,
     722
    ],
    "Z": [
     702,
     741
    ]
   },
   {
    "X": [
     722,
     723
    ],
    "Z": [
     703,
     742
    ]
   },
   {
    "X": [
     723,
     724
    ],
    "Z": [
     704,
     743
    ]
   },
   {
    "X": [
     724,
     725
    ],
    "Z": [
     705,
     744
    ]
   },
   {
    "X": [
     725,
     726
    ],
    "Z": [
     706,
     745
    ]
   },
   {
    "X": [
     726,
     727
    ],
    "Z": [
     707,
     746
    ]
   },
   {
    "X": [
     727,
     728
    ],
    "Z": [
     708,
     747
    ]
   },
   {
    "X": [
     728,
     729
    ],
    "Z": [
     709,
     748
    ]
   },
   {
    "X": [
     729,
     730
    ],
    "Z": [
     710,
     749
    ]
   },
   {
    "X": [
     730,
     731
    ],
    "Z": [
     711,
     750
    ]
   },
   {
    "X": [
     731,
     732
    ],
    "Z": [
     712,
     751
    ]
   },
   {
    "X": [
     732,
     733
    ],
    "Z": [
     713,
     752
    ]
   },
   {
    "X": [
     733,
     734
    ],
    "Z": [
     714,
     753
    ]
   },
   {
    "X": [
     734,
     735
    ],
    "Z": [
     715,
     754
    ]
   },
   {
    "X": [
     735,
     736
    ],
    "Z": [
     716,
     755
    ]
   },
   {
    "X": [
     736,
     737
    ],
    "Z": [
     717,
     756
    ]
   },
   {
    "X": [
     737,
     738
    ],
    "Z": [
     718,
     757
    ]
   },
   {
    "X": [
     738,
     739
    ],
    "Z": [
     719,
     758
    ]
   },
   {
    "X": [
     739,
     740
    ],
    "Z": [
     720,
     759
    ]
   },
   {
    "X": [
     740,
     741
    ],
    "Z": [
     721,
     760
    ]
   },
   {
    "X": [
     741,
     742
    ],
    "Z": [
     0,
     722
    ]
   },
   {
    "X": [
     742,
     743
    ],
    "Z": [
     1,
     723
    ]
   },
   {
    "X": [
     743,
     744
    ],
    "Z": [
     2,
     724
    ]
   },
   {
    "X": [
     744,
     745
    ],
    "Z": [
     3,
     725
    ]
   },
   {
    "X": [
     745,
     746
    ],
    "Z": [
     4,
     726
    ]
   },
   {
    "X": [
     746,
     747
    ],
    "Z": [
     5,
     727
    ]
   },
   {
    "X": [
     747,
     748
    ],
    "Z": [
     6,
     728
    ]
   },
   {
    "X": [
     748,
     749
    ],
    "Z": [
     7,
     729
    ]
   },
   {
    "X": [
     749,
     750
    ],
    "Z": [
     8,
     730
    ]
   },
   {
    "X": [
     750,
     751
    ],
    "Z": [
     9,
     731
    ]
   },
   {
    "X": [
     751,
     752
    ],
    "Z": [
     10,
     732
    ]
   },
   {
    "X": [
     752,
     753
    ],
    "Z": [
     11,
     733
    ]
   },
   {
    "X": [
     753,
     754
    ],
    "Z": [
     12,
     734
    ]
   },
   {
    "X": [
     754,
     755
    ],
    "Z": [
     13,
     735
    ]
   },
   {
    "X": [
     755,
     756
    ],
    "Z": [
     14,
     736
    ]
   },
   {
    "X": [
     756,
     757
    ],
    "Z": [
     15,
     737
    ]
   },
   {
    "X": [
     757,
     758
    ],
    "Z": [
     16,
     738
    ]
   },
   {
    "X": [
     758,
     759
    ],
    "Z": [
     17,
     739
    ]
   },
   {
    "X": [
     759,
     760
    ],
    "Z": [
     18,
     740
    ]
   },
   {
    "X": [
     0,
     760
    ],
    "Z": [
     19,
     741
    ]
   },
   {
    "X": [
     0,
     1
    ],
    "Z": [
     20,
     742
    ]
   },
   {
    "X": [
     1,
     2
    ],
    "Z": [
     21,
     743
    ]
   },
   {
    "X": [
     2,
     3
    ],
    "Z": [
     22,
     744
    ]
   },
   {
    "X": [
     3,
     4
    ],
    "Z": [
     23,
     745
    ]
   },
   {
    "X": [
     4,
     5
    ],
    "Z": [
     24,
     746
    ]
   },
   {
    "X": [
     5,
     6
    ],
    "Z": [
     25,
     747
    ]
   },
   {
    "X": [
     6,
     7
    ],
    "Z": [
     26,
     748
    ]
   },
   {
    "X": [
     7,
     8
    ],
    "Z": [
     27,
     749
    ]
   },
   {
    "X": [
     8,
     9
    ],
    "Z": [
     28,
     750
    ]
   },
   {
    "X": [
     9,
     10
    ],
    "Z": [
     29,
     751
    ]
   },
   {
    "X": [
     10,
     11
    ],
    "Z": [
     30,
     752
    ]
   },
   {
    "X": [
     11,
     12
    ],
    "Z": [
     31,
     753
    ]
   },
   {
    "X": [
     12,
     13
    ],
    "Z": [
     32,
     754
    ]
   },
   {
    "X": [
     13,
     14
    ],
    "Z": [
     33,
     755
    ]
   },
   {
    "X": [
     14,
     15
    ],
    "Z": [
     34,
     756
    ]
   },
   {
    "X": [
     15,
     16
    ],
    "Z": [
     35,
     757
    ]
   },
   {
    "X": [
     16,
     17
    ],
    "Z": [
     36,
     758
    ]
   },
   {
    "X": [
     17,
     18
    ],
    "Z": [
     37,
     759
    ]
   },
   {
    "X": [
     18,
     19
    ],
    "Z": [
     38,
     760
    ]
   }
  ]
 },
 "distance": {
  "d": 39,
  "P": {
   "value": 39,
   "confidence": "upper_bound",
   "witness": {
    "X": [
     19
    ],
    "Z": [
     0,
     1,
     2,
     3,
     4,
     5,
     6,
     7,
     8,
     9,
     10,
     11,
     12,
     13,
     14,
     15,
     16,
     17,
     18,
     19,
     20,
     21,
     22,
     23,
     24,
     25,
     26,
     27,
     28,
     29,
     30,
     31,
     32,
     33,
     34,
     35,
     36,
     37,
     38
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "@mrvee-qC-bee"
  ],
  "origin": "submission",
  "date": "2026-10-01",
  "model": "GPT-6 Astra",
  "novelty": "known_parameters",
  "references": [
   "https://doi.org/10.1103/PhysRevA.84.062319"
  ],
  "construction": "Published cyclic toric family of Alexey A. Kovalev, Ilya Dumer, and Leonid P. Pryadko (2011), Example 11. Set t=19, d=2t+1=39, n=t^2+(t+1)^2=761. Generator i has X on {i+t,i+t+1} mod n and Z on {i,i+d} mod n. The affine relabelling q -> 2t*q+(2t+2) mod n maps the seed to X on {1,d}, Z on {0,d+1}, the published ZX I^(2t-1) XZ generator.",
  "notes": "Reproduction of a known family, not a new construction or new parameters. The submission distance remains a witness-backed upper bound because the challenge does not certify non-CSS distances. Explicit logical: X on {t}, Z on {0,...,d-1}. Commutation and nontriviality are checked by the trusted verifier; odd X parity establishes nontriviality since every stabilizer generator has even X parity. No locality layout is claimed."
 }
}