{
  "status": "PASS",
  "checks": 3856,
  "arithmetic": "80-place integer outward intervals; rational Machin bounds; integer sqrt(2); reduced Taylor remainder",
  "energy": "8/3",
  "critical": {
    "first_N": 48,
    "N47_squared_bound": {
      "lower": "0.00000105471630290622413804548466957481551145857102734597795280229215460658109024",
      "upper": "0.00000105471630290622413804548466957481551145857102734597795280229215460658109056"
    },
    "N48_squared_bound": {
      "lower": "0.00000099016032549038726747229776881931849361765064174751762328009601388634863744",
      "upper": "0.00000099016032549038726747229776881931849361765064174751762328009601388634863776"
    },
    "target_t1": {
      "lower": "0.81056946913870217155103570567782111123487019737797239076487225515338496769788344",
      "upper": "0.81056946913870217155103570567782111123487019737797239076487225515338496769788360"
    }
  },
  "undersampling": {
    "spectral_positive_endpoints": [
      "7/60",
      "13/60"
    ],
    "g_at_3_over_2": {
      "lower": "0.96339776200411591821438218317520328304632181896265956529994672770319528513255410",
      "upper": "0.96339776200411591821438218317520328304632181896265956529994672770319528513255518"
    }
  },
  "localized": {
    "first_N": 24,
    "N23_total_bound": {
      "lower": "0.00010631761713350710521182003630505383829877091550275872888168201272255195161909",
      "upper": "0.00010631761713350710521182003630505383829877091550275872888168201272255195162166"
    },
    "N24_total_bound": {
      "lower": "0.00009768734490554585026475812837477101692857574699318029961287231254332786184245",
      "upper": "0.00009768734490554585026475812837477101692857574699318029961287231254332786184502"
    },
    "noise_bound": {
      "lower": "0.00003431708407416106514653107117033463333704610592133917172294616765460154903093",
      "upper": "0.00003431708407416106514653107117033463333704610592133917172294616765460154903094"
    },
    "generic_tail_N24": {
      "lower": "0.01842203338951595844434172058358684343715614084949937251738346034439511290222462",
      "upper": "0.01842203338951595844434172058358684343715614084949937251738346034439511290222464"
    },
    "sample_decay_tail_N24": {
      "lower": "0.00006337026083138478511822705720443638359152964107184112788992614488872631281152",
      "upper": "0.00006337026083138478511822705720443638359152964107184112788992614488872631281408"
    },
    "half_point_partial": {
      "lower": "0.94964395404299174001738769525305219184232350413037971887790171888109273304503902",
      "upper": "0.94964395404299174001738769525305219184232350413037971887790171888109273304503988"
    },
    "half_point_target": {
      "lower": "0.94964120355178363474056626458030184027898429624660004405221696027531718082667592",
      "upper": "0.94964120355178363474056626458030184027898429624660004405221696027531718082667613"
    },
    "half_point_coefficients_A_B": [
      "4",
      "127270252527346649625212868005184052672/4907891830652163613824240024222249375"
    ],
    "half_point_evaluation_width_budget": "1/10000000000000000000000000000000000000000000000000000000000000000000000"
  },
  "adversarial_noise": [
    {
      "N": 4,
      "sinc_noise": {
        "lower": "0.00002204927529057242048556853153516357701328196488924926801062921553882621031351",
        "upper": "0.00002204927529057242048556853153516357701328196488924926801062921553882621031352"
      },
      "localized_adversarial_noise": {
        "lower": "0.00001350010064896840498495104228093893518475733476771253739873385172682859762004",
        "upper": "0.00001350010064896840498495104228093893518475733476771253739873385172682859762005"
      }
    },
    {
      "N": 8,
      "sinc_noise": {
        "lower": "0.00002611684470502504314250967126721175612521965542306706368380146534195821838241",
        "upper": "0.00002611684470502504314250967126721175612521965542306706368380146534195821838243"
      },
      "localized_adversarial_noise": {
        "lower": "0.00001380420755887445374118889071705586119467128900371558972299039447703836839610",
        "upper": "0.00001380420755887445374118889071705586119467128900371558972299039447703836839611"
      }
    },
    {
      "N": 16,
      "sinc_noise": {
        "lower": "0.00003034489161095078920058654797541878354795709003600891088191426228724723336205",
        "upper": "0.00003034489161095078920058654797541878354795709003600891088191426228724723336207"
      },
      "localized_adversarial_noise": {
        "lower": "0.00001396834477853865050133663203691591650080169706237816232110237879338706328928",
        "upper": "0.00001396834477853865050133663203691591650080169706237816232110237879338706328929"
      }
    },
    {
      "N": 32,
      "sinc_noise": {
        "lower": "0.00003466185357378009497367784515128883131677979151145930217510073171562787293593",
        "upper": "0.00003466185357378009497367784515128883131677979151145930217510073171562787293594"
      },
      "localized_adversarial_noise": {
        "lower": "0.00001405394337904568796933019464041326421463057515393371911531977330767512144088",
        "upper": "0.00001405394337904568796933019464041326421463057515393371911531977330767512144089"
      }
    },
    {
      "N": 64,
      "sinc_noise": {
        "lower": "0.00003902578020388701734793194506847201147673242224308198327057905762892171018926",
        "upper": "0.00003902578020388701734793194506847201147673242224308198327057905762892171018928"
      },
      "localized_adversarial_noise": {
        "lower": "0.00001409770290056235562988085488745581083945660182149439149288689190481713475266",
        "upper": "0.00001409770290056235562988085488745581083945660182149439149288689190481713475267"
      }
    },
    {
      "N": 128,
      "sinc_noise": {
        "lower": "0.00004341386446671694430275187406707516916190666889013728507927240860384898250783",
        "upper": "0.00004341386446671694430275187406707516916190666889013728507927240860384898250784"
      },
      "localized_adversarial_noise": {
        "lower": "0.00001411983348546744195230180593790507256916102723156264724352111904804168848273",
        "upper": "0.00001411983348546744195230180593790507256916102723156264724352111904804168848274"
      }
    },
    {
      "N": 256,
      "sinc_noise": {
        "lower": "0.00004781420287215659333500146232709716924619161788148172937160904324064048288716",
        "upper": "0.00004781420287215659333500146232709716924619161788148172937160904324064048288717"
      },
      "localized_adversarial_noise": {
        "lower": "0.00001413096290208985308298220036844296316843060961559377361844445935059209480448",
        "upper": "0.00001413096290208985308298220036844296316843060961559377361844445935059209480449"
      }
    }
  ],
  "invalid_contracts_rejected": 9,
  "scope": "Theorems and uniform tail/noise bounds are proved in the pages. Rational point evaluations are finite diagnostics, not a substitute for whole-window proofs."
}