{
 "schema_version": "0.4",
 "name": "[[36,6,6]]",
 "code_type": "stabilizer",
 "n": 36,
 "k": 6,
 "checks": {
  "S": [
   {
    "X": [
     1,
     11,
     12
    ],
    "Z": [
     0,
     1,
     20
    ]
   },
   {
    "X": [
     0,
     10,
     17
    ],
    "Z": [
     1,
     2,
     21
    ]
   },
   {
    "X": [
     5,
     9,
     16
    ],
    "Z": [
     2,
     3,
     22
    ]
   },
   {
    "X": [
     4,
     8,
     15
    ],
    "Z": [
     3,
     4,
     23
    ]
   },
   {
    "X": [
     3,
     7,
     14
    ],
    "Z": [
     4,
     5,
     18
    ]
   },
   {
    "X": [
     2,
     6,
     13
    ],
    "Z": [
     0,
     5,
     19
    ]
   },
   {
    "X": [
     5,
     6,
     31
    ],
    "Z": [
     6,
     7,
     26
    ]
   },
   {
    "X": [
     4,
     11,
     30
    ],
    "Z": [
     7,
     8,
     27
    ]
   },
   {
    "X": [
     3,
     10,
     35
    ],
    "Z": [
     8,
     9,
     28
    ]
   },
   {
    "X": [
     2,
     9,
     34
    ],
    "Z": [
     9,
     10,
     29
    ]
   },
   {
    "X": [
     1,
     8,
     33
    ],
    "Z": [
     10,
     11,
     24
    ]
   },
   {
    "X": [
     0,
     7,
     32
    ],
    "Z": [
     6,
     11,
     25
    ]
   },
   {
    "X": [
     0,
     25,
     35
    ],
    "Z": [
     12,
     13,
     32
    ]
   },
   {
    "X": [
     5,
     24,
     34
    ],
    "Z": [
     13,
     14,
     33
    ]
   },
   {
    "X": [
     4,
     29,
     33
    ],
    "Z": [
     14,
     15,
     34
    ]
   },
   {
    "X": [
     3,
     28,
     32
    ],
    "Z": [
     15,
     16,
     35
    ]
   },
   {
    "X": [
     2,
     27,
     31
    ],
    "Z": [
     16,
     17,
     30
    ]
   },
   {
    "X": [
     1,
     26,
     30
    ],
    "Z": [
     12,
     17,
     31
    ]
   },
   {
    "X": [
     19,
     29,
     30
    ],
    "Z": [
     2,
     18,
     19
    ]
   },
   {
    "X": [
     18,
     28,
     35
    ],
    "Z": [
     3,
     19,
     20
    ]
   },
   {
    "X": [
     23,
     27,
     34
    ],
    "Z": [
     4,
     20,
     21
    ]
   },
   {
    "X": [
     22,
     26,
     33
    ],
    "Z": [
     5,
     21,
     22
    ]
   },
   {
    "X": [
     21,
     25,
     32
    ],
    "Z": [
     0,
     22,
     23
    ]
   },
   {
    "X": [
     20,
     24,
     31
    ],
    "Z": [
     1,
     18,
     23
    ]
   },
   {
    "X": [
     13,
     23,
     24
    ],
    "Z": [
     8,
     24,
     25
    ]
   },
   {
    "X": [
     12,
     22,
     29
    ],
    "Z": [
     9,
     25,
     26
    ]
   },
   {
    "X": [
     17,
     21,
     28
    ],
    "Z": [
     10,
     26,
     27
    ]
   },
   {
    "X": [
     16,
     20,
     27
    ],
    "Z": [
     11,
     27,
     28
    ]
   },
   {
    "X": [
     15,
     19,
     26
    ],
    "Z": [
     6,
     28,
     29
    ]
   },
   {
    "X": [
     14,
     18,
     25
    ],
    "Z": [
     7,
     24,
     29
    ]
   },
   {
    "X": [
     7,
     17,
     18
    ],
    "Z": [
     14,
     30,
     31
    ]
   },
   {
    "X": [
     6,
     16,
     23
    ],
    "Z": [
     15,
     31,
     32
    ]
   },
   {
    "X": [
     11,
     15,
     22
    ],
    "Z": [
     16,
     32,
     33
    ]
   },
   {
    "X": [
     10,
     14,
     21
    ],
    "Z": [
     17,
     33,
     34
    ]
   },
   {
    "X": [
     9,
     13,
     20
    ],
    "Z": [
     12,
     34,
     35
    ]
   },
   {
    "X": [
     8,
     12,
     19
    ],
    "Z": [
     13,
     30,
     35
    ]
   }
  ]
 },
 "distance": {
  "d": 6,
  "P": {
   "value": 6,
   "confidence": "upper_bound",
   "witness": {
    "X": [
     13,
     17,
     30,
     31,
     32,
     33
    ],
    "Z": []
   }
  }
 },
 "provenance": {
  "authors": [
   "@MathysRennela"
  ],
  "construction": "Mirror-family non-CSS stabilizer code; the construction printed in full as Eqs. (142)-(143) of arXiv:2610.17612 (Nelson, Danageozian, Cao, Economou, Barnes, 'From Syndromes to Computation') and introduced by Khesin and Lu, arXiv:2603.05496. Physical qubits are the 36 sites of the torus Z_6 x Z_6, site (i,j) numbered 6i+j. For each lattice site u the stabilizer is S(u) = (-i)^(m(u)) Z(A+u) X(B-u) with m(u) = |(A+u) and (B-u)|, using A = {0,1,20} and B = {1,11,12} as site ids, each of size 3, so every generator has Pauli weight at most 6. The 36 generators commute for any A, B: the two counts entering the symplectic product, |B and (A+u+v)| and |A and (B-u-v)|, count the same pairs (a,b) in A x B with b-a = u+v, so their sum is even. The (-i)^(m(u)) phase gives the product over any identity-support subset of generators the phase (-1)^|T|, which is +1 because |A| = 3 is odd, so -I never occurs and the code is a valid encoding. Parameters found by sweeping this family; the distinct [[36,6,6]] member is not the one printed in that paper (which uses A = {(1,2),(4,3),(4,4)}, B = {(2,4),(3,1),(4,1)}).",
  "date": "2026-10-15",
  "model": "Space Bunny Alpha 1.0",
  "notes": "Known parameters, and a tie rather than a gain. The board already holds a [[36,6,6]] at codes/36-6-6.json, a one-block cyclic Camara-Ollivier-Tillich code; this entry has the same n, k, d and maximum check weight and beats it on no axis. It is filed under a suffixed slug 36-6-6-m because the unsuffixed slug is taken, and it is a second, independently constructed code in a cell that had one: codes/36-6-6.json carries a two-layer layout and so also competes local-2d-bilayer, while this one carries no layout and is unrestricted-only. Distance is a witness-backed upper bound d <= 6 from random search over the logical space plus the gate's independent refutation on a fresh seed; no lower bound is proven. The [[36,6,6]] member printed in arXiv:2610.17612 uses different patterns (A = {(1,2),(4,3),(4,4)}, B = {(2,4),(3,1),(4,1)}); this one was found by sweeping the family, not by copying it. Construction credited to the Mirror-family equations (142)-(143) of arXiv:2610.17612, on which the family is based.",
  "novelty": "known_parameters",
  "origin": "submission",
  "references": [
   "arXiv:2610.17612",
   "arXiv:2603.05496"
  ],
  "search_budget": {
   "candidates_screened": 18,
   "ris_trials_per_side": 200000,
   "cpu_hours": 7.0,
   "gpu_hours": 0.0,
   "wall_clock_hours": 0.75,
   "tool": "research/mirror_sweep.py + research/mirror_stage.py",
   "notes": "n=36 sweep: 4,325,616 (A,B) pairs, exhaustive over the offset ansatz, 8 processes, 7m39s wall. Witness search and gating: 3m10s wall. The 7 CPU-hours includes ~5 core-hours from an n=48..60 sweep that exceeded a 40-minute budget and was abandoned without staging."
  }
 },
 "family": "other"
}