{
  "schema": "nsrl.production_atomic_ising_audit.v1",
  "analysis_role": "proposal_only_calibration",
  "source_result_sha256": "7d7432057cfa2b86796abdcaf73604541699a9fed1a939a57ad94b42bf9ce7ca",
  "source_contract_sha256": "a55fa73adf8c2650e36cc367dcae6aca1fec87a6bb422fa337e0d0b00a306184",
  "audit_contract_sha256": "18b2e0bf250e3cd752185b9ec48423775ed34d4344916dcde3ee5fb7a0898bd8",
  "rank": 6,
  "vertices": 64,
  "bindings": {
    "source_fnv64": "0xc19b8402483e9d33",
    "binary_fnv64": "0xfa0351bca0c5631e",
    "model_hash": "0xb10996e0707ab342",
    "tokenizer_hash": "0xf4fe71d93c438c1a",
    "token_stream_hash": "0xda195778ceb603ab",
    "source_index_hash": "0x75f51a06dd94fda8",
    "move_fingerprint": "0x48eccb62ab07b717",
    "manifest_hash": "0x2ce8888292aa6852"
  },
  "implementation": {
    "kernel_sha256": "e19d478df519ca2cbc0cae16379633c467906671fe6286113574f67deedbe996",
    "analyzer_sha256": "8a0a3766a94f1519fa072e9168dc43477a58be8feec5da49696190f2ebf3e740",
    "checker_sha256": "fee46cb8d7c5d57771c688cd2a3d524d93ee5790c1a844218ba3efabe2458ba7"
  },
  "arithmetic": {
    "objective_integer_type": "arbitrary_precision_signed",
    "objective_floating_point_operations": 0,
    "walsh_normalization_denominator": 64,
    "dyadic_weight_shift": 128,
    "dyadic_weight_formula": "delta=q*T+r; weight=(2*T-r)*2^(127-q); require 0<=q<128",
    "rational_encoding": "reduced_decimal_numerator_denominator"
  },
  "q20": {
    "fractional_bits": 20,
    "ising_walsh": {
      "spin_convention": "s_i=(-1)^bit_i",
      "hamiltonian": "loss(mask)=sum_A coupling_numerator[A]*product_(i in A)s_i/64",
      "normalization_denominator": 64,
      "coupling_numerators": [
        "111721475788",
        "144",
        "-16",
        "-44",
        "4",
        "24",
        "-8",
        "20",
        "132",
        "16",
        "12",
        "8",
        "-4",
        "0",
        "4",
        "0",
        "460",
        "-4",
        "-8",
        "0",
        "-4",
        "-4",
        "0",
        "0",
        "-8",
        "0",
        "0",
        "0",
        "0",
        "0",
        "0",
        "0",
        "1896",
        "4",
        "-12",
        "8",
        "-24",
        "-12",
        "20",
        "0",
        "12",
        "-16",
        "-4",
        "-8",
        "20",
        "0",
        "-12",
        "0",
        "16",
        "-8",
        "-12",
        "-4",
        "24",
        "0",
        "-12",
        "4",
        "16",
        "0",
        "0",
        "0",
        "-8",
        "0",
        "0",
        "0"
      ],
      "energy_numerator_squared_by_order": [
        "12481688152248670220944",
        "3844848",
        "4288",
        "2816",
        "432",
        "16",
        "0"
      ],
      "nonzero_couplings": 42,
      "ground_state_masks": [
        63
      ],
      "walsh_inversion_verified": true,
      "parseval_verified": true
    },
    "temperature_sweep": [
      {
        "temperature_units": "1",
        "maximum_energy_bucket": 86,
        "partition_weight": "507406268140334861026617274784211271680",
        "minimum_vertex_weight": "4398046511104",
        "maximum_vertex_weight": "340282366920938463463374607431768211456",
        "ground_state_probability": {
          "numerator": "38685626227668133590597632",
          "denominator": "57685414065001039151254335"
        },
        "expected_energy_above_ground": {
          "numerator": "73703143913473736341722826",
          "denominator": "57685414065001039151254335"
        },
        "selected_ground_state_overlap": {
          "numerator": "56415889077014167560794573",
          "denominator": "69222496878001246981505202"
        },
        "edwards_anderson_replica_overlap": {
          "numerator": "4616672619543092012242361927740611791258826896530939",
          "denominator": "6655213991701239423931529916564557758772007712584450"
        },
        "magnetic_susceptibility_per_spin": {
          "numerator": "395412733517460593729828023480055006866285869961781",
          "denominator": "798625679004148730871783589987746931052640925510134"
        },
        "spin_glass_susceptibility": {
          "numerator": "7054033645217511580886707376168692346887451619538093",
          "denominator": "1996564197510371827179458974969367327631602313775335"
        },
        "magnetization_by_atom": [
          {
            "numerator": "-44169722184023999685839233",
            "denominator": "57685414065001039151254335"
          },
          {
            "numerator": "-10230405544418849795019889",
            "denominator": "19228471355000346383751445"
          },
          {
            "numerator": "-13148641257548544187700414",
            "denominator": "19228471355000346383751445"
          },
          {
            "numerator": "-17468389872879741199795067",
            "denominator": "19228471355000346383751445"
          },
          {
            "numerator": "-11536399822300878734101133",
            "denominator": "11537082813000207830250867"
          },
          {
            "numerator": "-57685414065001038900081857",
            "denominator": "57685414065001039151254335"
          }
        ],
        "all_vertex_weights_positive": true
      },
      {
        "temperature_units": "2",
        "maximum_energy_bucket": 43,
        "partition_weight": "2175738540416433713348913932645429149696",
        "minimum_vertex_weight": "77371252455336267181195264",
        "maximum_vertex_weight": "680564733841876926926749214863536422912",
        "ground_state_probability": {
          "numerator": "8796093022208",
          "denominator": "28120761540889"
        },
        "expected_energy_above_ground": {
          "numerator": "92223150942251",
          "denominator": "28120761540889"
        },
        "selected_ground_state_overlap": {
          "numerator": "16823207948893",
          "denominator": "28120761540889"
        },
        "edwards_anderson_replica_overlap": {
          "numerator": "1087081540593120171076688039",
          "denominator": "2372331688918625656856730963"
        },
        "magnetic_susceptibility_per_spin": {
          "numerator": "800398901485671463248268748",
          "denominator": "2372331688918625656856730963"
        },
        "spin_glass_susceptibility": {
          "numerator": "1544563447418738270773067062",
          "denominator": "790777229639541885618910321"
        },
        "magnetization_by_atom": [
          {
            "numerator": "-13957033127999",
            "denominator": "28120761540889"
          },
          {
            "numerator": "-4039953616667",
            "denominator": "28120761540889"
          },
          {
            "numerator": "-9304509761587",
            "denominator": "28120761540889"
          },
          {
            "numerator": "-17768816601171",
            "denominator": "28120761540889"
          },
          {
            "numerator": "-27748173127527",
            "denominator": "28120761540889"
          },
          {
            "numerator": "-28120761458407",
            "denominator": "28120761540889"
          }
        ],
        "all_vertex_weights_positive": true
      },
      {
        "temperature_units": "4",
        "maximum_energy_bucket": 21,
        "partition_weight": "9259750751564353120952485091478979215360",
        "minimum_vertex_weight": "486777830487640090174734030864384",
        "maximum_vertex_weight": "1361129467683753853853498429727072845824",
        "ground_state_probability": {
          "numerator": "2097152",
          "denominator": "14266905"
        },
        "expected_energy_above_ground": {
          "numerator": "165998143",
          "denominator": "28533810"
        },
        "selected_ground_state_overlap": {
          "numerator": "3775720",
          "denominator": "8560143"
        },
        "edwards_anderson_replica_overlap": {
          "numerator": "87654665718001",
          "denominator": "271392771038700"
        },
        "magnetic_susceptibility_per_spin": {
          "numerator": "44859429707119",
          "denominator": "244253493934830"
        },
        "spin_glass_susceptibility": {
          "numerator": "849125462366627",
          "denominator": "610633734837075"
        },
        "magnetization_by_atom": [
          {
            "numerator": "-859384",
            "denominator": "2853381"
          },
          {
            "numerator": "-66356",
            "denominator": "2853381"
          },
          {
            "numerator": "-3825527",
            "denominator": "28533810"
          },
          {
            "numerator": "-3290583",
            "denominator": "9511270"
          },
          {
            "numerator": "-4004677",
            "denominator": "4755635"
          },
          {
            "numerator": "-4755277",
            "denominator": "4755635"
          }
        ],
        "all_vertex_weights_positive": true
      },
      {
        "temperature_units": "8",
        "maximum_energy_bucket": 10,
        "partition_weight": "34981957779069523485145942308927968378880",
        "minimum_vertex_weight": "1661534994731144841129758825350430720",
        "maximum_vertex_weight": "2722258935367507707706996859454145691648",
        "ground_state_probability": {
          "numerator": "4096",
          "denominator": "52635"
        },
        "expected_energy_above_ground": {
          "numerator": "160726",
          "denominator": "17545"
        },
        "selected_ground_state_overlap": {
          "numerator": "203333",
          "denominator": "631620"
        },
        "edwards_anderson_replica_overlap": {
          "numerator": "14812260493",
          "denominator": "66490637400"
        },
        "magnetic_susceptibility_per_spin": {
          "numerator": "53414902691",
          "denominator": "531925099200"
        },
        "spin_glass_susceptibility": {
          "numerator": "500706979",
          "denominator": "443270916"
        },
        "magnetization_by_atom": [
          {
            "numerator": "-8929",
            "denominator": "52635"
          },
          {
            "numerator": "-9",
            "denominator": "17545"
          },
          {
            "numerator": "-923",
            "denominator": "17545"
          },
          {
            "numerator": "-6121",
            "denominator": "35090"
          },
          {
            "numerator": "-1917",
            "denominator": "3509"
          },
          {
            "numerator": "-3467",
            "denominator": "3509"
          }
        ],
        "all_vertex_weights_positive": true
      },
      {
        "temperature_units": "16",
        "maximum_energy_bucket": 5,
        "partition_weight": "114664523828389982860174012248023644504064",
        "minimum_vertex_weight": "138239711561631250781995934269155835904",
        "maximum_vertex_weight": "5444517870735015415413993718908291383296",
        "ground_state_probability": {
          "numerator": "512",
          "denominator": "10783"
        },
        "expected_energy_above_ground": {
          "numerator": "164497",
          "denominator": "10783"
        },
        "selected_ground_state_overlap": {
          "numerator": "4795",
          "denominator": "21566"
        },
        "edwards_anderson_replica_overlap": {
          "numerator": "97464205",
          "denominator": "697638534"
        },
        "magnetic_susceptibility_per_spin": {
          "numerator": "607856821",
          "denominator": "11162216544"
        },
        "spin_glass_susceptibility": {
          "numerator": "357967273",
          "denominator": "348819267"
        },
        "magnetization_by_atom": [
          {
            "numerator": "-909",
            "denominator": "10783"
          },
          {
            "numerator": "1",
            "denominator": "263"
          },
          {
            "numerator": "-209",
            "denominator": "10783"
          },
          {
            "numerator": "-844",
            "denominator": "10783"
          },
          {
            "numerator": "-3215",
            "denominator": "10783"
          },
          {
            "numerator": "-9249",
            "denominator": "10783"
          }
        ],
        "all_vertex_weights_positive": true
      },
      {
        "temperature_units": "32",
        "maximum_energy_bucket": 2,
        "partition_weight": "350278161449241030827611236525076402667520",
        "minimum_vertex_weight": "1786482426334926933182716689016783110144",
        "maximum_vertex_weight": "10889035741470030830827987437816582766592",
        "ground_state_probability": {
          "numerator": "256",
          "denominator": "8235"
        },
        "expected_energy_above_ground": {
          "numerator": "207253",
          "denominator": "8235"
        },
        "selected_ground_state_overlap": {
          "numerator": "1088",
          "denominator": "8235"
        },
        "edwards_anderson_replica_overlap": {
          "numerator": "11707043",
          "denominator": "203445675"
        },
        "magnetic_susceptibility_per_spin": {
          "numerator": "5336413",
          "denominator": "180840600"
        },
        "spin_glass_susceptibility": {
          "numerator": "203952314",
          "denominator": "203445675"
        },
        "magnetization_by_atom": [
          {
            "numerator": "-367",
            "denominator": "8235"
          },
          {
            "numerator": "7",
            "denominator": "2745"
          },
          {
            "numerator": "-41",
            "denominator": "8235"
          },
          {
            "numerator": "-65",
            "denominator": "1647"
          },
          {
            "numerator": "-1139",
            "denominator": "8235"
          },
          {
            "numerator": "-1559",
            "denominator": "2745"
          }
        ],
        "all_vertex_weights_positive": true
      },
      {
        "temperature_units": "64",
        "maximum_energy_bucket": 1,
        "partition_weight": "948622168383846201520022561867911831486464",
        "minimum_vertex_weight": "9017482723404869281779427096941857603584",
        "maximum_vertex_weight": "21778071482940061661655974875633165533184",
        "ground_state_probability": {
          "numerator": "256",
          "denominator": "11151"
        },
        "expected_energy_above_ground": {
          "numerator": "123971",
          "denominator": "3717"
        },
        "selected_ground_state_overlap": {
          "numerator": "110",
          "denominator": "1593"
        },
        "edwards_anderson_replica_overlap": {
          "numerator": "237149",
          "denominator": "13816089"
        },
        "magnetic_susceptibility_per_spin": {
          "numerator": "728243",
          "denominator": "47369448"
        },
        "spin_glass_susceptibility": {
          "numerator": "373087682",
          "denominator": "373034403"
        },
        "magnetization_by_atom": [
          {
            "numerator": "-227",
            "denominator": "11151"
          },
          {
            "numerator": "17",
            "denominator": "11151"
          },
          {
            "numerator": "-13",
            "denominator": "11151"
          },
          {
            "numerator": "-205",
            "denominator": "11151"
          },
          {
            "numerator": "-695",
            "denominator": "11151"
          },
          {
            "numerator": "-3497",
            "denominator": "11151"
          }
        ],
        "all_vertex_weights_positive": true
      },
      {
        "temperature_units": "128",
        "maximum_energy_bucket": 0,
        "partition_weight": "2317322918731590936185581076610341520015360",
        "minimum_vertex_weight": "28924001188279769394386841631700297973760",
        "maximum_vertex_weight": "43556142965880123323311949751266331066368",
        "ground_state_probability": {
          "numerator": "64",
          "denominator": "3405"
        },
        "expected_energy_above_ground": {
          "numerator": "26401",
          "denominator": "681"
        },
        "selected_ground_state_overlap": {
          "numerator": "131",
          "denominator": "4086"
        },
        "edwards_anderson_replica_overlap": {
          "numerator": "80101",
          "denominator": "23188050"
        },
        "magnetic_susceptibility_per_spin": {
          "numerator": "13837921",
          "denominator": "1780842240"
        },
        "spin_glass_susceptibility": {
          "numerator": "34782343",
          "denominator": "34782075"
        },
        "magnetization_by_atom": [
          {
            "numerator": "-12",
            "denominator": "1135"
          },
          {
            "numerator": "4",
            "denominator": "3405"
          },
          {
            "numerator": "-1",
            "denominator": "3405"
          },
          {
            "numerator": "-11",
            "denominator": "1135"
          },
          {
            "numerator": "-23",
            "denominator": "681"
          },
          {
            "numerator": "-158",
            "denominator": "1135"
          }
        ],
        "all_vertex_weights_positive": true
      }
    ],
    "sigma_delta_residual": {
      "retained_walsh_degree": 3,
      "residual_characters": 22,
      "vertex_order": "binary_reflected_gray_code",
      "quantizer_denominator": 64,
      "rounding": "nearest_ties_away_from_zero",
      "trace_columns": [
        "step",
        "vertex_mask",
        "input_residual_numerator",
        "accumulator_before",
        "emitted_integer_residual",
        "accumulator_after"
      ],
      "residual_energy_numerator_squared": "448",
      "residual_oscillation_numerator": "96",
      "surrogate_minimizers": [
        63
      ],
      "selected_minimizer": 63,
      "exact_gap": "0",
      "input_sum_numerator": "0",
      "emitted_sum": "0",
      "final_accumulator": "0",
      "maximum_absolute_accumulator": "32",
      "conservation_verified": true,
      "bounded_carry_verified": true,
      "trace": [
        [
          0,
          0,
          "-40",
          "0",
          "-1",
          "24"
        ],
        [
          1,
          1,
          "-24",
          "24",
          "0",
          "0"
        ],
        [
          2,
          3,
          "8",
          "0",
          "0",
          "8"
        ],
        [
          3,
          2,
          "24",
          "8",
          "1",
          "-32"
        ],
        [
          4,
          6,
          "0",
          "-32",
          "-1",
          "32"
        ],
        [
          5,
          7,
          "-32",
          "32",
          "0",
          "0"
        ],
        [
          6,
          5,
          "48",
          "0",
          "1",
          "-16"
        ],
        [
          7,
          4,
          "16",
          "-16",
          "0",
          "0"
        ],
        [
          8,
          12,
          "-8",
          "0",
          "0",
          "-8"
        ],
        [
          9,
          13,
          "-8",
          "-8",
          "0",
          "-16"
        ],
        [
          10,
          15,
          "-8",
          "-16",
          "0",
          "-24"
        ],
        [
          11,
          14,
          "-8",
          "-24",
          "-1",
          "32"
        ],
        [
          12,
          10,
          "0",
          "32",
          "1",
          "-32"
        ],
        [
          13,
          11,
          "16",
          "-32",
          "0",
          "-16"
        ],
        [
          14,
          9,
          "0",
          "-16",
          "0",
          "-16"
        ],
        [
          15,
          8,
          "16",
          "-16",
          "0",
          "0"
        ],
        [
          16,
          24,
          "24",
          "0",
          "0",
          "24"
        ],
        [
          17,
          25,
          "8",
          "24",
          "1",
          "-32"
        ],
        [
          18,
          27,
          "-24",
          "-32",
          "-1",
          "8"
        ],
        [
          19,
          26,
          "-40",
          "8",
          "-1",
          "32"
        ],
        [
          20,
          30,
          "16",
          "32",
          "1",
          "-16"
        ],
        [
          21,
          31,
          "48",
          "-16",
          "1",
          "-32"
        ],
        [
          22,
          29,
          "-32",
          "-32",
          "-1",
          "0"
        ],
        [
          23,
          28,
          "0",
          "0",
          "0",
          "0"
        ],
        [
          24,
          20,
          "-8",
          "0",
          "0",
          "-8"
        ],
        [
          25,
          21,
          "-8",
          "-8",
          "0",
          "-16"
        ],
        [
          26,
          23,
          "-8",
          "-16",
          "0",
          "-24"
        ],
        [
          27,
          22,
          "-8",
          "-24",
          "-1",
          "32"
        ],
        [
          28,
          18,
          "16",
          "32",
          "1",
          "-16"
        ],
        [
          29,
          19,
          "0",
          "-16",
          "0",
          "-16"
        ],
        [
          30,
          17,
          "16",
          "-16",
          "0",
          "0"
        ],
        [
          31,
          16,
          "0",
          "0",
          "0",
          "0"
        ],
        [
          32,
          48,
          "0",
          "0",
          "0",
          "0"
        ],
        [
          33,
          49,
          "-16",
          "0",
          "0",
          "-16"
        ],
        [
          34,
          51,
          "0",
          "-16",
          "0",
          "-16"
        ],
        [
          35,
          50,
          "-16",
          "-16",
          "-1",
          "32"
        ],
        [
          36,
          54,
          "8",
          "32",
          "1",
          "-24"
        ],
        [
          37,
          55,
          "8",
          "-24",
          "0",
          "-16"
        ],
        [
          38,
          53,
          "8",
          "-16",
          "0",
          "-8"
        ],
        [
          39,
          52,
          "8",
          "-8",
          "0",
          "0"
        ],
        [
          40,
          60,
          "0",
          "0",
          "0",
          "0"
        ],
        [
          41,
          61,
          "32",
          "0",
          "1",
          "-32"
        ],
        [
          42,
          63,
          "-48",
          "-32",
          "-1",
          "-16"
        ],
        [
          43,
          62,
          "-16",
          "-16",
          "-1",
          "32"
        ],
        [
          44,
          58,
          "40",
          "32",
          "1",
          "8"
        ],
        [
          45,
          59,
          "24",
          "8",
          "1",
          "-32"
        ],
        [
          46,
          57,
          "-8",
          "-32",
          "-1",
          "24"
        ],
        [
          47,
          56,
          "-24",
          "24",
          "0",
          "0"
        ],
        [
          48,
          40,
          "-16",
          "0",
          "0",
          "-16"
        ],
        [
          49,
          41,
          "0",
          "-16",
          "0",
          "-16"
        ],
        [
          50,
          43,
          "-16",
          "-16",
          "-1",
          "32"
        ],
        [
          51,
          42,
          "0",
          "32",
          "1",
          "-32"
        ],
        [
          52,
          46,
          "8",
          "-32",
          "0",
          "-24"
        ],
        [
          53,
          47,
          "8",
          "-24",
          "0",
          "-16"
        ],
        [
          54,
          45,
          "8",
          "-16",
          "0",
          "-8"
        ],
        [
          55,
          44,
          "8",
          "-8",
          "0",
          "0"
        ],
        [
          56,
          36,
          "-16",
          "0",
          "0",
          "-16"
        ],
        [
          57,
          37,
          "-48",
          "-16",
          "-1",
          "0"
        ],
        [
          58,
          39,
          "32",
          "0",
          "1",
          "-32"
        ],
        [
          59,
          38,
          "0",
          "-32",
          "-1",
          "32"
        ],
        [
          60,
          34,
          "-24",
          "32",
          "0",
          "8"
        ],
        [
          61,
          35,
          "-8",
          "8",
          "0",
          "0"
        ],
        [
          62,
          33,
          "24",
          "0",
          "0",
          "24"
        ],
        [
          63,
          32,
          "40",
          "24",
          "1",
          "0"
        ]
      ]
    }
  },
  "q32": {
    "fractional_bits": 32,
    "ising_walsh": {
      "spin_convention": "s_i=(-1)^bit_i",
      "hamiltonian": "loss(mask)=sum_A coupling_numerator[A]*product_(i in A)s_i/64",
      "normalization_denominator": 64,
      "coupling_numerators": [
        "457611164635720",
        "554238",
        "-66808",
        "-199014",
        "17716",
        "66030",
        "-16680",
        "65694",
        "496538",
        "65840",
        "48634",
        "34180",
        "-14682",
        "0",
        "16082",
        "0",
        "1841016",
        "14",
        "8",
        "2",
        "-16",
        "2",
        "-4",
        "2",
        "-2",
        "4",
        "-2",
        "0",
        "-2",
        "0",
        "2",
        "0",
        "8328716",
        "-22",
        "20",
        "14",
        "32",
        "10",
        "-4",
        "2",
        "-6",
        "-8",
        "-6",
        "-4",
        "-10",
        "0",
        "2",
        "0",
        "-20",
        "10",
        "-12",
        "-10",
        "-28",
        "-10",
        "8",
        "-2",
        "22",
        "4",
        "6",
        "0",
        "-2",
        "0",
        "2",
        "0"
      ],
      "energy_numerator_squared_by_order": [
        "209407977999260034760299918400",
        "73315357032520",
        "51160491040",
        "5742606832",
        "352",
        "8",
        "0"
      ],
      "nonzero_couplings": 54,
      "ground_state_masks": [
        63
      ],
      "walsh_inversion_verified": true,
      "parseval_verified": true
    },
    "temperature_sweep": [
      {
        "temperature_units": "4096",
        "maximum_energy_bucket": 87,
        "partition_weight": "4702436592500050435547908145094220341837824",
        "minimum_vertex_weight": "8939029533818880",
        "maximum_vertex_weight": "1393796574908163946345982392040522594123776",
        "ground_state_probability": {
          "numerator": "79228162514264337593543950336",
          "denominator": "267302572893871140169489316639"
        },
        "expected_energy_above_ground": {
          "numerator": "9180480399871930993449937507729505",
          "denominator": "2138420583150969121355914533112"
        },
        "selected_ground_state_overlap": {
          "numerator": "4072411968653412670227926355391",
          "denominator": "6415261749452907364067743599336"
        },
        "edwards_anderson_replica_overlap": {
          "numerator": "3851950701271608906651623110174985436405819118086930468455533",
          "denominator": "6859263885665596263048925032591072807223144835976499416606816"
        },
        "magnetic_susceptibility_per_spin": {
          "numerator": "3553470663728036663418478364202617061370691007983281043671175",
          "denominator": "28095544875686282293448396933493034218386001248159741610421518336"
        },
        "spin_glass_susceptibility": {
          "numerator": "8351942932964826185948473928339884547337495615770622539058949",
          "denominator": "3429631942832798131524462516295536403611572417988249708303408"
        },
        "magnetization_by_atom": [
          {
            "numerator": "-217410506434538147322380588977",
            "denominator": "267302572893871140169489316639"
          },
          {
            "numerator": "-96776647167623003710545588949",
            "denominator": "534605145787742280338978633278"
          },
          {
            "numerator": "7712941232011600167310966947",
            "denominator": "1069210291575484560677957266556"
          },
          {
            "numerator": "-219658924877024336029979293883",
            "denominator": "267302572893871140169489316639"
          },
          {
            "numerator": "-267270899682110942261258495201",
            "denominator": "267302572893871140169489316639"
          },
          {
            "numerator": "-267302572893871140129918158049",
            "denominator": "267302572893871140169489316639"
          }
        ],
        "all_vertex_weights_positive": true
      },
      {
        "temperature_units": "8192",
        "maximum_energy_bucket": 43,
        "partition_weight": "15734947087042069538047247028945202972721152",
        "minimum_vertex_weight": "236485233129735300639323324416",
        "maximum_vertex_weight": "2787593149816327892691964784081045188247552",
        "ground_state_probability": {
          "numerator": "144115188075855872",
          "denominator": "813477698121808597"
        },
        "expected_energy_above_ground": {
          "numerator": "119778237758113845695",
          "denominator": "13335699969209977"
        },
        "selected_ground_state_overlap": {
          "numerator": "422510431327645843",
          "denominator": "813477698121808597"
        },
        "edwards_anderson_replica_overlap": {
          "numerator": "284518696154289971310509281939841381",
          "denominator": "661745965341556358183176746303108409"
        },
        "magnetic_susceptibility_per_spin": {
          "numerator": "299850002386576836478214960202777913",
          "denominator": "4065767211058522264677437929286298064896"
        },
        "spin_glass_susceptibility": {
          "numerator": "3499273895724699647064758361183644474",
          "denominator": "1985237896024669074549530238909325227"
        },
        "magnetization_by_atom": [
          {
            "numerator": "-458808335332751035",
            "denominator": "813477698121808597"
          },
          {
            "numerator": "-23782075739845489",
            "denominator": "813477698121808597"
          },
          {
            "numerator": "932583425797779",
            "denominator": "813477698121808597"
          },
          {
            "numerator": "-438876388538055555",
            "denominator": "813477698121808597"
          },
          {
            "numerator": "-801050674103904043",
            "denominator": "813477698121808597"
          },
          {
            "numerator": "-813477697677116715",
            "denominator": "813477698121808597"
          }
        ],
        "all_vertex_weights_positive": true
      },
      {
        "temperature_units": "16384",
        "maximum_energy_bucket": 21,
        "partition_weight": "52590892613506803046950997420912403359465472",
        "minimum_vertex_weight": "1656504957149439226864619907031498752",
        "maximum_vertex_weight": "5575186299632655785383929568162090376495104",
        "ground_state_probability": {
          "numerator": "68719476736",
          "denominator": "648232799273"
        },
        "expected_energy_above_ground": {
          "numerator": "11216213528701617",
          "denominator": "648232799273"
        },
        "selected_ground_state_overlap": {
          "numerator": "798288195895",
          "denominator": "1944698397819"
        },
        "edwards_anderson_replica_overlap": {
          "numerator": "398979807611274929394347",
          "denominator": "1260617286159928527985587"
        },
        "magnetic_susceptibility_per_spin": {
          "numerator": "27263762119104865368431",
          "denominator": "645436050513883406328620544"
        },
        "spin_glass_susceptibility": {
          "numerator": "568265728990917827308134",
          "denominator": "420205762053309509328529"
        },
        "magnetization_by_atom": [
          {
            "numerator": "-209910828187",
            "denominator": "648232799273"
          },
          {
            "numerator": "8178999303",
            "denominator": "648232799273"
          },
          {
            "numerator": "-5649207325",
            "denominator": "648232799273"
          },
          {
            "numerator": "-198603020271",
            "denominator": "648232799273"
          },
          {
            "numerator": "-542380972535",
            "denominator": "648232799273"
          },
          {
            "numerator": "-648211362775",
            "denominator": "648232799273"
          }
        ],
        "all_vertex_weights_positive": true
      },
      {
        "temperature_units": "32768",
        "maximum_energy_bucket": 10,
        "partition_weight": "169108117763662162448364479873138939096203264",
        "minimum_vertex_weight": "6114781087609559244325738429054655135744",
        "maximum_vertex_weight": "11150372599265311570767859136324180752990208",
        "ground_state_probability": {
          "numerator": "33554432",
          "denominator": "508891231"
        },
        "expected_energy_above_ground": {
          "numerator": "14993598439841",
          "denominator": "508891231"
        },
        "selected_ground_state_overlap": {
          "numerator": "157104329",
          "denominator": "508891231"
        },
        "edwards_anderson_replica_overlap": {
          "numerator": "57521298841601092",
          "denominator": "258970284988695361"
        },
        "magnetic_susceptibility_per_spin": {
          "numerator": "301903159223576231",
          "denominator": "12728907447764354383872"
        },
        "spin_glass_susceptibility": {
          "numerator": "870947645269975582",
          "denominator": "776910854966086083"
        },
        "magnetization_by_atom": [
          {
            "numerator": "-88162274",
            "denominator": "508891231"
          },
          {
            "numerator": "387943",
            "denominator": "26783749"
          },
          {
            "numerator": "-1988940",
            "denominator": "508891231"
          },
          {
            "numerator": "-78894351",
            "denominator": "508891231"
          },
          {
            "numerator": "-276173181",
            "denominator": "508891231"
          },
          {
            "numerator": "-504778145",
            "denominator": "508891231"
          }
        ],
        "all_vertex_weights_positive": true
      },
      {
        "temperature_units": "65536",
        "maximum_energy_bucket": 5,
        "partition_weight": "503500048371970652144839275849824256483393536",
        "minimum_vertex_weight": "544122138530546882404919227739879612874752",
        "maximum_vertex_weight": "22300745198530623141535718272648361505980416",
        "ground_state_probability": {
          "numerator": "2097152",
          "denominator": "47348917"
        },
        "expected_energy_above_ground": {
          "numerator": "2493334469509",
          "denominator": "47348917"
        },
        "selected_ground_state_overlap": {
          "numerator": "31286614",
          "denominator": "142046751"
        },
        "edwards_anderson_replica_overlap": {
          "numerator": "326880697437020",
          "denominator": "2241919941072889"
        },
        "magnetic_susceptibility_per_spin": {
          "numerator": "2875570605610643",
          "denominator": "220389697887229280256"
        },
        "spin_glass_susceptibility": {
          "numerator": "2301059689910994",
          "denominator": "2241919941072889"
        },
        "magnetization_by_atom": [
          {
            "numerator": "-3714148",
            "denominator": "47348917"
          },
          {
            "numerator": "361621",
            "denominator": "47348917"
          },
          {
            "numerator": "-96730",
            "denominator": "47348917"
          },
          {
            "numerator": "-304207",
            "denominator": "4304447"
          },
          {
            "numerator": "-1281305",
            "denominator": "4304447"
          },
          {
            "numerator": "-41683339",
            "denominator": "47348917"
          }
        ],
        "all_vertex_weights_positive": true
      },
      {
        "temperature_units": "131072",
        "maximum_energy_bucket": 2,
        "partition_weight": "1466767321164832102093379503763753974982770688",
        "minimum_vertex_weight": "7140570258060702951931318606000082091245568",
        "maximum_vertex_weight": "44601490397061246283071436545296723011960832",
        "ground_state_probability": {
          "numerator": "524288",
          "denominator": "17241767"
        },
        "expected_energy_above_ground": {
          "numerator": "1636178148297",
          "denominator": "17241767"
        },
        "selected_ground_state_overlap": {
          "numerator": "13853701",
          "denominator": "103450602"
        },
        "edwards_anderson_replica_overlap": {
          "numerator": "37391884738827",
          "denominator": "594557058564578"
        },
        "magnetic_susceptibility_per_spin": {
          "numerator": "1667576332134217",
          "denominator": "233789348340529102848"
        },
        "spin_glass_susceptibility": {
          "numerator": "894132432676321",
          "denominator": "891835587846867"
        },
        "magnetization_by_atom": [
          {
            "numerator": "-693750",
            "denominator": "17241767"
          },
          {
            "numerator": "82589",
            "denominator": "17241767"
          },
          {
            "numerator": "-23057",
            "denominator": "17241767"
          },
          {
            "numerator": "-621613",
            "denominator": "17241767"
          },
          {
            "numerator": "-2302221",
            "denominator": "17241767"
          },
          {
            "numerator": "-10295649",
            "denominator": "17241767"
          }
        ],
        "all_vertex_weights_positive": true
      },
      {
        "temperature_units": "262144",
        "maximum_energy_bucket": 1,
        "partition_weight": "3903094044467788828425219545616089047734681600",
        "minimum_vertex_weight": "36581885714652029045398355484648525688471552",
        "maximum_vertex_weight": "89202980794122492566142873090593446023921664",
        "ground_state_probability": {
          "numerator": "524288",
          "denominator": "22940325"
        },
        "expected_energy_above_ground": {
          "numerator": "1009001681857",
          "denominator": "7646775"
        },
        "selected_ground_state_overlap": {
          "numerator": "9742303",
          "denominator": "137641950"
        },
        "edwards_anderson_replica_overlap": {
          "numerator": "60069815302541",
          "denominator": "3157551066633750"
        },
        "magnetic_susceptibility_per_spin": {
          "numerator": "3097175258177441",
          "denominator": "827733066811637760000"
        },
        "spin_glass_susceptibility": {
          "numerator": "1579049825101889",
          "denominator": "1578775533316875"
        },
        "magnetization_by_atom": [
          {
            "numerator": "-83324",
            "denominator": "4588065"
          },
          {
            "numerator": "1967",
            "denominator": "917613"
          },
          {
            "numerator": "-2843",
            "denominator": "4588065"
          },
          {
            "numerator": "-124447",
            "denominator": "7646775"
          },
          {
            "numerator": "-1381703",
            "denominator": "22940325"
          },
          {
            "numerator": "-7605599",
            "denominator": "22940325"
          }
        ],
        "all_vertex_weights_positive": true
      },
      {
        "temperature_units": "524288",
        "maximum_energy_bucket": 0,
        "partition_weight": "9489052833131244223216240895412950626383953920",
        "minimum_vertex_weight": "117765261826365304373868147514593774388903936",
        "maximum_vertex_weight": "178405961588244985132285746181186892047843328",
        "ground_state_probability": {
          "numerator": "131072",
          "denominator": "6971455"
        },
        "expected_energy_above_ground": {
          "numerator": "1091647100384",
          "denominator": "6971455"
        },
        "selected_ground_state_overlap": {
          "numerator": "1396427",
          "denominator": "41828730"
        },
        "edwards_anderson_replica_overlap": {
          "numerator": "1832883925813",
          "denominator": "466571374243440"
        },
        "magnetic_susceptibility_per_spin": {
          "numerator": "96581335564617",
          "denominator": "50962035970696806400"
        },
        "spin_glass_susceptibility": {
          "numerator": "58321741533499",
          "denominator": "58321421780430"
        },
        "magnetization_by_atom": [
          {
            "numerator": "-277119",
            "denominator": "27885820"
          },
          {
            "numerator": "8351",
            "denominator": "6971455"
          },
          {
            "numerator": "-4429",
            "denominator": "13942910"
          },
          {
            "numerator": "-8561",
            "denominator": "961580"
          },
          {
            "numerator": "-230127",
            "denominator": "6971455"
          },
          {
            "numerator": "-2082179",
            "denominator": "13942910"
          }
        ],
        "all_vertex_weights_positive": true
      }
    ],
    "sigma_delta_residual": {
      "retained_walsh_degree": 3,
      "residual_characters": 22,
      "vertex_order": "binary_reflected_gray_code",
      "quantizer_denominator": 64,
      "rounding": "nearest_ties_away_from_zero",
      "trace_columns": [
        "step",
        "vertex_mask",
        "input_residual_numerator",
        "accumulator_before",
        "emitted_integer_residual",
        "accumulator_after"
      ],
      "residual_energy_numerator_squared": "360",
      "residual_oscillation_numerator": "76",
      "surrogate_minimizers": [
        63
      ],
      "selected_minimizer": 63,
      "exact_gap": "0",
      "input_sum_numerator": "0",
      "emitted_sum": "0",
      "final_accumulator": "0",
      "maximum_absolute_accumulator": "32",
      "conservation_verified": true,
      "bounded_carry_verified": true,
      "trace": [
        [
          0,
          0,
          "0",
          "0",
          "0",
          "0"
        ],
        [
          1,
          1,
          "36",
          "0",
          "1",
          "-28"
        ],
        [
          2,
          3,
          "-28",
          "-28",
          "-1",
          "8"
        ],
        [
          3,
          2,
          "-16",
          "8",
          "0",
          "-8"
        ],
        [
          4,
          6,
          "40",
          "-8",
          "1",
          "-32"
        ],
        [
          5,
          7,
          "-20",
          "-32",
          "-1",
          "12"
        ],
        [
          6,
          5,
          "-4",
          "12",
          "0",
          "8"
        ],
        [
          7,
          4,
          "-8",
          "8",
          "0",
          "0"
        ],
        [
          8,
          12,
          "-12",
          "0",
          "0",
          "-12"
        ],
        [
          9,
          13,
          "-8",
          "-12",
          "0",
          "-20"
        ],
        [
          10,
          15,
          "-8",
          "-20",
          "0",
          "-28"
        ],
        [
          11,
          14,
          "20",
          "-28",
          "0",
          "-8"
        ],
        [
          12,
          10,
          "-4",
          "-8",
          "0",
          "-12"
        ],
        [
          13,
          11,
          "16",
          "-12",
          "0",
          "4"
        ],
        [
          14,
          9,
          "16",
          "4",
          "0",
          "20"
        ],
        [
          15,
          8,
          "-20",
          "20",
          "0",
          "0"
        ],
        [
          16,
          24,
          "28",
          "0",
          "0",
          "28"
        ],
        [
          17,
          25,
          "-32",
          "28",
          "0",
          "-4"
        ],
        [
          18,
          27,
          "0",
          "-4",
          "0",
          "-4"
        ],
        [
          19,
          26,
          "-4",
          "-4",
          "0",
          "-8"
        ],
        [
          20,
          30,
          "-28",
          "-8",
          "-1",
          "28"
        ],
        [
          21,
          31,
          "8",
          "28",
          "1",
          "-28"
        ],
        [
          22,
          29,
          "8",
          "-28",
          "0",
          "-20"
        ],
        [
          23,
          28,
          "20",
          "-20",
          "0",
          "0"
        ],
        [
          24,
          20,
          "-8",
          "0",
          "0",
          "-8"
        ],
        [
          25,
          21,
          "12",
          "-8",
          "0",
          "4"
        ],
        [
          26,
          23,
          "12",
          "4",
          "0",
          "16"
        ],
        [
          27,
          22,
          "-24",
          "16",
          "0",
          "-8"
        ],
        [
          28,
          18,
          "16",
          "-8",
          "0",
          "8"
        ],
        [
          29,
          19,
          "20",
          "8",
          "0",
          "28"
        ],
        [
          30,
          17,
          "-28",
          "28",
          "0",
          "0"
        ],
        [
          31,
          16,
          "0",
          "0",
          "0",
          "0"
        ],
        [
          32,
          48,
          "-8",
          "0",
          "0",
          "-8"
        ],
        [
          33,
          49,
          "28",
          "-8",
          "0",
          "20"
        ],
        [
          34,
          51,
          "-20",
          "20",
          "0",
          "0"
        ],
        [
          35,
          50,
          "-8",
          "0",
          "0",
          "-8"
        ],
        [
          36,
          54,
          "16",
          "-8",
          "0",
          "8"
        ],
        [
          37,
          55,
          "-12",
          "8",
          "0",
          "-4"
        ],
        [
          38,
          53,
          "-12",
          "-4",
          "0",
          "-16"
        ],
        [
          39,
          52,
          "16",
          "-16",
          "0",
          "0"
        ],
        [
          40,
          60,
          "-20",
          "0",
          "0",
          "-20"
        ],
        [
          41,
          61,
          "-16",
          "-20",
          "-1",
          "28"
        ],
        [
          42,
          63,
          "0",
          "28",
          "0",
          "28"
        ],
        [
          43,
          62,
          "28",
          "28",
          "1",
          "-8"
        ],
        [
          44,
          58,
          "4",
          "-8",
          "0",
          "-4"
        ],
        [
          45,
          59,
          "-8",
          "-4",
          "0",
          "-12"
        ],
        [
          46,
          57,
          "40",
          "-12",
          "0",
          "28"
        ],
        [
          47,
          56,
          "-28",
          "28",
          "0",
          "0"
        ],
        [
          48,
          40,
          "20",
          "0",
          "0",
          "20"
        ],
        [
          49,
          41,
          "-24",
          "20",
          "0",
          "-4"
        ],
        [
          50,
          43,
          "-8",
          "-4",
          "0",
          "-12"
        ],
        [
          51,
          42,
          "4",
          "-12",
          "0",
          "-8"
        ],
        [
          52,
          46,
          "-20",
          "-8",
          "0",
          "-28"
        ],
        [
          53,
          47,
          "0",
          "-28",
          "0",
          "-28"
        ],
        [
          54,
          45,
          "16",
          "-28",
          "0",
          "-12"
        ],
        [
          55,
          44,
          "12",
          "-12",
          "0",
          "0"
        ],
        [
          56,
          36,
          "0",
          "0",
          "0",
          "0"
        ],
        [
          57,
          37,
          "4",
          "0",
          "0",
          "4"
        ],
        [
          58,
          39,
          "20",
          "4",
          "0",
          "24"
        ],
        [
          59,
          38,
          "-32",
          "24",
          "0",
          "-8"
        ],
        [
          60,
          34,
          "8",
          "-8",
          "0",
          "0"
        ],
        [
          61,
          35,
          "28",
          "0",
          "0",
          "28"
        ],
        [
          62,
          33,
          "-36",
          "28",
          "0",
          "-8"
        ],
        [
          63,
          32,
          "8",
          "-8",
          "0",
          "0"
        ]
      ]
    }
  },
  "gates": {
    "proposal_only_firewall_verified": true,
    "integer_walsh_reconstruction_verified": true,
    "temperature_sweeps_verified": true,
    "overlap_and_susceptibility_metrics_verified": true,
    "sigma_delta_conservation_verified": true,
    "optimizer_control_tuple_matches": true
  },
  "decision": {
    "audit_contract_passed": true,
    "structure_certificate_selected": false,
    "default_optimizer": "integer_residual_sgd",
    "optimizer_change_authorized": false,
    "paid_scaling_authorized": false
  }
}
