{
  "status": "PASS",
  "scope": "Arithmetic-engine validation and independent high-precision scalar diagnostics of the complete disk-bound certificate.",
  "summary": {
    "all_assertions_passed": true,
    "exact_sqrt_enclosure_cases": 305,
    "exact_cosine_enclosure_cases": 31,
    "Machin_tangent_identity_exact": true,
    "decimal_precisions": [
      80,
      120
    ],
    "negative_radical_rejected": true,
    "division_through_zero_rejected": true,
    "all_final_scalar_margins_positive": true
  },
  "diagnostics": [
    {
      "precision": 80,
      "positive_values": {
        "rotated_reward_contradiction_margin": "7.51216020030550947321128335408978435742416293813817123658781899267330060E-14",
        "additive_monotonicity_slack": "2.479715963450800150937565824608164866528055654793699088438884832080631125E-7",
        "final_eta_positive_for_W_at_most_delta": "0.006811175334759050138524753954243150393212490982089819551335168919133590765848515",
        "eta_positive_at_certified_initial_reward": "0.0068111752731781833076488989601615569743054731663172332888242391008909336402721985",
        "neighbor_branch_dominates_on_whole_eta_interval": "0.9154675927256917693359522174843174441464082489803547475479213412371757405963450",
        "opposed_second_derivative_positive_on_whole_eta_interval": "15.999985178323907818311575754936282890506378607698091619280815374196262913137468",
        "opposed_localized_projection_slack": "0.41221241613627959809438884594012527341676685146713275249522668939903727051299436",
        "neighbor_localized_projection_slack": "0.012186641748629311250339371776424639895186572978892481548941609154909368757969489",
        "near_coefficient_dominates_far": "1634.3164788549009945910600812537043948896705777914926750030048909641338969920805",
        "rotation_factor_gate_t_minus_cos_pi_over_4kappa": "9.3487083950610038538620620289733996870043348359430582632150856333296883E-10",
        "robust_missed_line_coefficient_upper_slack": "5.0499630697143263748405121627637448141922267645371144870388557087105285E-10"
      },
      "certified_initial_rotated_reward": "0.0000084450517751216020030550947321128335408978435742416293813817123658781899267330060",
      "robust_missed_line_coefficient": "0.50038830149500369302856736251594878372362551858077732354628855129611442912894715"
    },
    {
      "precision": 120,
      "positive_values": {
        "rotated_reward_contradiction_margin": "7.512160200305509473211283354089784357424162938138171236587818992673300554014650058710789209990523642449848427303E-14",
        "additive_monotonicity_slack": "2.4797159634508001509375658246081648665280556547936990884388848320806311252409948080304441808570724249447944354961E-7",
        "final_eta_positive_for_W_at_most_delta": "0.0068111753347590501385247539542431503932124909820898195513351689191335907658485151088952921128463039843926973862194375247",
        "eta_positive_at_certified_initial_reward": "0.0068111752731781833076488989601615569743054731663172332888242391008909336402721988883190087721143067183632591177793617546",
        "neighbor_branch_dominates_on_whole_eta_interval": "0.91546759272569176933595221748431744414640824898035474754792134123717574059634503592551858645278710348085908524640120786",
        "opposed_second_derivative_positive_on_whole_eta_interval": "15.9999851783239078183115757549362828905063786076980916192808153741962629131374691398268333190902068672708262016412852729",
        "opposed_localized_projection_slack": "0.412212416136279598094388845940125273416766851467132752495226689399037270512994363603117981242706656140775040961452139529",
        "neighbor_localized_projection_slack": "0.0121866417486293112503393717764246398951865729788924815489416091549093687579694887835303089670383694786808044264594017971",
        "near_coefficient_dominates_far": "1634.31647885490099459106008125370439488967057779149267500300489096413389699208046493504714767130232401534655407217243037",
        "rotation_factor_gate_t_minus_cos_pi_over_4kappa": "9.34870839506100385386206202897339968700433483594305826321508563332968844929778384047152132923731190320914575384E-10",
        "robust_missed_line_coefficient_upper_slack": "5.04996306971432637484051216276374481419222676453711448703885570871052851606991787821075089287994976729533361587E-10"
      },
      "certified_initial_rotated_reward": "0.00000844505177512160200305509473211283354089784357424162938138171236587818992673300554014650058710789209990523642449848427303",
      "robust_missed_line_coefficient": "0.500388301495003693028567362515948783723625518580777323546288551296114429128947148393008212178924910712005023270466638413"
    }
  ]
}