{
  "inputs": {
    "threshold": 5,
    "capacities": [
      5,
      6,
      7,
      8,
      9,
      10
    ],
    "background": "0.01",
    "growth": "1",
    "loading": "4",
    "blank_limit": "0.01",
    "miss_limit": "0.05",
    "grid_step": 0.1,
    "clock_multiplier": 2.0,
    "headrooms": [
      0,
      1,
      2,
      3,
      5,
      10,
      20
    ],
    "quadrature_tolerance": 2e-11,
    "root_tolerance": 1e-11,
    "poisson_tail_tolerance": 1e-13
  },
  "windows": [
    {
      "capacity": 5,
      "earliest": 5.735811555762309,
      "latest": 4.459372751098365,
      "width": 0.0,
      "status": "empty",
      "grid_frames": [],
      "blank_boundary_miss": 0.08956568714120407
    },
    {
      "capacity": 6,
      "earliest": 4.268227195917699,
      "latest": 3.8886083763996395,
      "width": 0.0,
      "status": "empty",
      "grid_frames": [],
      "blank_boundary_miss": 0.06145403545996126
    },
    {
      "capacity": 7,
      "earliest": 3.720748273566182,
      "latest": 3.632428550283653,
      "width": 0.0,
      "status": "empty",
      "grid_frames": [],
      "blank_boundary_miss": 0.05258500825935717
    },
    {
      "capacity": 8,
      "earliest": 3.423709636804733,
      "latest": 3.4822469074285056,
      "width": 0.058537270623772564,
      "status": "feasible",
      "grid_frames": [],
      "blank_boundary_miss": 0.04832033106200362
    },
    {
      "capacity": 9,
      "earliest": 3.2346346791941323,
      "latest": 3.3824446636799403,
      "width": 0.14780998448580807,
      "status": "feasible",
      "grid_frames": [
        3.3000000000000003
      ],
      "blank_boundary_miss": 0.045814326906156444
    },
    {
      "capacity": 10,
      "earliest": 3.102874095127593,
      "latest": 3.310949574131842,
      "width": 0.20807547900424916,
      "status": "feasible",
      "grid_frames": [
        3.2,
        3.3000000000000003
      ],
      "blank_boundary_miss": 0.04416179529225204
    }
  ],
  "limit_laws": [
    {
      "headroom": "0",
      "cutoff_y": 0.19364808907426898,
      "blank": 0.010000000000000004,
      "miss": 0.109138951814011,
      "poisson_tail_bound": 3.531828887154817e-14,
      "quadrature_error_estimate": 1.7109803595288104e-11,
      "status": "empty limit"
    },
    {
      "headroom": "1",
      "cutoff_y": 0.44676511555148696,
      "blank": 0.010000000000009803,
      "miss": 0.06108087409583871,
      "poisson_tail_bound": 3.531828887154817e-14,
      "quadrature_error_estimate": 1.5903347395558717e-11,
      "status": "empty limit"
    },
    {
      "headroom": "2",
      "cutoff_y": 0.7068248052542927,
      "blank": 0.010000000000000711,
      "miss": 0.05027400832304092,
      "poisson_tail_bound": 3.531828887154817e-14,
      "quadrature_error_estimate": 5.530080829586804e-12,
      "status": "empty limit"
    },
    {
      "headroom": "3",
      "cutoff_y": 0.9692363229572319,
      "blank": 0.010000000000000002,
      "miss": 0.04639499541818466,
      "poisson_tail_bound": 3.531828887154817e-14,
      "quadrature_error_estimate": 1.6091810185501137e-11,
      "status": "feasible limit"
    },
    {
      "headroom": "5",
      "cutoff_y": 1.4966738205073706,
      "blank": 0.010000000000000285,
      "miss": 0.043464749365948414,
      "poisson_tail_bound": 3.531828887154817e-14,
      "quadrature_error_estimate": 1.9400913254691298e-11,
      "status": "feasible limit"
    },
    {
      "headroom": "10",
      "cutoff_y": 2.819557808359051,
      "blank": 0.009999999999999957,
      "miss": 0.041455724121489665,
      "poisson_tail_bound": 3.531828887154817e-14,
      "quadrature_error_estimate": 1.6766943290577573e-11,
      "status": "feasible limit"
    },
    {
      "headroom": "20",
      "cutoff_y": 5.468769991006365,
      "blank": 0.010000000000000002,
      "miss": 0.04051860926251313,
      "poisson_tail_bound": 3.531828887154817e-14,
      "quadrature_error_estimate": 1.7230274403558717e-11,
      "status": "feasible limit"
    },
    {
      "headroom": "growing reserve",
      "cutoff_y": 0.265052550251763,
      "blank": 0.009999999999994805,
      "miss": 0.03962487596974944,
      "poisson_tail_bound": 3.531828887154817e-14,
      "quadrature_error_estimate": 0.0,
      "status": "feasible limit"
    }
  ],
  "clock_identity_error": 0.0,
  "initially_positive": 0.3711630648201267,
  "large_threshold": {
    "threshold": 100000000,
    "assumptions": "b/g=.01, loading=4, blank limit=.01, miss limit=.05; paper scalar bounds imported",
    "doubled_deadline": 20.317800720454514,
    "saturated_separating_deadline": 38.73848148901677,
    "bounds": {
      "doubled_blank_upper": "5923448/618765625",
      "doubled_miss_upper": "19377564310118803/396010000000000000",
      "saturated_blank_lower": "398542869/39601000000",
      "saturated_miss_lower": "1100451591/19800500000"
    },
    "approximate_bounds": {
      "doubled_blank_upper": 0.009573007550314386,
      "doubled_miss_upper": 0.04893200755061439,
      "saturated_blank_lower": 0.010063959723239313,
      "saturated_miss_lower": 0.05557695972323931
    }
  },
  "evidence": "Rational small-threshold enclosures; numerical finite windows and limit quadratures; imported large-threshold scalar theorem constants. No Lean compilation."
}