{
  "specified_environment_not_posterior_sample": true,
  "productive_candidates": 224,
  "singleton_witness_candidates": 248,
  "food_catalyst_candidates": 192,
  "product_catalyst_candidates": 32,
  "deterministic": {
    "window_export": 119.07466397465414,
    "deleted_window_export": 4.956263529315089e-05,
    "signed_local_input_0_to_100": 120.31367541466754,
    "local_input_over_window_export": 1.0104053322399225,
    "nonfood_balance_error": 4.263256414560601e-14,
    "mass_error": 7.105427357601002e-15,
    "independent_solver_max_difference": 3.261583003677515e-09
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  "proof_budgets": {
    "mixed_half_drift": "50589/12500000000",
    "mixed_noise_plus_drift": "21/2000",
    "mixed_export_contradiction_threshold": "3/100",
    "outsider_export_budget": "83950361/937500000",
    "outsider_export_threshold": "1/10",
    "other_input_budget": "3186831/156250000",
    "other_input_limit": "1/40",
    "washout_margin": 64
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  "bounds_at_simulation_volume": {
    "applicable": false,
    "reason": "Requires V>=2n/d and n/V<=1/200000; small simulations do not satisfy these."
  },
  "source_moments": [
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      "first_moment_bound_over_p": "4.0",
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        "scope": "Evaluated theorem inequalities, not interval-rounded probabilities. The huge fixed rectangle makes this finite-n posterior bound vacuous in the displayed range."
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        "applicable": true,
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        "scope": "Evaluated theorem inequalities, not interval-rounded probabilities. The huge fixed rectangle makes this finite-n posterior bound vacuous in the displayed range."
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      "first_moment_bound_over_p": "4.0",
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      "theorem_bounds": {
        "applicable": true,
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        "log10_success_lower": "-6.35124741386289121330582346305",
        "fixed_Kstar_multiplicity_upper": "1.0",
        "posterior_no_productive_candidate_upper": "1.0",
        "scope": "Evaluated theorem inequalities, not interval-rounded probabilities. The huge fixed rectangle makes this finite-n posterior bound vacuous in the displayed range."
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    },
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      "n": 32,
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      "actual_two_or_more_over_p": "0.29204806498824031727060237662202909",
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      "pair_count_bound_over_p": "0.29204806516649462182951546615595904",
      "first_moment_bound_over_p": "4.0",
      "wrong_independent_pair_bound_over_p": "0.00000000096857756963596772717299704776300422",
      "theorem_bounds": {
        "applicable": true,
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        "log10_deletion_probability_upper": "-1026360006059.81729832481655302",
        "log10_success_lower": "-11.1864505604411126698612489013",
        "fixed_Kstar_multiplicity_upper": "1.0",
        "posterior_no_productive_candidate_upper": "1.0",
        "scope": "Evaluated theorem inequalities, not interval-rounded probabilities. The huge fixed rectangle makes this finite-n posterior bound vacuous in the displayed range."
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    },
    {
      "n": 64,
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      "q2_over_p": "0.077252765531283997410056259532261146",
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      "conditional_mean_degree": "176707687347993938392.16665336161998",
      "actual_two_or_more_over_p": "0.15450553106256799492703433057047649",
      "excess_count_bound_over_p": "0.15450553106256799493637695111668174",
      "pair_count_bound_over_p": "0.15450553106256799494590725709068665",
      "first_moment_bound_over_p": "4.0",
      "wrong_independent_pair_bound_over_p": "1.886921070392465414187427071636314e-19",
      "theorem_bounds": {
        "applicable": true,
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        "log10_deletion_probability_upper": "-1990987615061.50619936850242218",
        "log10_success_lower": "-20.8468523809624059906589719308",
        "fixed_Kstar_multiplicity_upper": "1.0",
        "posterior_no_productive_candidate_upper": "1.0",
        "scope": "Evaluated theorem inequalities, not interval-rounded probabilities. The huge fixed rectangle makes this finite-n posterior bound vacuous in the displayed range."
      }
    },
    {
      "n": 128,
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      "conditional_mean_degree": "3.4246041877603613199126668399058101e+39",
      "actual_two_or_more_over_p": "0.079873072946719308112076368831738576",
      "excess_count_bound_over_p": "0.079873072946719308112076368831738576",
      "pair_count_bound_over_p": "0.079873072946719308112076368831738576",
      "first_moment_bound_over_p": "4.0",
      "wrong_independent_pair_bound_over_p": "9.208633285011608073916445544658171e-39",
      "theorem_bounds": {
        "applicable": true,
        "at_sufficient_quadratic_envelope": true,
        "log10_deletion_probability_upper": "-3920949692573.19007539410841982",
        "log10_success_lower": "-40.13433767708217357750406815",
        "fixed_Kstar_multiplicity_upper": "1.0",
        "posterior_no_productive_candidate_upper": "1.0",
        "scope": "Evaluated theorem inequalities, not interval-rounded probabilities. The huge fixed rectangle makes this finite-n posterior bound vacuous in the displayed range."
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    },
    {
      "n": 256,
      "X_times_p": "0.9833355363427705544526654270726581",
      "q2_over_p": "0.020352908673917221679667705971213668",
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      "conditional_mean_degree": "1.1972065552438582399404203934712222e+78",
      "actual_two_or_more_over_p": "0.040705817347834443359335411942427336",
      "excess_count_bound_over_p": "0.040705817347834443359335411942427336",
      "pair_count_bound_over_p": "0.040705817347834443359335411942427336",
      "first_moment_bound_over_p": "4.0",
      "wrong_independent_pair_bound_over_p": "2.5476754314211096560909014249762157e-77",
      "theorem_bounds": {
        "applicable": true,
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        "log10_deletion_probability_upper": "-7781227277350.71086441443754475",
        "log10_success_lower": "-78.6805718748186461542818523473",
        "fixed_Kstar_multiplicity_upper": "1.0",
        "posterior_no_productive_candidate_upper": "1.0",
        "scope": "Evaluated theorem inequalities, not interval-rounded probabilities. The huge fixed rectangle makes this finite-n posterior bound vacuous in the displayed range."
      }
    },
    {
      "n": 1024,
      "X_times_p": "0.93269098719545744551410029854730975",
      "q2_over_p": "0.0051729235879311727754787395398885979",
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      "conditional_mean_degree": "1.9007828928114830914719144842246937e+309",
      "actual_two_or_more_over_p": "0.010345847175862345550957479079777196",
      "excess_count_bound_over_p": "0.010345847175862345550957479079777196",
      "pair_count_bound_over_p": "0.010345847175862345550957479079777196",
      "first_moment_bound_over_p": "4.0",
      "wrong_independent_pair_bound_over_p": "1.5564797502554154427996608709320763e-308",
      "theorem_bounds": {
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        "log10_success_lower": "-309.885803900700194963122123977",
        "fixed_Kstar_multiplicity_upper": "1.0",
        "posterior_no_productive_candidate_upper": "1.0",
        "scope": "Evaluated theorem inequalities, not interval-rounded probabilities. The huge fixed rectangle makes this finite-n posterior bound vacuous in the displayed range."
      }
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  ],
  "finite_candidate_probabilities": [
    {
      "n": 4,
      "p": "0.16275622472725313726723819105111972",
      "productive_union_over_p": "6.1434262121102138087209848348838202",
      "singleton_union_over_p": "6.1435604880797233010100937967883535",
      "cap_atom": "0.093183614814288856839610669148275586"
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    {
      "n": 5,
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      "productive_union_over_p": "14.611320877979450387788632616179142",
      "singleton_union_over_p": "14.639702927997816126380223577871867",
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      "productive_union_over_p": "30.000996312017915662799149161472111",
      "singleton_union_over_p": "30.353424967120245338026034564081064",
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      "n": 7,
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      "productive_union_over_p": "49.329940442851972321717908484472511",
      "singleton_union_over_p": "50.633214086277024204093586911049588",
      "cap_atom": "0.0041597344875044290133690381503578599"
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      "n": 8,
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      "singleton_union_over_p": "70.372063887610283414662206632251496",
      "cap_atom": "0.0016452506966131709733561906485054402"
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  ]
}