{
  "status": "PASS",
  "checks": 15285,
  "arithmetic": "Fraction identities; 80-place outward integer fixed point",
  "gaussian_matrices": 182,
  "unit_normals": 13,
  "finite_angle_null_models": 9,
  "specific_projection": {
    "det": "3",
    "d": "74/25",
    "b": "-7/25",
    "c": "26/25",
    "mean": "-1/2",
    "width": "75/26",
    "frequency": "26/75"
  },
  "budgets": {
    "1/2": {
      "tail": {
        "lower": "0.32239694194483444925236693456012945983779030342535985391105028650880450635005676",
        "upper": "0.32239694194483444925236693456012945983779030342535985391105028650880450635005719"
      },
      "noise": {
        "lower": "0.00070710678118654752440084436210484903928483593768847403658833986899536623923105",
        "upper": "0.00070710678118654752440084436210484903928483593768847403658833986899536623923106"
      },
      "triangle": {
        "lower": "0.32310404872602099677676777892223430887707513936304832794763862637779987258928781",
        "upper": "0.32310404872602099677676777892223430887707513936304832794763862637779987258928825"
      },
      "orthogonal": {
        "lower": "0.32239771738550034944085427642539514165095937797014167550553650082599326148310240",
        "upper": "0.32239771738550034944085427642539514165095937797014167550553650082599326148310289"
      },
      "center": {
        "lower": "0.54406187223400376323407870527197058058339563476214813000370902057084035477555975",
        "upper": "0.54406187223400376323407870527197058058339563476214813000370902057084035477556033"
      }
    },
    "3/4": {
      "tail": {
        "lower": "0.12078786450491177141621648300240223372804867364410991530420024441259408140593589",
        "upper": "0.12078786450491177141621648300240223372804867364410991530420024441259408140593622"
      },
      "noise": {
        "lower": "0.00086602540378443864676372317075293618347140262690519031402790348972596650845440",
        "upper": "0.00086602540378443864676372317075293618347140262690519031402790348972596650845441"
      },
      "triangle": {
        "lower": "0.12165388990869621006298020617315516991152007627101510561822814790232004791439029",
        "upper": "0.12165388990869621006298020617315516991152007627101510561822814790232004791439063"
      },
      "orthogonal": {
        "lower": "0.12079096908153740369418526893503955621736796155258370654674893537505274816863364",
        "upper": "0.12079096908153740369418526893503955621736796155258370654674893537505274816863411"
      },
      "center": {
        "lower": "0.82918016384707000304763088042280537291806716594150499898833080423954941045271684",
        "upper": "0.82918016384707000304763088042280537291806716594150499898833080423954941045271728"
      }
    },
    "1": {
      "tail": {
        "lower": "0.03055685464595455392688364987662469865960149807599774736828677313198005269764937",
        "upper": "0.03055685464595455392688364987662469865960149807599774736828677313198005269764954"
      },
      "noise": {
        "lower": "0.00100000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "0.00100000000000000000000000000000000000000000000000000000000000000000000000000000"
      },
      "triangle": {
        "lower": "0.03155685464595455392688364987662469865960149807599774736828677313198005269764937",
        "upper": "0.03155685464595455392688364987662469865960149807599774736828677313198005269764954"
      },
      "orthogonal": {
        "lower": "0.03057321320787192638216285428656422074860163250395003128634031218545176053617275",
        "upper": "0.03057321320787192638216285428656422074860163250395003128634031218545176053617308"
      },
      "center": {
        "lower": "0.95678608173622775022558226282827198872427189018936691701928031259894923424298196",
        "upper": "0.95678608173622775022558226282827198872427189018936691701928031259894923424298219"
      }
    },
    "5/4": {
      "tail": {
        "lower": "0.00521971690397085465312323716744259988623290094855137620506261638319990477987855",
        "upper": "0.00521971690397085465312323716744259988623290094855137620506261638319990477987863"
      },
      "noise": {
        "lower": "0.00111803398874989484820458683436563811772030917980576286213544862270526046281890",
        "upper": "0.00111803398874989484820458683436563811772030917980576286213544862270526046281891"
      },
      "triangle": {
        "lower": "0.00633775089272074950132782400180823800395321012835713906719806500590516524269745",
        "upper": "0.00633775089272074950132782400180823800395321012835713906719806500590516524269754"
      },
      "orthogonal": {
        "lower": "0.00533811245269328176003635120954622221207649777397519082086582193943095755761512",
        "upper": "0.00533811245269328176003635120954622221207649777397519082086582193943095755761887"
      },
      "center": {
        "lower": "0.99261820556265631516380430674757198325795523822024155507619310966836884013836007",
        "upper": "0.99261820556265631516380430674757198325795523822024155507619310966836884013836016"
      }
    },
    "3/2": {
      "tail": {
        "lower": "0.00060205782595976352395817054621493985917716015327483375069456063186020245948395",
        "upper": "0.00060205782595976352395817054621493985917716015327483375069456063186020245948397"
      },
      "noise": {
        "lower": "0.00122474487139158904909864203735294569598297374032833506421634628362548018872865",
        "upper": "0.00122474487139158904909864203735294569598297374032833506421634628362548018872866"
      },
      "triangle": {
        "lower": "0.00182680269735135257305681258356788555516013389360316881491090691548568264821260",
        "upper": "0.00182680269735135257305681258356788555516013389360316881491090691548568264821263"
      },
      "orthogonal": {
        "lower": "0.00136472474360194587387794957232206303707674414610271884301596887783245922653162",
        "upper": "0.00136472474360194587387794957232206303707674414610271884301596887783245922654262"
      },
      "center": {
        "lower": "0.99914856165719484196414754670439991423004967524383807540851837161133741652822634",
        "upper": "0.99914856165719484196414754670439991423004967524383807540851837161133741652822635"
      }
    },
    "2": {
      "tail": {
        "lower": "0.00000246592342839445324872171616194286585383578991091683032535968685302663354072",
        "upper": "0.00000246592342839445324872171616194286585383578991091683032535968685302663354073"
      },
      "noise": {
        "lower": "0.00141421356237309504880168872420969807856967187537694807317667973799073247846210",
        "upper": "0.00141421356237309504880168872420969807856967187537694807317667973799073247846211"
      },
      "triangle": {
        "lower": "0.00141667948580148950205041044037164094442350766528786490350203942484375911200282",
        "upper": "0.00141667948580148950205041044037164094442350766528786490350203942484375911200284"
      },
      "orthogonal": {
        "lower": "0.00141421571225126568548230931338795041055683642429194640307056501449058969802845",
        "upper": "0.00141421571225126568548230931338795041055683642429194640307056501449058969803906"
      },
      "center": {
        "lower": "0.99999651265764379100450822473373479187221179664492093884684887262441513254725373",
        "upper": "0.99999651265764379100450822473373479187221179664492093884684887262441513254725374"
      }
    },
    "3": {
      "tail": {
        "lower": "0.00000000000037161892063795360222348415554621745032933267818579410236464990059586",
        "upper": "0.00000000000037161892063795360222348415554621745032933267818579410236464990059588"
      },
      "noise": {
        "lower": "0.00173205080756887729352744634150587236694280525381038062805580697945193301690880",
        "upper": "0.00173205080756887729352744634150587236694280525381038062805580697945193301690881"
      },
      "triangle": {
        "lower": "0.00173205080794049621416539994372935652248902270413971330624160108181658291750466",
        "upper": "0.00173205080794049621416539994372935652248902270413971330624160108181658291750469"
      },
      "orthogonal": {
        "lower": "0.00173205080756887729356731255720019053250902666033611550461890406583122942531045",
        "upper": "0.00173205080756887729356731255720019053250902666033611550461890406583122942531912"
      },
      "center": {
        "lower": "0.99999999999947445148239935514447774716411265197324677806707192242782591704113005",
        "upper": "0.99999999999947445148239935514447774716411265197324677806707192242782591704113006"
      }
    },
    "4": {
      "tail": {
        "lower": "0.00000000000000000000010458354065562197178918008297289550115056522068081290435438",
        "upper": "0.00000000000000000000010458354065562197178918008297289550115056522068081290435439"
      },
      "noise": {
        "lower": "0.00200000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "0.00200000000000000000000000000000000000000000000000000000000000000000000000000000"
      },
      "triangle": {
        "lower": "0.00200000000000000000010458354065562197178918008297289550115056522068081290435438",
        "upper": "0.00200000000000000000010458354065562197178918008297289550115056522068081290435439"
      },
      "orthogonal": {
        "lower": "0.00200000000000000000000000000000000000000273442924401653346320633586058267891999",
        "upper": "0.00200000000000000000000000000000000000000273442924401653346320633586058267892250"
      },
      "center": {
        "lower": "0.99999999999999999999985209653840382143474579744548336844541113876440455186364587",
        "upper": "0.99999999999999999999985209653840382143474579744548336844541113876440455186364588"
      }
    }
  },
  "annulus_ratios_at_K_5_4": [
    {
      "epsilon": "5/8",
      "ratio_squared": "15/16"
    },
    {
      "epsilon": "5/16",
      "ratio_squared": "35/32"
    },
    {
      "epsilon": "5/32",
      "ratio_squared": "75/64"
    },
    {
      "epsilon": "5/64",
      "ratio_squared": "155/128"
    },
    {
      "epsilon": "5/128",
      "ratio_squared": "315/256"
    },
    {
      "epsilon": "5/256",
      "ratio_squared": "635/512"
    },
    {
      "epsilon": "5/512",
      "ratio_squared": "1275/1024"
    },
    {
      "epsilon": "5/1024",
      "ratio_squared": "2555/2048"
    },
    {
      "epsilon": "5/2048",
      "ratio_squared": "5115/4096"
    },
    {
      "epsilon": "5/4096",
      "ratio_squared": "10235/8192"
    },
    {
      "epsilon": "5/8192",
      "ratio_squared": "20475/16384"
    },
    {
      "epsilon": "5/16384",
      "ratio_squared": "40955/32768"
    }
  ],
  "abel_coefficients": [
    {
      "degree": 0,
      "C_n": "2",
      "D_n": "1/2"
    },
    {
      "degree": 1,
      "C_n": "4/3",
      "D_n": "3/8"
    },
    {
      "degree": 2,
      "C_n": "16/15",
      "D_n": "5/16"
    },
    {
      "degree": 3,
      "C_n": "32/35",
      "D_n": "35/128"
    },
    {
      "degree": 4,
      "C_n": "256/315",
      "D_n": "63/256"
    },
    {
      "degree": 5,
      "C_n": "512/693",
      "D_n": "231/1024"
    },
    {
      "degree": 6,
      "C_n": "2048/3003",
      "D_n": "429/2048"
    },
    {
      "degree": 7,
      "C_n": "4096/6435",
      "D_n": "6435/32768"
    },
    {
      "degree": 8,
      "C_n": "65536/109395",
      "D_n": "12155/65536"
    }
  ],
  "layer_interior_checks": 133,
  "layer_values": {
    "1/2": "2",
    "3/2": "1",
    "3": "0"
  },
  "rejected_contracts": 12,
  "scope": "Continuous full-angle analytic data. Finite algebraic checks supplement the general proofs, not a finite-angle scanner certificate."
}
