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      "schema": "random-sat-audit-v1",
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        "work": 82
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      "limits": {
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        "max_clauses": 2048,
        "max_n": 128,
        "max_exact_n": 16,
        "max_work": 5000000
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    }
  },
  {
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    "seed": 3,
    "input": {
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      "law": "iid_proper_with_replacement",
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      "declared_law": "iid_proper_with_replacement",
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        {
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        {
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        {
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        {
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        {
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        {
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          "basis": "exhaustive_assignment_bitset"
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      ],
      "run": {
        "stop": "first_unsat",
        "work": 114
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      "limits": {
        "max_bytes": 1048576,
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        "max_n": 128,
        "max_exact_n": 16,
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      "python": "3.12.14"
    }
  },
  {
    "n": 6,
    "seed": 10,
    "input": {
      "schema": "random-sat-stream-v1",
      "n": 6,
      "k": 3,
      "law": "iid_proper_with_replacement",
      "clauses": [
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        [
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          5
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        [
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        [
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        [
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        [
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        [
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        [
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          5
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          5
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
          2,
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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        [
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      ]
    },
    "report": {
      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 6,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
      "actual_randomness_or_iid_verified": false,
      "source_proof_verified": false,
      "asymptotic_threshold_estimated": false,
      "duplicate_clause_count": 12,
      "clause_type_count": 160,
      "conditional_first_moment_survival_upper": "508021860739623365322188197652216501772434524836001/23945242826029513411849172299223580994042798784118784",
      "summary": {
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        "independent_H_upper": 51,
        "solver_claimed_H_upper": 51,
        "independently_exact_H": 51,
        "independently_exact_last_sat": 50,
        "independently_exact_clipped_H": 51,
        "cap": 60,
        "observed_survival_through_stream": false,
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        {
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        {
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        {
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        {
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        {
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        {
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          "status": "UNSAT",
          "basis": "exhaustive_assignment_bitset"
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      ],
      "run": {
        "stop": "first_unsat",
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        "max_n": 128,
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  },
  {
    "n": 6,
    "seed": 11,
    "input": {
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      "k": 3,
      "law": "iid_proper_with_replacement",
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        [
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    },
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      "schema": "random-sat-audit-v1",
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      "n": 6,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
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      "summary": {
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        "work": 158
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      "limits": {
        "max_bytes": 1048576,
        "max_clauses": 2048,
        "max_n": 128,
        "max_exact_n": 16,
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      "python": "3.12.14"
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  },
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    "seed": 12,
    "input": {
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      "k": 3,
      "law": "iid_proper_with_replacement",
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        [
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    },
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      "schema": "random-sat-audit-v1",
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      "n": 6,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
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      "summary": {
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        "solver_claimed_H_upper": 34,
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    },
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      "n": 6,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
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      "duplicate_clause_count": 7,
      "clause_type_count": 160,
      "conditional_first_moment_survival_upper": "508021860739623365322188197652216501772434524836001/23945242826029513411849172299223580994042798784118784",
      "summary": {
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        "solver_claimed_H_upper": 26,
        "independently_exact_H": 26,
        "independently_exact_last_sat": 25,
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        "cap": 60,
        "observed_survival_through_stream": false,
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        "unknown_prefixes": [],
        "first_failure_determined": true
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        {
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        "solver_claimed_H_upper": 33,
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        "independently_exact_last_sat": 32,
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        {
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    },
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      "n": 6,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
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      "source_proof_verified": false,
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      "duplicate_clause_count": 6,
      "clause_type_count": 160,
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  },
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      "law": "iid_proper_with_replacement",
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      "k": 3,
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          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 12,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 13,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 14,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 15,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 16,
          "status": "SAT",
          "basis": "checked_assignment",
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        },
        {
          "prefix": 17,
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          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 18,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 19,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 20,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 21,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 22,
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          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 23,
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          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 24,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 25,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 26,
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          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 27,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 28,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 29,
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          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 30,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 31,
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          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 32,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 33,
          "status": "UNSAT",
          "basis": "exhaustive_assignment_bitset"
        }
      ],
      "run": {
        "stop": "first_unsat",
        "work": 138
      },
      "limits": {
        "max_bytes": 1048576,
        "max_clauses": 2048,
        "max_n": 128,
        "max_exact_n": 16,
        "max_work": 5000000
      },
      "python": "3.12.14"
    }
  },
  {
    "n": 10,
    "seed": 0,
    "input": {
      "schema": "random-sat-stream-v1",
      "n": 10,
      "k": 3,
      "law": "iid_proper_with_replacement",
      "clauses": [
        [
          -5,
          -8,
          -10
        ],
        [
          -2,
          5,
          -6
        ],
        [
          -4,
          -8,
          -9
        ],
        [
          6,
          8,
          9
        ],
        [
          -2,
          5,
          10
        ],
        [
          1,
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          -8
        ],
        [
          1,
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        ],
        [
          3,
          4,
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        ],
        [
          2,
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          -10
        ],
        [
          -2,
          5,
          8
        ],
        [
          -7,
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          10
        ],
        [
          -5,
          6,
          -7
        ],
        [
          5,
          -7,
          -10
        ],
        [
          -2,
          3,
          6
        ],
        [
          -2,
          -8,
          -9
        ],
        [
          -2,
          4,
          7
        ],
        [
          3,
          -5,
          10
        ],
        [
          6,
          -8,
          -10
        ],
        [
          7,
          -8,
          -9
        ],
        [
          1,
          6,
          8
        ],
        [
          -3,
          -4,
          5
        ],
        [
          -1,
          4,
          7
        ],
        [
          -2,
          -3,
          -4
        ],
        [
          1,
          4,
          7
        ],
        [
          4,
          -7,
          10
        ],
        [
          1,
          -3,
          -8
        ],
        [
          3,
          -7,
          -8
        ],
        [
          -5,
          6,
          -9
        ],
        [
          -1,
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          -10
        ],
        [
          7,
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          -9
        ],
        [
          3,
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        ],
        [
          -4,
          6,
          -7
        ],
        [
          5,
          -6,
          10
        ],
        [
          -3,
          -6,
          -9
        ],
        [
          6,
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          -10
        ],
        [
          -1,
          4,
          8
        ],
        [
          2,
          -3,
          7
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        [
          1,
          -3,
          8
        ],
        [
          4,
          6,
          -10
        ],
        [
          1,
          3,
          -5
        ],
        [
          -6,
          -9,
          -10
        ],
        [
          -5,
          8,
          10
        ],
        [
          -4,
          -5,
          8
        ],
        [
          -2,
          3,
          -10
        ],
        [
          2,
          7,
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        [
          3,
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          7
        ],
        [
          1,
          3,
          8
        ],
        [
          -2,
          4,
          -7
        ],
        [
          -2,
          -6,
          8
        ],
        [
          2,
          3,
          -8
        ],
        [
          3,
          -6,
          -10
        ],
        [
          3,
          7,
          10
        ],
        [
          -7,
          8,
          9
        ],
        [
          1,
          -6,
          -7
        ],
        [
          3,
          -5,
          6
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        [
          -2,
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        ],
        [
          2,
          -6,
          9
        ],
        [
          -6,
          7,
          8
        ],
        [
          3,
          -4,
          7
        ],
        [
          -1,
          8,
          -9
        ],
        [
          1,
          2,
          10
        ],
        [
          -5,
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          -10
        ],
        [
          -7,
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          10
        ],
        [
          3,
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          -6
        ],
        [
          7,
          -8,
          -10
        ],
        [
          -1,
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          4
        ],
        [
          1,
          3,
          7
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        [
          -4,
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        ],
        [
          -5,
          -8,
          9
        ],
        [
          -2,
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          -8
        ],
        [
          4,
          6,
          7
        ],
        [
          -5,
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          9
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        [
          5,
          6,
          -7
        ],
        [
          -4,
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          6
        ],
        [
          -3,
          -7,
          -9
        ],
        [
          1,
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          -3
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        [
          -3,
          6,
          -10
        ],
        [
          2,
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        ],
        [
          5,
          7,
          9
        ],
        [
          -6,
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        [
          2,
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          10
        ],
        [
          1,
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          -9
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        [
          4,
          6,
          -10
        ],
        [
          2,
          -3,
          9
        ],
        [
          -4,
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          -7
        ],
        [
          6,
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          -9
        ],
        [
          -1,
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          -4
        ],
        [
          1,
          5,
          -9
        ],
        [
          7,
          8,
          -10
        ],
        [
          3,
          -5,
          8
        ],
        [
          1,
          6,
          -9
        ],
        [
          -1,
          -7,
          8
        ],
        [
          -5,
          6,
          9
        ],
        [
          1,
          -4,
          -8
        ],
        [
          -5,
          6,
          9
        ],
        [
          -3,
          -4,
          10
        ],
        [
          -2,
          6,
          -10
        ],
        [
          1,
          -3,
          7
        ],
        [
          -1,
          3,
          -6
        ],
        [
          2,
          3,
          8
        ]
      ]
    },
    "report": {
      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 10,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
      "actual_randomness_or_iid_verified": false,
      "source_proof_verified": false,
      "asymptotic_threshold_estimated": false,
      "duplicate_clause_count": 4,
      "clause_type_count": 960,
      "conditional_first_moment_survival_upper": "3234476509624757991344647769100216810857203198904625400933895331391691459636928060001/1989292945639146568621528992587283360401824603189390869761855907572637988050133502132224",
      "summary": {
        "independent_H_lower": 50,
        "independent_H_upper": 50,
        "solver_claimed_H_upper": 50,
        "independently_exact_H": 50,
        "independently_exact_last_sat": 49,
        "independently_exact_clipped_H": 50,
        "cap": 100,
        "observed_survival_through_stream": false,
        "right_censored_after_stream": false,
        "unknown_prefixes": [],
        "first_failure_determined": true
      },
      "observations": [
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          "prefix": 0,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 1,
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          "assignment": [
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        {
          "prefix": 2,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 3,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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          ]
        },
        {
          "prefix": 4,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 5,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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          "prefix": 6,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 7,
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          "prefix": 8,
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        {
          "prefix": 9,
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        {
          "prefix": 10,
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        {
          "prefix": 11,
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          "basis": "checked_assignment",
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        {
          "prefix": 13,
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          "prefix": 18,
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        {
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          "basis": "checked_assignment",
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        {
          "prefix": 25,
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        {
          "prefix": 26,
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          "basis": "checked_assignment",
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        {
          "prefix": 27,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 28,
          "status": "SAT",
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        {
          "prefix": 29,
          "status": "SAT",
          "basis": "checked_assignment",
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          "status": "SAT",
          "basis": "checked_assignment",
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        {
          "prefix": 31,
          "status": "SAT",
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          "assignment": [
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        {
          "prefix": 32,
          "status": "SAT",
          "basis": "checked_assignment",
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        {
          "prefix": 33,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 34,
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          "basis": "checked_assignment",
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          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 36,
          "status": "SAT",
          "basis": "checked_assignment",
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        {
          "prefix": 37,
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          "basis": "checked_assignment",
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        {
          "prefix": 38,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 39,
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          "assignment": [
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        {
          "prefix": 40,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 41,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 42,
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          "assignment": [
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        {
          "prefix": 44,
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          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 45,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 46,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 48,
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          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 49,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 50,
          "status": "UNSAT",
          "basis": "exhaustive_assignment_bitset"
        }
      ],
      "run": {
        "stop": "first_unsat",
        "work": 3360
      },
      "limits": {
        "max_bytes": 1048576,
        "max_clauses": 2048,
        "max_n": 128,
        "max_exact_n": 16,
        "max_work": 5000000
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      "python": "3.12.14"
    }
  },
  {
    "n": 10,
    "seed": 1,
    "input": {
      "schema": "random-sat-stream-v1",
      "n": 10,
      "k": 3,
      "law": "iid_proper_with_replacement",
      "clauses": [
        [
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          -7
        ],
        [
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          5,
          8
        ],
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          5,
          8,
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        [
          5,
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          9
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          9
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        [
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        [
          2,
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        [
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        [
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          -6,
          10
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        [
          2,
          7,
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        [
          3,
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          -10
        ],
        [
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          10
        ],
        [
          5,
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          7
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        [
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          6,
          7
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        [
          -1,
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        [
          2,
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        [
          1,
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        [
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          5,
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          10
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        [
          2,
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          6
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          6,
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        [
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          6,
          9
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        [
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          9
        ],
        [
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          -10
        ],
        [
          -1,
          2,
          -3
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          -4,
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        [
          -2,
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        ],
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        [
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          6
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        [
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          5
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          -1,
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          -6
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        [
          3,
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          -3,
          4,
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        [
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        [
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        [
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        ],
        [
          4,
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          -1,
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        [
          4,
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          -9
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        [
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        [
          -2,
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        [
          -7,
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        [
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          -2,
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        [
          3,
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        [
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        [
          3,
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        [
          -1,
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          -1,
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          9
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        [
          4,
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        [
          -8,
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        [
          -2,
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        [
          3,
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          5
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          5,
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          -10
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        [
          -7,
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          9
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        [
          -4,
          5,
          6
        ],
        [
          -1,
          5,
          -9
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        [
          -2,
          3,
          6
        ],
        [
          -2,
          3,
          -4
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        [
          3,
          -6,
          -7
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        [
          6,
          7,
          10
        ],
        [
          2,
          9,
          10
        ],
        [
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          8,
          -10
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        [
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          5
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        [
          -2,
          5,
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    },
    "report": {
      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 10,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
      "actual_randomness_or_iid_verified": false,
      "source_proof_verified": false,
      "asymptotic_threshold_estimated": false,
      "duplicate_clause_count": 8,
      "clause_type_count": 960,
      "conditional_first_moment_survival_upper": "3234476509624757991344647769100216810857203198904625400933895331391691459636928060001/1989292945639146568621528992587283360401824603189390869761855907572637988050133502132224",
      "summary": {
        "independent_H_lower": 49,
        "independent_H_upper": 49,
        "solver_claimed_H_upper": 49,
        "independently_exact_H": 49,
        "independently_exact_last_sat": 48,
        "independently_exact_clipped_H": 49,
        "cap": 100,
        "observed_survival_through_stream": false,
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        },
        {
          "prefix": 37,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 38,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 39,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 40,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 41,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 42,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 43,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 44,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 45,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 46,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 47,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 48,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 49,
          "status": "UNSAT",
          "basis": "exhaustive_assignment_bitset"
        }
      ],
      "run": {
        "stop": "first_unsat",
        "work": 3296
      },
      "limits": {
        "max_bytes": 1048576,
        "max_clauses": 2048,
        "max_n": 128,
        "max_exact_n": 16,
        "max_work": 5000000
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      "python": "3.12.14"
    }
  },
  {
    "n": 10,
    "seed": 2,
    "input": {
      "schema": "random-sat-stream-v1",
      "n": 10,
      "k": 3,
      "law": "iid_proper_with_replacement",
      "clauses": [
        [
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          7,
          -8
        ],
        [
          5,
          -8,
          10
        ],
        [
          1,
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        ],
        [
          1,
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        [
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          6
        ],
        [
          2,
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        ],
        [
          5,
          7,
          10
        ],
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          1,
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          6
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        [
          4,
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        [
          -5,
          -6,
          10
        ],
        [
          4,
          -5,
          6
        ],
        [
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          9,
          -10
        ],
        [
          2,
          3,
          -7
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        [
          1,
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        [
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          9
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        [
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        [
          3,
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          9
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          7
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        [
          3,
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        [
          4,
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          2,
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        [
          3,
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        [
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          5,
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        ],
        [
          -5,
          6,
          9
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        [
          -4,
          -6,
          9
        ],
        [
          -6,
          -7,
          -8
        ],
        [
          3,
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          -6
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        [
          -2,
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          9
        ],
        [
          3,
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          10
        ],
        [
          -8,
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          10
        ],
        [
          2,
          6,
          9
        ],
        [
          -3,
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          -5
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        [
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          -10
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        [
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          7
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        [
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          6
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        [
          -2,
          -4,
          8
        ],
        [
          -2,
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          9
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        [
          -8,
          9,
          -10
        ],
        [
          -2,
          3,
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        ],
        [
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        ],
        [
          2,
          -4,
          10
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        [
          2,
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        [
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        [
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          -8
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        [
          -1,
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        [
          3,
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          7
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        [
          1,
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        [
          1,
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          10
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        [
          -1,
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        [
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        [
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        [
          1,
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        [
          1,
          4,
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        [
          -3,
          4,
          -6
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        [
          -3,
          4,
          -6
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        [
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        [
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          -4,
          5,
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        [
          3,
          -5,
          7
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        [
          -1,
          5,
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        [
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        [
          5,
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        [
          -2,
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        [
          -4,
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        ],
        [
          3,
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        ],
        [
          -7,
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          -9
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        [
          -7,
          8,
          -9
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        [
          4,
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          9
        ],
        [
          -2,
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          8
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        [
          -5,
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        ],
        [
          3,
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          -2,
          4,
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          -2,
          4,
          -8
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        [
          5,
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        [
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          10
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        [
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        ],
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          2,
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        [
          -4,
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          8
        ],
        [
          -4,
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          8
        ],
        [
          -2,
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          -9
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        [
          -3,
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          10
        ],
        [
          3,
          4,
          8
        ],
        [
          1,
          7,
          9
        ],
        [
          2,
          -8,
          10
        ],
        [
          1,
          -9,
          10
        ],
        [
          7,
          9,
          -10
        ],
        [
          -2,
          9,
          10
        ],
        [
          -3,
          -4,
          -5
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        [
          3,
          4,
          6
        ],
        [
          5,
          7,
          -10
        ],
        [
          5,
          6,
          8
        ],
        [
          -2,
          4,
          -7
        ],
        [
          3,
          -9,
          10
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      ]
    },
    "report": {
      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 10,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
      "actual_randomness_or_iid_verified": false,
      "source_proof_verified": false,
      "asymptotic_threshold_estimated": false,
      "duplicate_clause_count": 7,
      "clause_type_count": 960,
      "conditional_first_moment_survival_upper": "3234476509624757991344647769100216810857203198904625400933895331391691459636928060001/1989292945639146568621528992587283360401824603189390869761855907572637988050133502132224",
      "summary": {
        "independent_H_lower": 62,
        "independent_H_upper": 62,
        "solver_claimed_H_upper": 62,
        "independently_exact_H": 62,
        "independently_exact_last_sat": 61,
        "independently_exact_clipped_H": 62,
        "cap": 100,
        "observed_survival_through_stream": false,
        "right_censored_after_stream": false,
        "unknown_prefixes": [],
        "first_failure_determined": true
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      "observations": [
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          "basis": "checked_assignment",
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        {
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        {
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          "basis": "checked_assignment",
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          "basis": "checked_assignment",
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        {
          "prefix": 38,
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          "basis": "checked_assignment",
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        {
          "prefix": 39,
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          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 40,
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          "basis": "checked_assignment",
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        {
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        {
          "prefix": 44,
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        {
          "prefix": 45,
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          "prefix": 46,
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        {
          "prefix": 47,
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        {
          "prefix": 48,
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        {
          "prefix": 49,
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        {
          "prefix": 50,
          "status": "SAT",
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        {
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          "prefix": 52,
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        {
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          "assignment": [
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        {
          "prefix": 56,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 57,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 58,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 59,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 60,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 61,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 62,
          "status": "UNSAT",
          "basis": "exhaustive_assignment_bitset"
        }
      ],
      "run": {
        "stop": "first_unsat",
        "work": 4128
      },
      "limits": {
        "max_bytes": 1048576,
        "max_clauses": 2048,
        "max_n": 128,
        "max_exact_n": 16,
        "max_work": 5000000
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      "python": "3.12.14"
    }
  },
  {
    "n": 10,
    "seed": 3,
    "input": {
      "schema": "random-sat-stream-v1",
      "n": 10,
      "k": 3,
      "law": "iid_proper_with_replacement",
      "clauses": [
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          7,
          -8
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          6,
          7
        ],
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          3,
          -4,
          10
        ],
        [
          1,
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          6
        ],
        [
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        ],
        [
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        [
          2,
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          -3,
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        ],
        [
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          5,
          -10
        ],
        [
          1,
          3,
          -4
        ],
        [
          -3,
          -6,
          9
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        [
          1,
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          4
        ],
        [
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          8,
          -9
        ],
        [
          5,
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          -2,
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        [
          1,
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        [
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          6
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        [
          1,
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        [
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          9
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          6,
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        [
          2,
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        [
          3,
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          -10
        ],
        [
          -5,
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          -9
        ],
        [
          -3,
          5,
          -6
        ],
        [
          2,
          7,
          10
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        [
          -2,
          5,
          7
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        [
          -3,
          7,
          10
        ],
        [
          6,
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        [
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        [
          1,
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          10
        ],
        [
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        [
          1,
          4,
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        [
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        [
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          10
        ],
        [
          3,
          4,
          7
        ],
        [
          2,
          5,
          6
        ],
        [
          4,
          7,
          8
        ],
        [
          1,
          2,
          4
        ],
        [
          4,
          5,
          6
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        [
          4,
          9,
          -10
        ],
        [
          1,
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          -4
        ],
        [
          1,
          4,
          -10
        ],
        [
          -4,
          -8,
          -9
        ],
        [
          3,
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          7
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        [
          1,
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        [
          -2,
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          6
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        [
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          10
        ],
        [
          1,
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          6
        ],
        [
          5,
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          -9
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        [
          -6,
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          8
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        [
          1,
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        [
          3,
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        [
          -4,
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        [
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        [
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        [
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          6
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        [
          4,
          6,
          -8
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        [
          5,
          6,
          7
        ],
        [
          7,
          8,
          10
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        [
          2,
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          7
        ],
        [
          -2,
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          7
        ],
        [
          4,
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          -10
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        [
          -5,
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        [
          -3,
          5,
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        [
          2,
          6,
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        [
          -8,
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          10
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        [
          1,
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        [
          6,
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        [
          -2,
          4,
          8
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        [
          1,
          3,
          -8
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        [
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          1,
          4,
          -7
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        [
          -2,
          9,
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        [
          -1,
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        [
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        ],
        [
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        [
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          -10
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          6
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          2,
          5,
          10
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        [
          3,
          4,
          5
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          5,
          -7,
          10
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        [
          2,
          5,
          -6
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        [
          3,
          5,
          -9
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        [
          2,
          4,
          6
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          -3,
          4,
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        [
          3,
          5,
          10
        ],
        [
          2,
          -5,
          -9
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        [
          -3,
          5,
          10
        ],
        [
          1,
          -6,
          10
        ],
        [
          6,
          -9,
          10
        ],
        [
          -2,
          -4,
          -5
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        [
          -4,
          5,
          -8
        ],
        [
          7,
          -8,
          -10
        ],
        [
          7,
          9,
          10
        ],
        [
          1,
          -2,
          6
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      ]
    },
    "report": {
      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 10,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
      "actual_randomness_or_iid_verified": false,
      "source_proof_verified": false,
      "asymptotic_threshold_estimated": false,
      "duplicate_clause_count": 4,
      "clause_type_count": 960,
      "conditional_first_moment_survival_upper": "3234476509624757991344647769100216810857203198904625400933895331391691459636928060001/1989292945639146568621528992587283360401824603189390869761855907572637988050133502132224",
      "summary": {
        "independent_H_lower": 53,
        "independent_H_upper": 53,
        "solver_claimed_H_upper": 53,
        "independently_exact_H": 53,
        "independently_exact_last_sat": 52,
        "independently_exact_clipped_H": 53,
        "cap": 100,
        "observed_survival_through_stream": false,
        "right_censored_after_stream": false,
        "unknown_prefixes": [],
        "first_failure_determined": true
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      "observations": [
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          "basis": "checked_assignment",
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        {
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        {
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        {
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        {
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        {
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        {
          "prefix": 30,
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          "prefix": 35,
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        {
          "prefix": 36,
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          "prefix": 37,
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          "prefix": 38,
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          "prefix": 39,
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        {
          "prefix": 47,
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          "assignment": [
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          "assignment": [
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        {
          "prefix": 49,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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          "prefix": 50,
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          "assignment": [
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        {
          "prefix": 51,
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          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 52,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 53,
          "status": "UNSAT",
          "basis": "exhaustive_assignment_bitset"
        }
      ],
      "run": {
        "stop": "first_unsat",
        "work": 3552
      },
      "limits": {
        "max_bytes": 1048576,
        "max_clauses": 2048,
        "max_n": 128,
        "max_exact_n": 16,
        "max_work": 5000000
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      "python": "3.12.14"
    }
  },
  {
    "n": 10,
    "seed": 4,
    "input": {
      "schema": "random-sat-stream-v1",
      "n": 10,
      "k": 3,
      "law": "iid_proper_with_replacement",
      "clauses": [
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          -7,
          -8
        ],
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          3,
          6
        ],
        [
          1,
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          -9
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        [
          -4,
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        [
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          8,
          -9
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        [
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        [
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        [
          -1,
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          4
        ],
        [
          -1,
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          5
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        [
          2,
          5,
          -8
        ],
        [
          -3,
          5,
          -6
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        [
          7,
          8,
          -10
        ],
        [
          -2,
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          -5
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        [
          5,
          6,
          -9
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        [
          4,
          8,
          9
        ],
        [
          -1,
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          10
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        [
          1,
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        [
          -3,
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          7
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        [
          3,
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          9
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        [
          -2,
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        [
          1,
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          -10
        ],
        [
          -4,
          9,
          10
        ],
        [
          -1,
          -5,
          -7
        ],
        [
          -5,
          7,
          9
        ],
        [
          -1,
          -3,
          9
        ],
        [
          -1,
          -8,
          9
        ],
        [
          1,
          6,
          -8
        ],
        [
          7,
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          10
        ],
        [
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        ],
        [
          -5,
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        ],
        [
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        [
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          6,
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        [
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          10
        ],
        [
          -1,
          5,
          9
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        [
          -1,
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        ],
        [
          2,
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          7
        ],
        [
          -2,
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        [
          -3,
          7,
          -9
        ],
        [
          -6,
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        ],
        [
          4,
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          10
        ],
        [
          5,
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          -10
        ],
        [
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        ],
        [
          6,
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          10
        ],
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          2,
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        [
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        [
          5,
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          -10
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        [
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        [
          2,
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        [
          4,
          5,
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        [
          2,
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          6
        ],
        [
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          4,
          5
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        [
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        [
          -1,
          5,
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        [
          1,
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        [
          -2,
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          10
        ],
        [
          -1,
          9,
          10
        ],
        [
          1,
          3,
          -7
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        [
          8,
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          10
        ],
        [
          5,
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          8
        ],
        [
          -6,
          7,
          8
        ],
        [
          -3,
          -5,
          -6
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        [
          -5,
          -8,
          9
        ],
        [
          2,
          3,
          -6
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        [
          1,
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          3
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        [
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          -2,
          3,
          -5
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        [
          -3,
          5,
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        [
          4,
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          -7
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        [
          6,
          7,
          10
        ],
        [
          2,
          3,
          7
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        [
          -5,
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          10
        ],
        [
          4,
          8,
          9
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        [
          -3,
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          1,
          5,
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          2,
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          2,
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        [
          2,
          3,
          4
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          2,
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        ],
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          10
        ],
        [
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          10
        ],
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          -2,
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        [
          1,
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        ],
        [
          -5,
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          -8
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        [
          -5,
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          -9
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        [
          -1,
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          8
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        [
          1,
          3,
          -6
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        [
          1,
          2,
          8
        ],
        [
          2,
          -7,
          -9
        ],
        [
          3,
          -7,
          -9
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        [
          1,
          9,
          10
        ],
        [
          3,
          4,
          -7
        ],
        [
          3,
          4,
          -9
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        [
          3,
          8,
          9
        ],
        [
          -2,
          7,
          -10
        ],
        [
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          10
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      ]
    },
    "report": {
      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 10,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
      "actual_randomness_or_iid_verified": false,
      "source_proof_verified": false,
      "asymptotic_threshold_estimated": false,
      "duplicate_clause_count": 4,
      "clause_type_count": 960,
      "conditional_first_moment_survival_upper": "3234476509624757991344647769100216810857203198904625400933895331391691459636928060001/1989292945639146568621528992587283360401824603189390869761855907572637988050133502132224",
      "summary": {
        "independent_H_lower": 69,
        "independent_H_upper": 69,
        "solver_claimed_H_upper": 69,
        "independently_exact_H": 69,
        "independently_exact_last_sat": 68,
        "independently_exact_clipped_H": 69,
        "cap": 100,
        "observed_survival_through_stream": false,
        "right_censored_after_stream": false,
        "unknown_prefixes": [],
        "first_failure_determined": true
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      "observations": [
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          "prefix": 0,
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          "basis": "checked_assignment",
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        {
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        {
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        {
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        {
          "prefix": 63,
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          "basis": "checked_assignment",
          "assignment": [
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          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 65,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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          "basis": "checked_assignment",
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        {
          "prefix": 67,
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          "basis": "checked_assignment",
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        {
          "prefix": 68,
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        },
        {
          "prefix": 69,
          "status": "UNSAT",
          "basis": "exhaustive_assignment_bitset"
        }
      ],
      "run": {
        "stop": "first_unsat",
        "work": 4576
      },
      "limits": {
        "max_bytes": 1048576,
        "max_clauses": 2048,
        "max_n": 128,
        "max_exact_n": 16,
        "max_work": 5000000
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      "python": "3.12.14"
    }
  },
  {
    "n": 10,
    "seed": 5,
    "input": {
      "schema": "random-sat-stream-v1",
      "n": 10,
      "k": 3,
      "law": "iid_proper_with_replacement",
      "clauses": [
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          8
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        [
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        [
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          8
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        [
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          9
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        [
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        [
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        [
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          10
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        [
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        [
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    },
    "report": {
      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 10,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
      "actual_randomness_or_iid_verified": false,
      "source_proof_verified": false,
      "asymptotic_threshold_estimated": false,
      "duplicate_clause_count": 6,
      "clause_type_count": 960,
      "conditional_first_moment_survival_upper": "3234476509624757991344647769100216810857203198904625400933895331391691459636928060001/1989292945639146568621528992587283360401824603189390869761855907572637988050133502132224",
      "summary": {
        "independent_H_lower": 55,
        "independent_H_upper": 55,
        "solver_claimed_H_upper": 55,
        "independently_exact_H": 55,
        "independently_exact_last_sat": 54,
        "independently_exact_clipped_H": 55,
        "cap": 100,
        "observed_survival_through_stream": false,
        "right_censored_after_stream": false,
        "unknown_prefixes": [],
        "first_failure_determined": true
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        {
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        {
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          "status": "UNSAT",
          "basis": "exhaustive_assignment_bitset"
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      ],
      "run": {
        "stop": "first_unsat",
        "work": 3680
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      "limits": {
        "max_bytes": 1048576,
        "max_clauses": 2048,
        "max_n": 128,
        "max_exact_n": 16,
        "max_work": 5000000
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      "python": "3.12.14"
    }
  },
  {
    "n": 10,
    "seed": 6,
    "input": {
      "schema": "random-sat-stream-v1",
      "n": 10,
      "k": 3,
      "law": "iid_proper_with_replacement",
      "clauses": [
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          8
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        [
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        [
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        [
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        [
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          3,
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          3,
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          -3,
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          10
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          5,
          7
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          5,
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        [
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    },
    "report": {
      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 10,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
      "actual_randomness_or_iid_verified": false,
      "source_proof_verified": false,
      "asymptotic_threshold_estimated": false,
      "duplicate_clause_count": 6,
      "clause_type_count": 960,
      "conditional_first_moment_survival_upper": "3234476509624757991344647769100216810857203198904625400933895331391691459636928060001/1989292945639146568621528992587283360401824603189390869761855907572637988050133502132224",
      "summary": {
        "independent_H_lower": 58,
        "independent_H_upper": 58,
        "solver_claimed_H_upper": 58,
        "independently_exact_H": 58,
        "independently_exact_last_sat": 57,
        "independently_exact_clipped_H": 58,
        "cap": 100,
        "observed_survival_through_stream": false,
        "right_censored_after_stream": false,
        "unknown_prefixes": [],
        "first_failure_determined": true
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      "observations": [
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          "basis": "checked_assignment",
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        {
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        {
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        "stop": "first_unsat",
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      "limits": {
        "max_bytes": 1048576,
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        "max_n": 128,
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  },
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    "n": 10,
    "seed": 7,
    "input": {
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      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 10,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
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      "source_proof_verified": false,
      "asymptotic_threshold_estimated": false,
      "duplicate_clause_count": 6,
      "clause_type_count": 960,
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      "summary": {
        "independent_H_lower": 43,
        "independent_H_upper": 43,
        "solver_claimed_H_upper": 43,
        "independently_exact_H": 43,
        "independently_exact_last_sat": 42,
        "independently_exact_clipped_H": 43,
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        {
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          "status": "UNSAT",
          "basis": "exhaustive_assignment_bitset"
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      ],
      "run": {
        "stop": "first_unsat",
        "work": 2912
      },
      "limits": {
        "max_bytes": 1048576,
        "max_clauses": 2048,
        "max_n": 128,
        "max_exact_n": 16,
        "max_work": 5000000
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      "python": "3.12.14"
    }
  },
  {
    "n": 10,
    "seed": 8,
    "input": {
      "schema": "random-sat-stream-v1",
      "n": 10,
      "k": 3,
      "law": "iid_proper_with_replacement",
      "clauses": [
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        [
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          10
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          5
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        [
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          5,
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        [
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        [
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          10
        ],
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          8
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          1,
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        [
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          5,
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    },
    "report": {
      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 10,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
      "actual_randomness_or_iid_verified": false,
      "source_proof_verified": false,
      "asymptotic_threshold_estimated": false,
      "duplicate_clause_count": 5,
      "clause_type_count": 960,
      "conditional_first_moment_survival_upper": "3234476509624757991344647769100216810857203198904625400933895331391691459636928060001/1989292945639146568621528992587283360401824603189390869761855907572637988050133502132224",
      "summary": {
        "independent_H_lower": 38,
        "independent_H_upper": 38,
        "solver_claimed_H_upper": 38,
        "independently_exact_H": 38,
        "independently_exact_last_sat": 37,
        "independently_exact_clipped_H": 38,
        "cap": 100,
        "observed_survival_through_stream": false,
        "right_censored_after_stream": false,
        "unknown_prefixes": [],
        "first_failure_determined": true
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        {
          "prefix": 34,
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          "basis": "checked_assignment",
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        {
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          "basis": "checked_assignment",
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        {
          "prefix": 37,
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          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 38,
          "status": "UNSAT",
          "basis": "exhaustive_assignment_bitset"
        }
      ],
      "run": {
        "stop": "first_unsat",
        "work": 2592
      },
      "limits": {
        "max_bytes": 1048576,
        "max_clauses": 2048,
        "max_n": 128,
        "max_exact_n": 16,
        "max_work": 5000000
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      "python": "3.12.14"
    }
  },
  {
    "n": 10,
    "seed": 9,
    "input": {
      "schema": "random-sat-stream-v1",
      "n": 10,
      "k": 3,
      "law": "iid_proper_with_replacement",
      "clauses": [
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          7,
          -9
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          4,
          9
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        [
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        [
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          -1,
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        [
          -2,
          4,
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        [
          -3,
          4,
          -5
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        [
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          7,
          -9
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        [
          6,
          8,
          10
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        [
          3,
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        [
          -1,
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        [
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          3,
          10
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        [
          3,
          5,
          6
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        [
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          10
        ],
        [
          3,
          6,
          10
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        [
          -4,
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          10
        ],
        [
          1,
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        [
          4,
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        [
          -2,
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          10
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        [
          1,
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          6
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        [
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        [
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          6,
          10
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        [
          -4,
          6,
          9
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        [
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          -1,
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        [
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          6
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        [
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          9
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        [
          1,
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          6
        ],
        [
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        [
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        ],
        [
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          7
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          -1,
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          -4
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        [
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          1,
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        [
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        [
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        [
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          -5,
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        [
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        [
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          2,
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          -1,
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        [
          2,
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          -5,
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          -3
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        [
          -1,
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          5
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        [
          -4,
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          -10
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        [
          -1,
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        [
          -6,
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          10
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        [
          -5,
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        [
          1,
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          10
        ],
        [
          -2,
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          -10
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        [
          -1,
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          -4
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        [
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          -10
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        [
          1,
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          6
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        [
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        [
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        [
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    },
    "report": {
      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 10,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
      "actual_randomness_or_iid_verified": false,
      "source_proof_verified": false,
      "asymptotic_threshold_estimated": false,
      "duplicate_clause_count": 2,
      "clause_type_count": 960,
      "conditional_first_moment_survival_upper": "3234476509624757991344647769100216810857203198904625400933895331391691459636928060001/1989292945639146568621528992587283360401824603189390869761855907572637988050133502132224",
      "summary": {
        "independent_H_lower": 54,
        "independent_H_upper": 54,
        "solver_claimed_H_upper": 54,
        "independently_exact_H": 54,
        "independently_exact_last_sat": 53,
        "independently_exact_clipped_H": 54,
        "cap": 100,
        "observed_survival_through_stream": false,
        "right_censored_after_stream": false,
        "unknown_prefixes": [],
        "first_failure_determined": true
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          "basis": "checked_assignment",
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          "assignment": [
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        {
          "prefix": 50,
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        {
          "prefix": 53,
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          "assignment": [
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        },
        {
          "prefix": 54,
          "status": "UNSAT",
          "basis": "exhaustive_assignment_bitset"
        }
      ],
      "run": {
        "stop": "first_unsat",
        "work": 3616
      },
      "limits": {
        "max_bytes": 1048576,
        "max_clauses": 2048,
        "max_n": 128,
        "max_exact_n": 16,
        "max_work": 5000000
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      "python": "3.12.14"
    }
  },
  {
    "n": 10,
    "seed": 10,
    "input": {
      "schema": "random-sat-stream-v1",
      "n": 10,
      "k": 3,
      "law": "iid_proper_with_replacement",
      "clauses": [
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          6,
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        [
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          5,
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        [
          1,
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          4
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        [
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          2,
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        [
          2,
          8,
          10
        ],
        [
          5,
          7,
          -9
        ],
        [
          -1,
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          10
        ],
        [
          3,
          -8,
          10
        ],
        [
          -5,
          6,
          10
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        [
          -1,
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          10
        ],
        [
          1,
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        [
          3,
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        [
          2,
          -8,
          10
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        [
          2,
          3,
          9
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        [
          1,
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          5
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        [
          1,
          7,
          9
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        [
          4,
          7,
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        [
          2,
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          -8
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        [
          1,
          -2,
          8
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        [
          -2,
          5,
          10
        ],
        [
          -6,
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          -8
        ],
        [
          -1,
          4,
          7
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        [
          3,
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          2,
          4,
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        [
          -2,
          4,
          10
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        [
          2,
          5,
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        [
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          3,
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          2,
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          2,
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        [
          1,
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          1,
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          1,
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          4,
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          2,
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          9
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          1,
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          -3,
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          -7,
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        [
          5,
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        [
          -1,
          3,
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          1,
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          2,
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          -6
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          -3,
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          8
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          2,
          4,
          9
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          -7,
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        [
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          3,
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        [
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    },
    "report": {
      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 10,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
      "actual_randomness_or_iid_verified": false,
      "source_proof_verified": false,
      "asymptotic_threshold_estimated": false,
      "duplicate_clause_count": 6,
      "clause_type_count": 960,
      "conditional_first_moment_survival_upper": "3234476509624757991344647769100216810857203198904625400933895331391691459636928060001/1989292945639146568621528992587283360401824603189390869761855907572637988050133502132224",
      "summary": {
        "independent_H_lower": 59,
        "independent_H_upper": 59,
        "solver_claimed_H_upper": 59,
        "independently_exact_H": 59,
        "independently_exact_last_sat": 58,
        "independently_exact_clipped_H": 59,
        "cap": 100,
        "observed_survival_through_stream": false,
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        "unknown_prefixes": [],
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        },
        {
          "prefix": 59,
          "status": "UNSAT",
          "basis": "exhaustive_assignment_bitset"
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      ],
      "run": {
        "stop": "first_unsat",
        "work": 3936
      },
      "limits": {
        "max_bytes": 1048576,
        "max_clauses": 2048,
        "max_n": 128,
        "max_exact_n": 16,
        "max_work": 5000000
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      "python": "3.12.14"
    }
  },
  {
    "n": 10,
    "seed": 11,
    "input": {
      "schema": "random-sat-stream-v1",
      "n": 10,
      "k": 3,
      "law": "iid_proper_with_replacement",
      "clauses": [
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        [
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        [
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          1,
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        [
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        [
          1,
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        [
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        [
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        [
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          2,
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        [
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          2,
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          -1,
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          4
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    },
    "report": {
      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 10,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
      "actual_randomness_or_iid_verified": false,
      "source_proof_verified": false,
      "asymptotic_threshold_estimated": false,
      "duplicate_clause_count": 4,
      "clause_type_count": 960,
      "conditional_first_moment_survival_upper": "3234476509624757991344647769100216810857203198904625400933895331391691459636928060001/1989292945639146568621528992587283360401824603189390869761855907572637988050133502132224",
      "summary": {
        "independent_H_lower": 87,
        "independent_H_upper": 87,
        "solver_claimed_H_upper": 87,
        "independently_exact_H": 87,
        "independently_exact_last_sat": 86,
        "independently_exact_clipped_H": 87,
        "cap": 100,
        "observed_survival_through_stream": false,
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        "unknown_prefixes": [],
        "first_failure_determined": true
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      "schema": "random-sat-audit-v1",
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    },
    "report": {
      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 10,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
      "actual_randomness_or_iid_verified": false,
      "source_proof_verified": false,
      "asymptotic_threshold_estimated": false,
      "duplicate_clause_count": 3,
      "clause_type_count": 960,
      "conditional_first_moment_survival_upper": "3234476509624757991344647769100216810857203198904625400933895331391691459636928060001/1989292945639146568621528992587283360401824603189390869761855907572637988050133502132224",
      "summary": {
        "independent_H_lower": 69,
        "independent_H_upper": 69,
        "solver_claimed_H_upper": 69,
        "independently_exact_H": 69,
        "independently_exact_last_sat": 68,
        "independently_exact_clipped_H": 69,
        "cap": 100,
        "observed_survival_through_stream": false,
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        {
          "prefix": 57,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 58,
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          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 59,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 60,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 61,
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          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 62,
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          "assignment": [
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        },
        {
          "prefix": 63,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 64,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 65,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 66,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 67,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 68,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 69,
          "status": "UNSAT",
          "basis": "exhaustive_assignment_bitset"
        }
      ],
      "run": {
        "stop": "first_unsat",
        "work": 4576
      },
      "limits": {
        "max_bytes": 1048576,
        "max_clauses": 2048,
        "max_n": 128,
        "max_exact_n": 16,
        "max_work": 5000000
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      "python": "3.12.14"
    }
  },
  {
    "n": 10,
    "seed": 16,
    "input": {
      "schema": "random-sat-stream-v1",
      "n": 10,
      "k": 3,
      "law": "iid_proper_with_replacement",
      "clauses": [
        [
          -2,
          4,
          -8
        ],
        [
          -2,
          -7,
          -10
        ],
        [
          -2,
          -8,
          9
        ],
        [
          2,
          3,
          -4
        ],
        [
          -2,
          5,
          -10
        ],
        [
          -1,
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          -10
        ],
        [
          2,
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        ],
        [
          1,
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          3
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        [
          2,
          5,
          -9
        ],
        [
          -5,
          9,
          -10
        ],
        [
          3,
          -9,
          -10
        ],
        [
          -4,
          -6,
          -8
        ],
        [
          1,
          -8,
          -9
        ],
        [
          1,
          7,
          -8
        ],
        [
          -3,
          7,
          -10
        ],
        [
          1,
          6,
          -9
        ],
        [
          -1,
          2,
          -4
        ],
        [
          2,
          3,
          5
        ],
        [
          2,
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          6
        ],
        [
          -5,
          7,
          -8
        ],
        [
          2,
          3,
          10
        ],
        [
          -4,
          5,
          -6
        ],
        [
          1,
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          -8
        ],
        [
          4,
          -7,
          -9
        ],
        [
          -3,
          -6,
          -9
        ],
        [
          2,
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          7
        ],
        [
          -1,
          2,
          5
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        [
          -5,
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        ],
        [
          1,
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        ],
        [
          3,
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        ],
        [
          1,
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        [
          -1,
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          5
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        [
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        ],
        [
          1,
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          9
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          5,
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        [
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          9
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        [
          4,
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          -6
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          -3,
          7,
          9
        ],
        [
          -1,
          -2,
          6
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        [
          2,
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        [
          2,
          7,
          -8
        ],
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          3,
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          8
        ],
        [
          3,
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          -4,
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        [
          2,
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          5
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        [
          1,
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        [
          2,
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          7
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          -2,
          4,
          -8
        ],
        [
          -1,
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        [
          -2,
          5,
          10
        ],
        [
          -5,
          6,
          7
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        [
          -1,
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        [
          -2,
          -4,
          6
        ],
        [
          -2,
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        [
          2,
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        [
          3,
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        [
          -3,
          8,
          -9
        ],
        [
          -1,
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        ],
        [
          -3,
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          -8
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        [
          -2,
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          5
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        [
          -3,
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        [
          1,
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          8
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        [
          2,
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          -4
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        [
          1,
          -3,
          6
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        [
          -5,
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          10
        ],
        [
          5,
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        [
          -1,
          2,
          3
        ],
        [
          3,
          4,
          7
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        [
          -2,
          4,
          9
        ],
        [
          -1,
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        ],
        [
          2,
          -8,
          10
        ],
        [
          -1,
          4,
          9
        ],
        [
          -2,
          -3,
          7
        ],
        [
          2,
          3,
          6
        ],
        [
          -2,
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          8
        ],
        [
          2,
          7,
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        [
          -2,
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        [
          1,
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          -4,
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          10
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        [
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          9
        ],
        [
          4,
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          -10
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        [
          -5,
          8,
          10
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        [
          1,
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          4
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        [
          2,
          6,
          9
        ],
        [
          -5,
          8,
          9
        ],
        [
          6,
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          8
        ],
        [
          2,
          8,
          10
        ],
        [
          -1,
          2,
          4
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        [
          -7,
          -8,
          10
        ],
        [
          -5,
          -8,
          9
        ],
        [
          -2,
          7,
          10
        ],
        [
          4,
          5,
          -10
        ],
        [
          -5,
          6,
          8
        ],
        [
          1,
          -4,
          5
        ],
        [
          2,
          -7,
          -8
        ],
        [
          -5,
          -7,
          10
        ],
        [
          3,
          6,
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        ],
        [
          -1,
          -3,
          -6
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      ]
    },
    "report": {
      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 10,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
      "actual_randomness_or_iid_verified": false,
      "source_proof_verified": false,
      "asymptotic_threshold_estimated": false,
      "duplicate_clause_count": 4,
      "clause_type_count": 960,
      "conditional_first_moment_survival_upper": "3234476509624757991344647769100216810857203198904625400933895331391691459636928060001/1989292945639146568621528992587283360401824603189390869761855907572637988050133502132224",
      "summary": {
        "independent_H_lower": 63,
        "independent_H_upper": 63,
        "solver_claimed_H_upper": 63,
        "independently_exact_H": 63,
        "independently_exact_last_sat": 62,
        "independently_exact_clipped_H": 63,
        "cap": 100,
        "observed_survival_through_stream": false,
        "right_censored_after_stream": false,
        "unknown_prefixes": [],
        "first_failure_determined": true
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      "observations": [
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          "basis": "checked_assignment",
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        {
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        {
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        {
          "prefix": 46,
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          "prefix": 47,
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          "prefix": 48,
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          "prefix": 49,
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          "prefix": 50,
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          "prefix": 55,
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        {
          "prefix": 57,
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          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 58,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 59,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 60,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 61,
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          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 62,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 63,
          "status": "UNSAT",
          "basis": "exhaustive_assignment_bitset"
        }
      ],
      "run": {
        "stop": "first_unsat",
        "work": 4192
      },
      "limits": {
        "max_bytes": 1048576,
        "max_clauses": 2048,
        "max_n": 128,
        "max_exact_n": 16,
        "max_work": 5000000
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      "python": "3.12.14"
    }
  },
  {
    "n": 10,
    "seed": 17,
    "input": {
      "schema": "random-sat-stream-v1",
      "n": 10,
      "k": 3,
      "law": "iid_proper_with_replacement",
      "clauses": [
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          -3,
          4,
          7
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          -5,
          6,
          -10
        ],
        [
          -2,
          3,
          6
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        [
          -2,
          4,
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        [
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        [
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        [
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        [
          -4,
          6,
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        [
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        [
          3,
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        [
          3,
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          10
        ],
        [
          -1,
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          10
        ],
        [
          -1,
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        [
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          8,
          -10
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        [
          1,
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        [
          -1,
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        [
          2,
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        [
          -5,
          7,
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        [
          -4,
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          9
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        [
          2,
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          10
        ],
        [
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          7,
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        ],
        [
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          -8
        ],
        [
          3,
          -4,
          -5
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        [
          5,
          -6,
          9
        ],
        [
          2,
          -3,
          8
        ],
        [
          3,
          7,
          10
        ],
        [
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        ],
        [
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          8
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        [
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        [
          2,
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          6
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        [
          1,
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          10
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        [
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          -8
        ],
        [
          -5,
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        [
          -6,
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        ],
        [
          1,
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        [
          -1,
          4,
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        [
          6,
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          10
        ],
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          -4,
          6,
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        [
          3,
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        [
          5,
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          -4,
          5,
          8
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        [
          1,
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        [
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        [
          -3,
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        ],
        [
          -1,
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          5
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        [
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        [
          -1,
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        [
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        [
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          3,
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        [
          3,
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          5
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        [
          5,
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        ],
        [
          2,
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          10
        ],
        [
          3,
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          10
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        [
          -3,
          6,
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          1,
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        [
          -4,
          5,
          -8
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        [
          5,
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        [
          -2,
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        [
          -5,
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        [
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        [
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          10
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          -2,
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          -5
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          -1,
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        [
          2,
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          -8
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        [
          2,
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        [
          3,
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        [
          -1,
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          9
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        [
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          1,
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          3
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          -6,
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        [
          2,
          5,
          8
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        [
          -1,
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          8
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          1,
          3,
          10
        ],
        [
          -3,
          5,
          -7
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        [
          -1,
          6,
          -8
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        [
          -1,
          7,
          9
        ],
        [
          3,
          4,
          -8
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        [
          -2,
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          -8
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        [
          1,
          2,
          -10
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        [
          1,
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          -10
        ],
        [
          1,
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          -4
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        [
          5,
          -6,
          7
        ],
        [
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          9,
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        [
          1,
          -5,
          9
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    },
    "report": {
      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 10,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
      "actual_randomness_or_iid_verified": false,
      "source_proof_verified": false,
      "asymptotic_threshold_estimated": false,
      "duplicate_clause_count": 6,
      "clause_type_count": 960,
      "conditional_first_moment_survival_upper": "3234476509624757991344647769100216810857203198904625400933895331391691459636928060001/1989292945639146568621528992587283360401824603189390869761855907572637988050133502132224",
      "summary": {
        "independent_H_lower": 68,
        "independent_H_upper": 68,
        "solver_claimed_H_upper": 68,
        "independently_exact_H": 68,
        "independently_exact_last_sat": 67,
        "independently_exact_clipped_H": 68,
        "cap": 100,
        "observed_survival_through_stream": false,
        "right_censored_after_stream": false,
        "unknown_prefixes": [],
        "first_failure_determined": true
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      "observations": [
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          "basis": "checked_assignment",
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        {
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        {
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        {
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        {
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        },
        {
          "prefix": 68,
          "status": "UNSAT",
          "basis": "exhaustive_assignment_bitset"
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      ],
      "run": {
        "stop": "first_unsat",
        "work": 4512
      },
      "limits": {
        "max_bytes": 1048576,
        "max_clauses": 2048,
        "max_n": 128,
        "max_exact_n": 16,
        "max_work": 5000000
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      "python": "3.12.14"
    }
  },
  {
    "n": 10,
    "seed": 18,
    "input": {
      "schema": "random-sat-stream-v1",
      "n": 10,
      "k": 3,
      "law": "iid_proper_with_replacement",
      "clauses": [
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          5
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          5
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        [
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        [
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        [
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          9
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        [
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        [
          3,
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          2,
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    },
    "report": {
      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 10,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
      "actual_randomness_or_iid_verified": false,
      "source_proof_verified": false,
      "asymptotic_threshold_estimated": false,
      "duplicate_clause_count": 4,
      "clause_type_count": 960,
      "conditional_first_moment_survival_upper": "3234476509624757991344647769100216810857203198904625400933895331391691459636928060001/1989292945639146568621528992587283360401824603189390869761855907572637988050133502132224",
      "summary": {
        "independent_H_lower": 38,
        "independent_H_upper": 38,
        "solver_claimed_H_upper": 38,
        "independently_exact_H": 38,
        "independently_exact_last_sat": 37,
        "independently_exact_clipped_H": 38,
        "cap": 100,
        "observed_survival_through_stream": false,
        "right_censored_after_stream": false,
        "unknown_prefixes": [],
        "first_failure_determined": true
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        {
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        {
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        {
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        {
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        {
          "prefix": 20,
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        {
          "prefix": 21,
          "status": "SAT",
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        {
          "prefix": 22,
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        {
          "prefix": 23,
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        {
          "prefix": 24,
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        {
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        {
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          "basis": "checked_assignment",
          "assignment": [
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        {
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          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 34,
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          "basis": "checked_assignment",
          "assignment": [
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        {
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          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 36,
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          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 37,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 38,
          "status": "UNSAT",
          "basis": "exhaustive_assignment_bitset"
        }
      ],
      "run": {
        "stop": "first_unsat",
        "work": 2592
      },
      "limits": {
        "max_bytes": 1048576,
        "max_clauses": 2048,
        "max_n": 128,
        "max_exact_n": 16,
        "max_work": 5000000
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      "python": "3.12.14"
    }
  },
  {
    "n": 10,
    "seed": 19,
    "input": {
      "schema": "random-sat-stream-v1",
      "n": 10,
      "k": 3,
      "law": "iid_proper_with_replacement",
      "clauses": [
        [
          4,
          -5,
          7
        ],
        [
          -1,
          -2,
          8
        ],
        [
          5,
          6,
          -7
        ],
        [
          -6,
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          10
        ],
        [
          -3,
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          7
        ],
        [
          1,
          4,
          -5
        ],
        [
          3,
          4,
          -6
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        [
          -1,
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          10
        ],
        [
          -2,
          5,
          -7
        ],
        [
          2,
          4,
          -6
        ],
        [
          3,
          -4,
          8
        ],
        [
          -2,
          -3,
          -5
        ],
        [
          -3,
          5,
          10
        ],
        [
          1,
          4,
          8
        ],
        [
          3,
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          -8
        ],
        [
          1,
          8,
          -9
        ],
        [
          -1,
          3,
          9
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        [
          -1,
          8,
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        [
          2,
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          9
        ],
        [
          2,
          3,
          9
        ],
        [
          -1,
          8,
          -10
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        [
          -5,
          7,
          10
        ],
        [
          -1,
          3,
          9
        ],
        [
          4,
          8,
          10
        ],
        [
          2,
          -3,
          9
        ],
        [
          -6,
          8,
          10
        ],
        [
          -2,
          3,
          7
        ],
        [
          1,
          2,
          5
        ],
        [
          -3,
          5,
          8
        ],
        [
          -3,
          -7,
          -8
        ],
        [
          -1,
          5,
          10
        ],
        [
          -6,
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          10
        ],
        [
          -1,
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        ],
        [
          -7,
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          10
        ],
        [
          1,
          5,
          10
        ],
        [
          -1,
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          10
        ],
        [
          3,
          4,
          -10
        ],
        [
          -2,
          7,
          -8
        ],
        [
          2,
          -5,
          6
        ],
        [
          -6,
          7,
          8
        ],
        [
          4,
          6,
          10
        ],
        [
          1,
          3,
          -5
        ],
        [
          -5,
          6,
          9
        ],
        [
          -1,
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          8
        ],
        [
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        [
          1,
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        [
          1,
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        [
          -3,
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        [
          4,
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          -10
        ],
        [
          2,
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          -7
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        [
          4,
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          10
        ],
        [
          5,
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        [
          2,
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        [
          -2,
          6,
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        [
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        ],
        [
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        [
          -3,
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        [
          -7,
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          -10
        ],
        [
          -3,
          4,
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        [
          5,
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          10
        ],
        [
          -1,
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        [
          -5,
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          -3,
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          10
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        [
          -2,
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        [
          -1,
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        [
          4,
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        [
          -3,
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        [
          -3,
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          10
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        [
          -5,
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          9
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        [
          -1,
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          7
        ],
        [
          2,
          5,
          6
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        [
          -1,
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          9
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          1,
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          7
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        [
          1,
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          3,
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          2,
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          1,
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        [
          -4,
          6,
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          2,
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          8
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        [
          1,
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          3
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          2,
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        [
          6,
          9,
          10
        ],
        [
          2,
          8,
          -9
        ],
        [
          -3,
          -6,
          -8
        ],
        [
          -1,
          4,
          -5
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        [
          -3,
          -4,
          7
        ],
        [
          2,
          8,
          -9
        ],
        [
          -5,
          -7,
          9
        ],
        [
          -3,
          -4,
          -5
        ],
        [
          2,
          -9,
          -10
        ],
        [
          2,
          -4,
          -9
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        [
          -2,
          6,
          7
        ],
        [
          6,
          -8,
          10
        ],
        [
          -3,
          4,
          -10
        ],
        [
          -6,
          7,
          8
        ],
        [
          1,
          5,
          -8
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        [
          6,
          8,
          9
        ]
      ]
    },
    "report": {
      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 10,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
      "actual_randomness_or_iid_verified": false,
      "source_proof_verified": false,
      "asymptotic_threshold_estimated": false,
      "duplicate_clause_count": 6,
      "clause_type_count": 960,
      "conditional_first_moment_survival_upper": "3234476509624757991344647769100216810857203198904625400933895331391691459636928060001/1989292945639146568621528992587283360401824603189390869761855907572637988050133502132224",
      "summary": {
        "independent_H_lower": 52,
        "independent_H_upper": 52,
        "solver_claimed_H_upper": 52,
        "independently_exact_H": 52,
        "independently_exact_last_sat": 51,
        "independently_exact_clipped_H": 52,
        "cap": 100,
        "observed_survival_through_stream": false,
        "right_censored_after_stream": false,
        "unknown_prefixes": [],
        "first_failure_determined": true
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      "observations": [
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          "basis": "checked_assignment",
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        {
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        {
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        {
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      "schema": "random-sat-audit-v1",
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      "n": 16,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
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      "summary": {
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        "independently_exact_last_sat": 83,
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      "k": 3,
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      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 16,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
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      "summary": {
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        "solver_claimed_H_upper": 68,
        "independently_exact_H": 68,
        "independently_exact_last_sat": 67,
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      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 16,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
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        "solver_claimed_H_upper": 77,
        "independently_exact_H": 77,
        "independently_exact_last_sat": 76,
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      "schema": "random-sat-audit-v1",
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      "n": 16,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
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      "duplicate_clause_count": 2,
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        "independently_exact_last_sat": 90,
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      "schema": "random-sat-audit-v1",
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      "k": 3,
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    "report": {
      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 16,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
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      "source_proof_verified": false,
      "asymptotic_threshold_estimated": false,
      "duplicate_clause_count": 5,
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      "summary": {
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        "independent_H_upper": 61,
        "solver_claimed_H_upper": 61,
        "independently_exact_H": 61,
        "independently_exact_last_sat": 60,
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        "cap": 160,
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        "max_n": 128,
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      "schema": "random-sat-audit-v1",
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      "n": 16,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
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      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 16,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
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        "independent_H_upper": 84,
        "solver_claimed_H_upper": 84,
        "independently_exact_H": 84,
        "independently_exact_last_sat": 83,
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      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 16,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
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        "solver_claimed_H_upper": 95,
        "independently_exact_H": 95,
        "independently_exact_last_sat": 94,
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      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 16,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
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        "solver_claimed_H_upper": 62,
        "independently_exact_H": 62,
        "independently_exact_last_sat": 61,
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          "prefix": 62,
          "status": "UNSAT",
          "basis": "exhaustive_assignment_bitset"
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      "run": {
        "stop": "first_unsat",
        "work": 270336
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      "limits": {
        "max_bytes": 1048576,
        "max_clauses": 2048,
        "max_n": 128,
        "max_exact_n": 16,
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      "python": "3.12.14"
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    "n": 16,
    "seed": 11,
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      "k": 3,
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      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 16,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
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      "duplicate_clause_count": 1,
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      "summary": {
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        "independently_exact_last_sat": 81,
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      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 16,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
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        "solver_claimed_H_upper": 98,
        "independently_exact_H": 98,
        "independently_exact_last_sat": 97,
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      "k": 3,
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      "schema": "random-sat-audit-v1",
      "backend": "exact",
      "n": 16,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
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        "solver_claimed_H_upper": 67,
        "independently_exact_H": 67,
        "independently_exact_last_sat": 66,
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      "schema": "random-sat-audit-v1",
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      "n": 16,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
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      "run": {
        "stop": "first_unsat",
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        "max_bytes": 1048576,
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        "max_n": 128,
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      "schema": "random-sat-audit-v1",
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      "n": 16,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
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