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          "a": "1e-3",
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          "strictly_below": "1e-5"
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          "strictly_below": "1e-45"
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          "strictly_below": "1e-629"
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      "configured_profile": {
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      },
      "seed_cost": {
        "q": "1/2",
        "m": 100,
        "L": 4830,
        "conservative_record_index_bit_length": 9669,
        "least_record_log2_approx": 4842.711322474788,
        "note": "Cost of the proof, not an estimate of the profile. Conservative index uses a rational Bernoulli bound."
      },
      "interior_attempt": {
        "status": "resource_limit",
        "reason": "Profile cap cannot be materialized: seed L=4930, conservative record-index bit length=9871; no interior evaluation."
      },
      "repair": [
        [
          "000",
          "1",
          "0001"
        ],
        [
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          "101",
          "000101"
        ],
        [
          "0001",
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          "00010"
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        [
          "00010",
          "1",
          "000101"
        ]
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      "restricted_field_escape": {
        "a": "1/2",
        "B": 4,
        "value": "3/16",
        "channels": [
          [
            "0",
            "00",
            "000"
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          [
            "00",
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            "000"
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          [
            "000",
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          [
            "0001",
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          [
            "00010",
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        ],
        "scope": "Only this explicit small subnetwork is random; omitted channels closed. Not full polymer escape or survival."
      },
      "full_escape_B2_at_half": "4294967295/4294967296"
    },
    "qt": {
      "finite": {
        "n": 16,
        "molecules": 131070,
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          "max_choices": 30,
          "max_total_length": 10,
          "max_cleavage_slots": 4
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      "low_openness_certificates": [
        {
          "a": "1e-3",
          "r": 8,
          "bound": "41352354649809/19531250000000000000",
          "strictly_below": "1e-5"
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          "a": "1e-4",
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          "strictly_below": "1e-15"
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          "strictly_below": "1e-45"
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          "strictly_below": "1e-629"
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      "configured_profile": {
        "method": "history_upper_bound",
        "history_depth": 12,
        "interval": {
          "lower": "0",
          "upper": "276989223223365578541693/781250000000000000000000000000000000000",
          "width": "276989223223365578541693/781250000000000000000000000000000000000"
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      },
      "seed_cost": {
        "q": "1/2",
        "m": 100,
        "L": 21520,
        "conservative_record_index_bit_length": 43049,
        "least_record_log2_approx": 21534.865136435586,
        "note": "Cost of the proof, not an estimate of the profile. Conservative index uses a rational Bernoulli bound."
      },
      "interior_attempt": {
        "status": "resource_limit",
        "reason": "Profile cap cannot be materialized: seed L=21950, conservative record-index bit length=43911; no interior evaluation."
      },
      "repair": [
        [
          "000",
          "1",
          "0001"
        ],
        [
          "000",
          "101",
          "000101"
        ],
        [
          "0001",
          "0",
          "00010"
        ],
        [
          "00010",
          "1",
          "000101"
        ]
      ],
      "restricted_field_escape": {
        "a": "1/2",
        "B": 4,
        "value": "1/8",
        "channels": [
          [
            "0",
            "00",
            "000"
          ],
          [
            "000",
            "1",
            "0001"
          ],
          [
            "000",
            "101",
            "000101"
          ],
          [
            "0001",
            "0",
            "00010"
          ],
          [
            "00010",
            "1",
            "000101"
          ]
        ],
        "scope": "Only this explicit small subnetwork is random; omitted channels closed. Not full polymer escape or survival."
      },
      "full_escape_B2_at_half": "1073741823/1073741824"
    }
  },
  "intensity_to_openness": {
    "lower": "600030001/6000600030001",
    "upper": "4000200006667/40004000200006667",
    "width": "2000000000000/240048004800320016000600016667"
  },
  "half_openness_to_intensity": {
    "lower": "108340675104753102419/156302554713764659200",
    "upper": "13542584389307205283/19537819339220582400",
    "width": "1/16106127360"
  },
  "dependence_counterexample": {
    "model": "One shared Bernoulli(a) mark opens all channels or none.",
    "survival": "a exactly",
    "scope": "Same marginals as the independent model, different survival. History powers require independence."
  },
  "scope": "Exact finite algebra and enumeration plus imported universal theorems. No Lean replay; no interior survival plot or kinetic interpretation."
}