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            "2673.09246937079767128841241083981814250746687773608178490278796226586695443353310673717763",
            "9746.8748380935392627468944772967993114586003094016764496251384029782855386729380462623144"
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          "psi_at_cutoff": "0.816490773684646540775155571422505458110132359616479533539606654088966440048851451608205287",
          "global_real_D_majorant": "0.000204403586082850372592060987910123259594880772112152474526922906123214426651885898921681591",
          "normalized_two_sided_tail_majorant_estimate": "5.01951831369375569672924393895883962781681579991420577598632708326309364673168031162762553e-138",
          "status": "analytic_formula_evaluated_without_outward_rounding"
        }
      },
      "tail_diagnostic": {
        "positive_numerator_coefficients": [
          "1.86660782618043566513149276265414234286623085430266162493278400011348348752212589320650512",
          "2673.09246937079767128841241083981814250746687773608178490278796226586695443353310673717763",
          "9746.8748380935392627468944772967993114586003094016764496251384029782855386729380462623144"
        ],
        "psi_at_cutoff": "1.03484514441437776908136357787191702952522604443912759096125321319165036912325273361427377",
        "global_real_D_majorant": "0.000204403586082850372592060987910123259594880772112152474526922906123214426651885898921681591",
        "normalized_two_sided_tail_majorant_estimate": "1.83817414616473693879410392617961671791535572950699484399405294204897146919276454164514304e-206",
        "status": "analytic_formula_evaluated_without_outward_rounding"
      },
      "panels": [
        0,
        2,
        4,
        6,
        8,
        10,
        12,
        14
      ],
      "integrand_evaluations": 1047,
      "elapsed_seconds": 18.254538999986835,
      "evidence_status": "uncertified_multiprecision_exact_integrand_quadrature",
      "setting": "90dps_C1_T14"
    },
    {
      "parameters": {
        "b": "1/160",
        "zeta": "-1",
        "contour_real": "5/4",
        "cutoff": 14,
        "digits": 90,
        "extra_terms": 2
      },
      "Q": "0.517966671856531011413677895359942125005538260412253146086420722770177679527794964523329602",
      "Airy_Q1": "0.538259870560441876157476167356942860456819235304293421502917559833756036351597524845974243",
      "Q_minus_Q1": "-0.0202931987039108647437982719970007354512809748920402754164968370635783568238025603226446413",
      "scaled_remainder": "-5.17675056001440178907649784558016104499407972312061734142013570063075227917911641332592392",
      "h": "0.000245436926061702596754894014318711162827903859326180142263667546274048156741110078017815221",
      "lambda": "0.0626104224857006573956936192401412419024262302425710615345716871855712548227089088695910309",
      "eta": "1.23142140143192566048390587227473243544555329218625492758942095617018305133084132690906677",
      "centered_real_arguments": [
        "0.112526480469465219769178771548720010543059391997638531557105554177237852512461734020577221",
        "0.191447653963494650198691627236330128193078677880815706208289926790485970443755344190308687",
        "0.975472991231655170327210032096129573248526398366998755146708002919590678618887031346765057",
        "0.911980997048879609903611196355150416208414209635362713296186442903171468868651234632657722",
        "0.303993665682959869967870398785050138736138069878454237765395480967723822956217078210885907"
      ],
      "centered_strip_epsilon_exact": "1/100",
      "D_terms": 27,
      "D_full_log_remainder_bound_exact": "17426083244385605675042740030061288117802734375/63133445163706719076992070078965590016935748900643599919117875262223932142827018923117802805701950340969573249736386977189521544911282091871690555392",
      "D_full_log_remainder_bound_decimal": "2.7601983701664472383665654974682565476554151345267610374429729662832125932193020310011567e-103",
      "D_propagated_error_estimate": "6.08191144738257370317818896848127445587572535348641325579704916374277733215637163022671617e-103",
      "normalized_absolute_integral_estimate": "2.20343273625504619412627638382504051532566106675725608378036353546462762878341583865901249",
      "quadrature_internal_error_estimate": "1.41471060526129187350133047881635095980302267746880185750276424072106598348411371915166136e-99",
      "absolute_quadrature_internal_error_estimate": "1.41471060526129187350118900775568321808714612265328286245823549566249279176998463290170318e-104",
      "quadrature_acceptance_threshold": "1.0e-75",
      "cutoff_comparison": {
        "shorter_cutoff": 12,
        "Q_at_shorter_cutoff": "0.517966671856531011413677895359942125005538260412253146086420722770177679527794964523329602",
        "extension_contribution": "-2.17244235209778623358905428693452289737447199171689945249160856184143810394881496019127985e-143",
        "shorter_tail_diagnostic": {
          "positive_numerator_coefficients": [
            "2.25892632101334843820373147142779744570458340482256412220086784926895445222100325976359429",
            "2484.33231352766304142864973435272012289589431118102079455392235762991900685021783253615687",
            "9044.77149071045949817483782639667553185507014455895158247052882856410358682328834239679087"
          ],
          "psi_at_cutoff": "0.824991328893943407066484661466679648890042247125789620825394454086120500633285310376133987",
          "global_real_D_majorant": "0.00020174985102045498664841377916276477927450885696411399381239168909008029442965044332222296",
          "normalized_two_sided_tail_majorant_estimate": "2.96755701923082806863555403853669940861046063913441802142266949682866794249145247696939876e-142",
          "status": "analytic_formula_evaluated_without_outward_rounding"
        }
      },
      "tail_diagnostic": {
        "positive_numerator_coefficients": [
          "2.25892632101334843820373147142779744570458340482256412220086784926895445222100325976359429",
          "2484.33231352766304142864973435272012289589431118102079455392235762991900685021783253615687",
          "9044.77149071045949817483782639667553185507014455895158247052882856410358682328834239679087"
        ],
        "psi_at_cutoff": "1.04142225647502597479349939296105251735056375037282254582436365585817049481538168998673136",
        "global_real_D_majorant": "0.00020174985102045498664841377916276477927450885696411399381239168909008029442965044332222296",
        "normalized_two_sided_tail_majorant_estimate": "3.03407549081653726256025231841761698212232103121138902295049782187630661984736868950054887e-211",
        "status": "analytic_formula_evaluated_without_outward_rounding"
      },
      "panels": [
        0,
        2,
        4,
        6,
        8,
        10,
        12,
        14
      ],
      "integrand_evaluations": 1047,
      "elapsed_seconds": 19.54814987501595,
      "evidence_status": "uncertified_multiprecision_exact_integrand_quadrature",
      "setting": "90dps_C5over4_T14_Kplus2"
    }
  ],
  "comparisons": [
    {
      "b": "0.0125",
      "zeta": "0",
      "low_high_precision_absolute_difference": "4.36288529590516197596476087059108170299913747863025002350064793005498834659316225396240061e-58",
      "low_high_acceptance_threshold": "1e-40",
      "changed_contour_and_D_terms_absolute_difference": "6.13636683162215819136971494373284455371901939062431195638943639648388156840214482057512236e-92",
      "changed_contour_acceptance_threshold": "1e-70",
      "historical_reported_Q": "0.459087",
      "new_minus_historical": "-0.000000511263921047940484529298912699521243527793320352977358255498283183314952299731522395314603",
      "compatible_with_nearest_six_decimal_rounding": false,
      "rounding_caveat": "historical rounding convention is unknown"
    },
    {
      "b": "0.00625",
      "zeta": "0",
      "low_high_precision_absolute_difference": "1.75971142620919521905358667736829343208291324965808237464752468303373572603461571290250474e-57",
      "low_high_acceptance_threshold": "1e-40",
      "changed_contour_and_D_terms_absolute_difference": "0.0",
      "changed_contour_acceptance_threshold": "1e-70",
      "historical_reported_Q": "0.422572",
      "new_minus_historical": "-0.00000000537185342321436830045337510050361050397215682544492481217675585072653892593529727655827559",
      "compatible_with_nearest_six_decimal_rounding": true,
      "rounding_caveat": "historical rounding convention is unknown"
    },
    {
      "b": "0.003125",
      "zeta": "0",
      "low_high_precision_absolute_difference": "2.71084559172720245811092214678875754516928154628011410314683738020132385522055903826360554e-57",
      "low_high_acceptance_threshold": "1e-40",
      "changed_contour_and_D_terms_absolute_difference": "0.0",
      "changed_contour_acceptance_threshold": "1e-70",
      "historical_reported_Q": "0.398047",
      "new_minus_historical": "-0.00000014014775145748396026731628455246245109228059778562837367861118215047006672946002005560459",
      "compatible_with_nearest_six_decimal_rounding": true,
      "rounding_caveat": "historical rounding convention is unknown"
    },
    {
      "b": "0.0125",
      "zeta": "1",
      "low_high_precision_absolute_difference": "3.82117052926822430134179601673493399495268993933958723823991044753192546445275309160889214e-58",
      "low_high_acceptance_threshold": "1e-40",
      "changed_contour_and_D_terms_absolute_difference": "0.0",
      "changed_contour_acceptance_threshold": "1e-70",
      "historical_reported_Q": "0.214333",
      "new_minus_historical": "-0.00000000513582353530359641425922623433705734887333189589650160306533280003442817122036430311324033",
      "compatible_with_nearest_six_decimal_rounding": true,
      "rounding_caveat": "historical rounding convention is unknown"
    },
    {
      "b": "0.00625",
      "zeta": "1",
      "low_high_precision_absolute_difference": "9.62286101867266872707191006085701705696676142241413139931377844202136516863620282829720813e-58",
      "low_high_acceptance_threshold": "1e-40",
      "changed_contour_and_D_terms_absolute_difference": "0.0",
      "changed_contour_acceptance_threshold": "1e-70",
      "historical_reported_Q": "0.182316",
      "new_minus_historical": "-0.0000000510458023649270735347996613154316269505543678081202283305830449900974612388816665739798852",
      "compatible_with_nearest_six_decimal_rounding": true,
      "rounding_caveat": "historical rounding convention is unknown"
    },
    {
      "b": "0.003125",
      "zeta": "1",
      "low_high_precision_absolute_difference": "2.66684751926272197363474833173927247110924846358295005750950153837032417979328934480990256e-57",
      "low_high_acceptance_threshold": "1e-40",
      "changed_contour_and_D_terms_absolute_difference": "0.0",
      "changed_contour_acceptance_threshold": "1e-70",
      "historical_reported_Q": "0.163805",
      "new_minus_historical": "-0.000000440935987256366991899582159562478835790026966241020146173847132985038465320242817774250815",
      "compatible_with_nearest_six_decimal_rounding": true,
      "rounding_caveat": "historical rounding convention is unknown"
    },
    {
      "b": "1/160",
      "zeta": "-1",
      "low_high_precision_absolute_difference": "3.96705306793319084462867951488734130322067120517265167717522780004000069938827373621162553e-57",
      "low_high_acceptance_threshold": "1e-40",
      "changed_contour_and_D_terms_absolute_difference": "1.22727336632443163827394298874656891074380387812486239127788727929677631368042896411502447e-91",
      "changed_contour_acceptance_threshold": "1e-70"
    }
  ],
  "elapsed_seconds": 418.11435445805546,
  "limitations": [
    "No interval arithmetic or outward-rounded quadrature was performed.",
    "The exact rational D bound controls the series truncation in the log, conditional on the declared centered strip; it does not bound floating-point evaluation error.",
    "Propagated D error uses a numerical absolute-integral estimate.",
    "Quadrature error estimates, tail formula evaluations, and sign checks are numerical diagnostics, not certificates.",
    "Agreement between precisions, contours, cutoffs, and independent formulas is finite numerical evidence and does not prove the asymptotic theorem.",
    "Historical values retain their original provenance and unknown rounding convention."
  ]
}