[
  {
    "n": 6,
    "seed": 0,
    "input": {
      "schema": "random-sat-stream-v1",
      "n": 6,
      "k": 3,
      "law": "iid_proper_with_replacement",
      "clauses": [
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          3,
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        [
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        [
          -1,
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          -4
        ],
        [
          -1,
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          -6
        ],
        [
          -3,
          4,
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        ],
        [
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          -5,
          6
        ],
        [
          2,
          3,
          6
        ],
        [
          1,
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          6
        ],
        [
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          5,
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        ],
        [
          2,
          3,
          -5
        ],
        [
          3,
          -5,
          6
        ],
        [
          1,
          3,
          6
        ],
        [
          3,
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        ],
        [
          1,
          3,
          -4
        ],
        [
          -1,
          -5,
          -6
        ],
        [
          1,
          3,
          -4
        ],
        [
          -1,
          -2,
          -6
        ],
        [
          -4,
          5,
          6
        ],
        [
          -1,
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          -6
        ],
        [
          -3,
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        ],
        [
          -4,
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        ],
        [
          1,
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          4
        ],
        [
          1,
          5,
          6
        ],
        [
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        ],
        [
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          -5
        ],
        [
          -2,
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          4
        ],
        [
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        ],
        [
          3,
          4,
          6
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        [
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        [
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          5
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        [
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        ],
        [
          -4,
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          6
        ],
        [
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          6
        ],
        [
          3,
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          6
        ],
        [
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          5,
          -6
        ],
        [
          2,
          -4,
          -6
        ],
        [
          3,
          -4,
          5
        ],
        [
          -1,
          4,
          -6
        ],
        [
          1,
          2,
          4
        ],
        [
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          6
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        [
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          -3
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        [
          1,
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          5
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        [
          -2,
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          6
        ],
        [
          -1,
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        ],
        [
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          6
        ],
        [
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          6
        ],
        [
          2,
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          4
        ],
        [
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        ],
        [
          2,
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        ],
        [
          -1,
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        [
          -1,
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        ],
        [
          3,
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        [
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        [
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          5
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        [
          -1,
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        [
          3,
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          -6
        ],
        [
          -2,
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          -6
        ],
        [
          1,
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          5
        ],
        [
          -1,
          -2,
          5
        ]
      ]
    },
    "report": {
      "schema": "random-sat-audit-v1",
      "backend": "ortools",
      "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": 6,
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      "conditional_first_moment_survival_upper": "508021860739623365322188197652216501772434524836001/23945242826029513411849172299223580994042798784118784",
      "summary": {
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        "independent_H_upper": null,
        "solver_claimed_H_upper": 31,
        "independently_exact_H": null,
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        "cap": 60,
        "observed_survival_through_stream": false,
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        "unknown_prefixes": [],
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      "observations": [
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        },
        {
          "prefix": 1,
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        },
        {
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          "assignment": [
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        },
        {
          "prefix": 3,
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          "assignment": [
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        },
        {
          "prefix": 4,
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          "assignment": [
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        },
        {
          "prefix": 5,
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          "assignment": [
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        },
        {
          "prefix": 6,
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          "assignment": [
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        },
        {
          "prefix": 7,
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        },
        {
          "prefix": 8,
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          "assignment": [
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        },
        {
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          "assignment": [
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        },
        {
          "prefix": 10,
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          "assignment": [
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        },
        {
          "prefix": 11,
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          "assignment": [
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        },
        {
          "prefix": 12,
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          "assignment": [
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        },
        {
          "prefix": 13,
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          "assignment": [
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        },
        {
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          "assignment": [
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        },
        {
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        },
        {
          "prefix": 16,
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          "assignment": [
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        {
          "prefix": 17,
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          "assignment": [
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        },
        {
          "prefix": 18,
          "solver_status": "OPTIMAL",
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        },
        {
          "prefix": 19,
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          "assignment": [
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        },
        {
          "prefix": 20,
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          "assignment": [
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        },
        {
          "prefix": 21,
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          "assignment": [
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        },
        {
          "prefix": 22,
          "solver_status": "OPTIMAL",
          "wall_seconds": 0.00023500000000000002,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
            1,
            1,
            1,
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          ]
        },
        {
          "prefix": 23,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
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            1,
            0,
            0,
            0
          ]
        },
        {
          "prefix": 24,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
            1,
            1,
            1,
            0,
            0,
            0
          ]
        },
        {
          "prefix": 25,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
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            1,
            1,
            0,
            0,
            0
          ]
        },
        {
          "prefix": 26,
          "solver_status": "OPTIMAL",
          "wall_seconds": 8.2e-05,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
            1,
            1,
            0,
            0,
            0,
            0
          ]
        },
        {
          "prefix": 27,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
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            1,
            0,
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            0,
            0
          ]
        },
        {
          "prefix": 28,
          "solver_status": "OPTIMAL",
          "wall_seconds": 8e-05,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
            0,
            0,
            0,
            0,
            0,
            1
          ]
        },
        {
          "prefix": 29,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
            0,
            0,
            0,
            0,
            0,
            1
          ]
        },
        {
          "prefix": 30,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
            0,
            0,
            0,
            0,
            0,
            1
          ]
        },
        {
          "prefix": 31,
          "solver_status": "INFEASIBLE",
          "wall_seconds": 5.8e-05,
          "status": "UNSAT",
          "basis": "solver_status_only"
        }
      ],
      "run": {
        "stop": "solver_unsat",
        "solver": "OR-Tools CP-SAT",
        "version": "9.15.6755",
        "calls": 6,
        "per_call_seconds": 0.05,
        "total_seconds": 10,
        "elapsed_seconds": 0.04471170800388791,
        "independent_unsat_proof_checked": false,
        "note": "Model retained, but each solve is a fresh CP-SAT call; no retained learned state. Time limits are not a hard process watchdog."
      },
      "limits": {
        "max_bytes": 1048576,
        "max_clauses": 2048,
        "max_n": 128,
        "max_exact_n": 16,
        "max_work": 5000000
      },
      "python": "3.12.14"
    },
    "exact_H": 31
  },
  {
    "n": 6,
    "seed": 1,
    "input": {
      "schema": "random-sat-stream-v1",
      "n": 6,
      "k": 3,
      "law": "iid_proper_with_replacement",
      "clauses": [
        [
          -1,
          3,
          -4
        ],
        [
          3,
          -5,
          -6
        ],
        [
          -1,
          -2,
          -5
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        [
          1,
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          -6
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        [
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          2,
          6
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        [
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          5,
          6
        ],
        [
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          4,
          -6
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        [
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          -6
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        [
          2,
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          -6
        ],
        [
          1,
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          6
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        [
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          -6
        ],
        [
          -2,
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          6
        ],
        [
          1,
          2,
          3
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        [
          2,
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          -6
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        [
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          5
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        [
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        [
          -1,
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          -3
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        [
          -2,
          4,
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        [
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        [
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        [
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          6
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        [
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          2,
          -6
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        [
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          -4
        ],
        [
          1,
          2,
          3
        ],
        [
          1,
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          3
        ],
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          2,
          3
        ],
        [
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          4,
          -6
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        [
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          -3
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        [
          2,
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          -6
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        [
          1,
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          5
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        [
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          3
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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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          6
        ],
        [
          3,
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          -5
        ]
      ]
    },
    "report": {
      "schema": "random-sat-audit-v1",
      "backend": "ortools",
      "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": 10,
      "clause_type_count": 160,
      "conditional_first_moment_survival_upper": "508021860739623365322188197652216501772434524836001/23945242826029513411849172299223580994042798784118784",
      "summary": {
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        "solver_claimed_H_upper": 15,
        "independently_exact_H": null,
        "independently_exact_last_sat": null,
        "independently_exact_clipped_H": null,
        "cap": 60,
        "observed_survival_through_stream": false,
        "right_censored_after_stream": false,
        "unknown_prefixes": [],
        "first_failure_determined": false
      },
      "observations": [
        {
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        },
        {
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        {
          "prefix": 2,
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        },
        {
          "prefix": 3,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 4,
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          "assignment": [
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        },
        {
          "prefix": 5,
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          "assignment": [
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        },
        {
          "prefix": 6,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
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            0
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        },
        {
          "prefix": 7,
          "status": "SAT",
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          "assignment": [
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            0
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        },
        {
          "prefix": 8,
          "status": "SAT",
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          "assignment": [
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            0,
            0
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        },
        {
          "prefix": 9,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
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            0,
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            0,
            0
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        },
        {
          "prefix": 10,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
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            0,
            0,
            0,
            0
          ]
        },
        {
          "prefix": 11,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
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            0
          ]
        },
        {
          "prefix": 12,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
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            0
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        },
        {
          "prefix": 13,
          "solver_status": "OPTIMAL",
          "wall_seconds": 6.1000000000000005e-05,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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            1,
            1,
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            1
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        },
        {
          "prefix": 14,
          "status": "SAT",
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          "assignment": [
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            1,
            1,
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            1
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        },
        {
          "prefix": 15,
          "solver_status": "INFEASIBLE",
          "wall_seconds": 3.2000000000000005e-05,
          "status": "UNSAT",
          "basis": "solver_status_only"
        }
      ],
      "run": {
        "stop": "solver_unsat",
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        "version": "9.15.6755",
        "calls": 2,
        "per_call_seconds": 0.05,
        "total_seconds": 10,
        "elapsed_seconds": 0.00015820900443941355,
        "independent_unsat_proof_checked": false,
        "note": "Model retained, but each solve is a fresh CP-SAT call; no retained learned state. Time limits are not a hard process watchdog."
      },
      "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"
    },
    "exact_H": 15
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  {
    "n": 6,
    "seed": 2,
    "input": {
      "schema": "random-sat-stream-v1",
      "n": 6,
      "k": 3,
      "law": "iid_proper_with_replacement",
      "clauses": [
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          -1,
          2,
          4
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        [
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          2,
          5
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        [
          1,
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          5
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        [
          -2,
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          5
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        [
          1,
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          -5
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        [
          -1,
          5,
          6
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        [
          -1,
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          -6
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        [
          4,
          5,
          -6
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        [
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          6
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        [
          4,
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        [
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        [
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          6
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        [
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        [
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          3
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        [
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          -6
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        [
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          5
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        [
          -3,
          4,
          5
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        [
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          -5
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        [
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          4,
          6
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        [
          1,
          -3,
          5
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        [
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          5
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        [
          1,
          4,
          -5
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        [
          -1,
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          3
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        [
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          5
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          3,
          -4
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        [
          -3,
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          -5
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        [
          -3,
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        [
          -2,
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          5
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        [
          3,
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          -5
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        [
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          6
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        [
          -1,
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          5
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        [
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          -6
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        [
          -2,
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          -5
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        [
          -3,
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          5
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        [
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          5
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        [
          3,
          5,
          6
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        [
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          -5
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        [
          -2,
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          5
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        [
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          -6
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        [
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          -5
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        [
          -2,
          3,
          6
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        [
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          6
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        [
          3,
          4,
          5
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        [
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        [
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        [
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          4,
          6
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      ]
    },
    "report": {
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      "duplicate_clause_count": 11,
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        {
          "prefix": 2,
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        {
          "prefix": 3,
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          "assignment": [
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          "assignment": [
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          "assignment": [
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            1,
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            0
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        },
        {
          "prefix": 6,
          "solver_status": "OPTIMAL",
          "wall_seconds": 0.000231,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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            1
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        },
        {
          "prefix": 7,
          "solver_status": "OPTIMAL",
          "wall_seconds": 6.7e-05,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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            0
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        {
          "prefix": 8,
          "status": "SAT",
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          "assignment": [
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        {
          "prefix": 9,
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          "assignment": [
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        {
          "prefix": 10,
          "status": "SAT",
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          "assignment": [
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        {
          "prefix": 11,
          "status": "SAT",
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          "assignment": [
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            0
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        },
        {
          "prefix": 12,
          "solver_status": "OPTIMAL",
          "wall_seconds": 6.400000000000001e-05,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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            1,
            1
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        {
          "prefix": 13,
          "solver_status": "OPTIMAL",
          "wall_seconds": 6.1000000000000005e-05,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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            1,
            1
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        },
        {
          "prefix": 14,
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          "assignment": [
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          "assignment": [
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            1
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        {
          "prefix": 17,
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          "assignment": [
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            1
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        {
          "prefix": 18,
          "solver_status": "OPTIMAL",
          "wall_seconds": 6.900000000000001e-05,
          "status": "SAT",
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          "assignment": [
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            1,
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            1,
            1
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        {
          "prefix": 19,
          "solver_status": "INFEASIBLE",
          "wall_seconds": 3.1e-05,
          "status": "UNSAT",
          "basis": "solver_status_only"
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      ],
      "run": {
        "stop": "solver_unsat",
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        "total_seconds": 10,
        "elapsed_seconds": 0.0007184580026660115,
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        "note": "Model retained, but each solve is a fresh CP-SAT call; no retained learned state. Time limits are not a hard process watchdog."
      },
      "limits": {
        "max_bytes": 1048576,
        "max_clauses": 2048,
        "max_n": 128,
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    "exact_H": 19
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  {
    "n": 10,
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      "n": 10,
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      "law": "iid_proper_with_replacement",
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          -10
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          -2,
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          9
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        [
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        [
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          10
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        [
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          -7
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          5
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        [
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          10
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        [
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          8
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    },
    "report": {
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      "n": 10,
      "k": 3,
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      "duplicate_clause_count": 4,
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      "summary": {
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        "solver_claimed_H_upper": 50,
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        "cap": 100,
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        },
        {
          "prefix": 12,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 13,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
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            1,
            0,
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            1,
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            0
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        },
        {
          "prefix": 14,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
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        },
        {
          "prefix": 15,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
            1,
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            0,
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        },
        {
          "prefix": 16,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
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        },
        {
          "prefix": 17,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
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        },
        {
          "prefix": 18,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 19,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 20,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 21,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 22,
          "solver_status": "OPTIMAL",
          "wall_seconds": 6e-05,
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          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 23,
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          "assignment": [
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        },
        {
          "prefix": 24,
          "solver_status": "OPTIMAL",
          "wall_seconds": 5.7e-05,
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          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 25,
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          "assignment": [
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        },
        {
          "prefix": 26,
          "status": "SAT",
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          "assignment": [
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        {
          "prefix": 27,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 28,
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          "assignment": [
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        {
          "prefix": 29,
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          "assignment": [
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        },
        {
          "prefix": 30,
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          "assignment": [
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        {
          "prefix": 31,
          "status": "SAT",
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          "assignment": [
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        {
          "prefix": 32,
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          "assignment": [
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        },
        {
          "prefix": 33,
          "solver_status": "OPTIMAL",
          "wall_seconds": 6.6e-05,
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          "assignment": [
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        },
        {
          "prefix": 34,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 35,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 36,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 37,
          "solver_status": "OPTIMAL",
          "wall_seconds": 7.400000000000001e-05,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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            1
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        },
        {
          "prefix": 38,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 39,
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          "assignment": [
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        },
        {
          "prefix": 40,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 41,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 42,
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          "assignment": [
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            1
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        },
        {
          "prefix": 43,
          "status": "SAT",
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          "assignment": [
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            1
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        },
        {
          "prefix": 44,
          "status": "SAT",
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          "assignment": [
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            1,
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            1
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        },
        {
          "prefix": 45,
          "solver_status": "OPTIMAL",
          "wall_seconds": 7.7e-05,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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            1,
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        },
        {
          "prefix": 46,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
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        },
        {
          "prefix": 47,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
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        },
        {
          "prefix": 48,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
            0,
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        },
        {
          "prefix": 49,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
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        },
        {
          "prefix": 50,
          "solver_status": "INFEASIBLE",
          "wall_seconds": 6.500000000000001e-05,
          "status": "UNSAT",
          "basis": "solver_status_only"
        }
      ],
      "run": {
        "stop": "solver_unsat",
        "solver": "OR-Tools CP-SAT",
        "version": "9.15.6755",
        "calls": 8,
        "per_call_seconds": 0.05,
        "total_seconds": 10,
        "elapsed_seconds": 0.0007732920057605952,
        "independent_unsat_proof_checked": false,
        "note": "Model retained, but each solve is a fresh CP-SAT call; no retained learned state. Time limits are not a hard process watchdog."
      },
      "limits": {
        "max_bytes": 1048576,
        "max_clauses": 2048,
        "max_n": 128,
        "max_exact_n": 16,
        "max_work": 5000000
      },
      "python": "3.12.14"
    },
    "exact_H": 50
  },
  {
    "n": 10,
    "seed": 1,
    "input": {
      "schema": "random-sat-stream-v1",
      "n": 10,
      "k": 3,
      "law": "iid_proper_with_replacement",
      "clauses": [
        [
          1,
          -4,
          -7
        ],
        [
          -3,
          5,
          8
        ],
        [
          5,
          8,
          -10
        ],
        [
          5,
          -6,
          9
        ],
        [
          -4,
          8,
          9
        ],
        [
          -1,
          -3,
          -4
        ],
        [
          1,
          -7,
          10
        ],
        [
          -1,
          -4,
          -5
        ],
        [
          2,
          9,
          -10
        ],
        [
          4,
          8,
          -9
        ],
        [
          -2,
          -6,
          10
        ],
        [
          2,
          7,
          -10
        ],
        [
          3,
          8,
          -10
        ],
        [
          -2,
          -4,
          10
        ],
        [
          5,
          6,
          7
        ],
        [
          -1,
          6,
          7
        ],
        [
          -1,
          -3,
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        [
          2,
          8,
          -10
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        [
          1,
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          6
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        [
          -6,
          8,
          -10
        ],
        [
          5,
          7,
          10
        ],
        [
          2,
          5,
          6
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        [
          2,
          6,
          -8
        ],
        [
          -3,
          6,
          9
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        [
          -4,
          -8,
          9
        ],
        [
          4,
          -8,
          -10
        ],
        [
          -1,
          2,
          -3
        ],
        [
          -4,
          -5,
          -10
        ],
        [
          -2,
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          -10
        ],
        [
          -1,
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        [
          5,
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          9
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        ],
        [
          3,
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          7
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        [
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        [
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          -10
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        [
          2,
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          8
        ],
        [
          1,
          2,
          6
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        [
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          2,
          5
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        [
          -1,
          2,
          -6
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        [
          3,
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        ],
        [
          -3,
          4,
          -10
        ],
        [
          1,
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          -4
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        [
          -6,
          7,
          10
        ],
        [
          -2,
          4,
          10
        ],
        [
          -4,
          5,
          8
        ],
        [
          1,
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          8
        ],
        [
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        [
          4,
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          9
        ],
        [
          1,
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          6
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        [
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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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          10
        ],
        [
          4,
          -5,
          7
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        [
          -1,
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        [
          4,
          8,
          -9
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        [
          -2,
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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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        ],
        [
          3,
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          -9
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        [
          -1,
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        [
          -1,
          5,
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        ],
        [
          -3,
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          9
        ],
        [
          4,
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          9
        ],
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          -6,
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          -8
        ],
        [
          2,
          3,
          5
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        [
          1,
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        ],
        [
          -4,
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        [
          -2,
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          10
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        [
          6,
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          10
        ],
        [
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          6,
          -9
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        [
          -4,
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          -8
        ],
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          -3,
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          -5
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        [
          -8,
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          10
        ],
        [
          -2,
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          -7
        ],
        [
          3,
          4,
          5
        ],
        [
          5,
          -7,
          -10
        ],
        [
          -7,
          -8,
          9
        ],
        [
          -4,
          5,
          6
        ],
        [
          -1,
          5,
          -9
        ],
        [
          -2,
          3,
          6
        ],
        [
          -2,
          3,
          -4
        ],
        [
          3,
          -6,
          -7
        ],
        [
          6,
          7,
          10
        ],
        [
          2,
          9,
          10
        ],
        [
          -5,
          8,
          -10
        ],
        [
          3,
          -4,
          5
        ],
        [
          -2,
          5,
          -7
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      ]
    },
    "report": {
      "schema": "random-sat-audit-v1",
      "backend": "ortools",
      "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": null,
        "solver_claimed_H_upper": 49,
        "independently_exact_H": null,
        "independently_exact_last_sat": null,
        "independently_exact_clipped_H": null,
        "cap": 100,
        "observed_survival_through_stream": false,
        "right_censored_after_stream": false,
        "unknown_prefixes": [],
        "first_failure_determined": false
      },
      "observations": [
        {
          "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",
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          "assignment": [
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        {
          "prefix": 3,
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          "assignment": [
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        },
        {
          "prefix": 4,
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          "assignment": [
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        },
        {
          "prefix": 5,
          "status": "SAT",
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          "assignment": [
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        {
          "prefix": 6,
          "status": "SAT",
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          "assignment": [
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        {
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          "assignment": [
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        {
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        },
        {
          "prefix": 9,
          "status": "SAT",
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        {
          "prefix": 10,
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          "assignment": [
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        {
          "prefix": 11,
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          "assignment": [
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        {
          "prefix": 12,
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          "assignment": [
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        {
          "prefix": 13,
          "status": "SAT",
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          "assignment": [
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        {
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          "assignment": [
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        },
        {
          "prefix": 15,
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          "wall_seconds": 6.500000000000001e-05,
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          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 16,
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          "assignment": [
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        {
          "prefix": 17,
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          "assignment": [
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        {
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          "assignment": [
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        {
          "prefix": 20,
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          "assignment": [
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        {
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        {
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        {
          "prefix": 25,
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          "assignment": [
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          "assignment": [
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        {
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          "assignment": [
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          "assignment": [
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        {
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          "assignment": [
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        {
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          "assignment": [
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        {
          "prefix": 33,
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        {
          "prefix": 34,
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          "assignment": [
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        {
          "prefix": 35,
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          "assignment": [
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        },
        {
          "prefix": 36,
          "status": "SAT",
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          "assignment": [
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        {
          "prefix": 37,
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          "assignment": [
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        },
        {
          "prefix": 38,
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          "wall_seconds": 8.7e-05,
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          "assignment": [
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        {
          "prefix": 39,
          "solver_status": "OPTIMAL",
          "wall_seconds": 8.300000000000001e-05,
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          "assignment": [
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        {
          "prefix": 40,
          "solver_status": "OPTIMAL",
          "wall_seconds": 8.6e-05,
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          "assignment": [
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        {
          "prefix": 41,
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          "assignment": [
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        {
          "prefix": 42,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 43,
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          "assignment": [
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        {
          "prefix": 44,
          "solver_status": "OPTIMAL",
          "wall_seconds": 9.7e-05,
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          "assignment": [
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        },
        {
          "prefix": 45,
          "solver_status": "OPTIMAL",
          "wall_seconds": 9e-05,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
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        },
        {
          "prefix": 46,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 47,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 48,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 49,
          "solver_status": "INFEASIBLE",
          "wall_seconds": 5.4000000000000005e-05,
          "status": "UNSAT",
          "basis": "solver_status_only"
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      ],
      "run": {
        "stop": "solver_unsat",
        "solver": "OR-Tools CP-SAT",
        "version": "9.15.6755",
        "calls": 8,
        "per_call_seconds": 0.05,
        "total_seconds": 10,
        "elapsed_seconds": 0.0008805000106804073,
        "independent_unsat_proof_checked": false,
        "note": "Model retained, but each solve is a fresh CP-SAT call; no retained learned state. Time limits are not a hard process watchdog."
      },
      "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"
    },
    "exact_H": 49
  },
  {
    "n": 10,
    "seed": 2,
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      "schema": "random-sat-stream-v1",
      "n": 10,
      "k": 3,
      "law": "iid_proper_with_replacement",
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          7,
          -8
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          10
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          6
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        [
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          10
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          10
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        [
          -2,
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          10
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          4,
          6
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          5,
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          -10
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        [
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        [
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    },
    "report": {
      "schema": "random-sat-audit-v1",
      "backend": "ortools",
      "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": null,
        "solver_claimed_H_upper": 62,
        "independently_exact_H": null,
        "independently_exact_last_sat": null,
        "independently_exact_clipped_H": null,
        "cap": 100,
        "observed_survival_through_stream": false,
        "right_censored_after_stream": false,
        "unknown_prefixes": [],
        "first_failure_determined": false
      },
      "observations": [
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        {
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        {
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        {
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        {
          "prefix": 5,
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        {
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        {
          "prefix": 7,
          "solver_status": "OPTIMAL",
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          "basis": "checked_assignment",
          "assignment": [
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        {
          "prefix": 8,
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          "assignment": [
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        {
          "prefix": 9,
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          "assignment": [
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        },
        {
          "prefix": 10,
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          "assignment": [
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        },
        {
          "prefix": 11,
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          "assignment": [
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        },
        {
          "prefix": 12,
          "solver_status": "OPTIMAL",
          "wall_seconds": 8.5e-05,
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          "assignment": [
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        },
        {
          "prefix": 13,
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          "assignment": [
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        },
        {
          "prefix": 14,
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          "assignment": [
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        {
          "prefix": 15,
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        {
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        {
          "prefix": 17,
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          "assignment": [
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        {
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        {
          "prefix": 19,
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          "assignment": [
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        },
        {
          "prefix": 20,
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          "assignment": [
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        },
        {
          "prefix": 21,
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          "assignment": [
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        },
        {
          "prefix": 22,
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          "assignment": [
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        },
        {
          "prefix": 23,
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          "assignment": [
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        },
        {
          "prefix": 24,
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          "assignment": [
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        },
        {
          "prefix": 25,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 26,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 27,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 28,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 29,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 30,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 31,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 32,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 33,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 34,
          "solver_status": "OPTIMAL",
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        },
        {
          "prefix": 35,
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          "assignment": [
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        },
        {
          "prefix": 36,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 37,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 38,
          "solver_status": "OPTIMAL",
          "wall_seconds": 0.00010300000000000001,
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          "assignment": [
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        {
          "prefix": 39,
          "status": "SAT",
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          "assignment": [
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        {
          "prefix": 40,
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          "assignment": [
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        {
          "prefix": 41,
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          "assignment": [
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        },
        {
          "prefix": 42,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 43,
          "status": "SAT",
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          "assignment": [
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        {
          "prefix": 44,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 45,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 46,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 47,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 48,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 49,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 50,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
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        },
        {
          "prefix": 51,
          "status": "SAT",
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          "assignment": [
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            1,
            0
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        },
        {
          "prefix": 52,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
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            0
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        },
        {
          "prefix": 53,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
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            0
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        },
        {
          "prefix": 54,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
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            1,
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            1,
            0
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        },
        {
          "prefix": 55,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
            0,
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            1,
            0,
            0,
            0,
            1,
            0,
            1,
            0
          ]
        },
        {
          "prefix": 56,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
            0,
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            1,
            0,
            0,
            0,
            1,
            0,
            1,
            0
          ]
        },
        {
          "prefix": 57,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
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            1,
            0,
            0,
            0,
            1,
            0,
            1,
            0
          ]
        },
        {
          "prefix": 58,
          "solver_status": "OPTIMAL",
          "wall_seconds": 0.000115,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
            1,
            0,
            1,
            0,
            0,
            0,
            1,
            0,
            1,
            0
          ]
        },
        {
          "prefix": 59,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
            1,
            0,
            1,
            0,
            0,
            0,
            1,
            0,
            1,
            0
          ]
        },
        {
          "prefix": 60,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
            1,
            0,
            1,
            0,
            0,
            0,
            1,
            0,
            1,
            0
          ]
        },
        {
          "prefix": 61,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
            1,
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            1,
            0,
            0,
            0,
            1,
            0,
            1,
            0
          ]
        },
        {
          "prefix": 62,
          "solver_status": "INFEASIBLE",
          "wall_seconds": 6.8e-05,
          "status": "UNSAT",
          "basis": "solver_status_only"
        }
      ],
      "run": {
        "stop": "solver_unsat",
        "solver": "OR-Tools CP-SAT",
        "version": "9.15.6755",
        "calls": 6,
        "per_call_seconds": 0.05,
        "total_seconds": 10,
        "elapsed_seconds": 0.0008768340048845857,
        "independent_unsat_proof_checked": false,
        "note": "Model retained, but each solve is a fresh CP-SAT call; no retained learned state. Time limits are not a hard process watchdog."
      },
      "limits": {
        "max_bytes": 1048576,
        "max_clauses": 2048,
        "max_n": 128,
        "max_exact_n": 16,
        "max_work": 5000000
      },
      "python": "3.12.14"
    },
    "exact_H": 62
  },
  {
    "n": 16,
    "seed": 0,
    "input": {
      "schema": "random-sat-stream-v1",
      "n": 16,
      "k": 3,
      "law": "iid_proper_with_replacement",
      "clauses": [
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          15,
          -16
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        [
          6,
          -12,
          13
        ],
        [
          1,
          5,
          -8
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        [
          3,
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          -14
        ],
        [
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          16
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        [
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          -12,
          16
        ],
        [
          6,
          -9,
          12
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        [
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          15
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        [
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        ],
        [
          5,
          -8,
          16
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        [
          3,
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          11
        ],
        [
          -9,
          12,
          14
        ],
        [
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          -6,
          8
        ],
        [
          -4,
          -6,
          10
        ],
        [
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          -6,
          -9
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        [
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        [
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          14
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        [
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          13,
          -15
        ],
        [
          2,
          6,
          -16
        ],
        [
          -4,
          -9,
          15
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        [
          1,
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          -16
        ],
        [
          -1,
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          15
        ],
        [
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          -16
        ],
        [
          8,
          10,
          -11
        ],
        [
          -1,
          -14,
          -16
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        [
          -5,
          8,
          -12
        ],
        [
          -7,
          -8,
          13
        ],
        [
          -4,
          10,
          15
        ],
        [
          3,
          5,
          -7
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        [
          8,
          10,
          -16
        ],
        [
          -7,
          9,
          -15
        ],
        [
          -10,
          12,
          16
        ],
        [
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          -12,
          15
        ],
        [
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          7,
          11
        ],
        [
          1,
          3,
          -4
        ],
        [
          -1,
          -12,
          13
        ],
        [
          6,
          8,
          -13
        ],
        [
          1,
          -2,
          -4
        ],
        [
          9,
          10,
          -12
        ],
        [
          5,
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          -8
        ],
        [
          -3,
          9,
          13
        ],
        [
          -4,
          -12,
          -16
        ],
        [
          1,
          7,
          -12
        ],
        [
          2,
          -15,
          16
        ],
        [
          -3,
          -6,
          -15
        ],
        [
          -3,
          8,
          -15
        ],
        [
          2,
          6,
          11
        ],
        [
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          -15
        ],
        [
          7,
          -10,
          14
        ],
        [
          1,
          11,
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        [
          1,
          9,
          -15
        ],
        [
          4,
          -11,
          14
        ],
        [
          9,
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          -15
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        [
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          -15
        ],
        [
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          10
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        [
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          13
        ],
        [
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        [
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          4,
          14
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        [
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          7
        ],
        [
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          14,
          -15
        ],
        [
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          -6
        ],
        [
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          16
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        [
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          11
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        [
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          11,
          15
        ],
        [
          5,
          -15,
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          -10,
          16
        ],
        [
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          9,
          11
        ],
        [
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          12,
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        [
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          14,
          15
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        [
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          -15
        ],
        [
          -1,
          4,
          11
        ],
        [
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          12,
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        ],
        [
          8,
          10,
          15
        ],
        [
          1,
          -8,
          10
        ],
        [
          1,
          11,
          13
        ],
        [
          -2,
          5,
          -9
        ],
        [
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        ],
        [
          -1,
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          6
        ],
        [
          1,
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        [
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          15
        ],
        [
          6,
          -7,
          13
        ],
        [
          10,
          -14,
          -15
        ],
        [
          4,
          -5,
          -14
        ],
        [
          -10,
          13,
          -14
        ],
        [
          3,
          -8,
          -12
        ],
        [
          -3,
          6,
          -8
        ],
        [
          6,
          11,
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      "schema": "random-sat-audit-v1",
      "backend": "ortools",
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      "k": 3,
      "declared_law": "iid_proper_with_replacement",
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        {
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          "assignment": [
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        {
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          "assignment": [
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        {
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          "solver_status": "OPTIMAL",
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        {
          "prefix": 83,
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          "assignment": [
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        {
          "prefix": 84,
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          "wall_seconds": 8.300000000000001e-05,
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          "basis": "solver_status_only"
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      ],
      "run": {
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        "note": "Model retained, but each solve is a fresh CP-SAT call; no retained learned state. Time limits are not a hard process watchdog."
      },
      "limits": {
        "max_bytes": 1048576,
        "max_clauses": 2048,
        "max_n": 128,
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    "exact_H": 84
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  {
    "n": 16,
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      "schema": "random-sat-audit-v1",
      "backend": "ortools",
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        {
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        {
          "prefix": 73,
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          "assignment": [
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        {
          "prefix": 74,
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          "assignment": [
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        {
          "prefix": 75,
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          "assignment": [
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        },
        {
          "prefix": 76,
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          "assignment": [
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        },
        {
          "prefix": 77,
          "status": "SAT",
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          "assignment": [
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        },
        {
          "prefix": 78,
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          "assignment": [
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        },
        {
          "prefix": 79,
          "solver_status": "INFEASIBLE",
          "wall_seconds": 9.6e-05,
          "status": "UNSAT",
          "basis": "solver_status_only"
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      ],
      "run": {
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        "solver": "OR-Tools CP-SAT",
        "version": "9.15.6755",
        "calls": 9,
        "per_call_seconds": 0.05,
        "total_seconds": 10,
        "elapsed_seconds": 0.0011378749914001673,
        "independent_unsat_proof_checked": false,
        "note": "Model retained, but each solve is a fresh CP-SAT call; no retained learned state. Time limits are not a hard process watchdog."
      },
      "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"
    },
    "exact_H": 79
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  {
    "n": 16,
    "seed": 2,
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      "schema": "random-sat-audit-v1",
      "backend": "ortools",
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      "k": 3,
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          "assignment": [
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            1,
            1
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        {
          "prefix": 56,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
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            0,
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            1,
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            1,
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            0,
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            1,
            1
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        },
        {
          "prefix": 57,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
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            0,
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            1,
            1,
            0,
            0,
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            1,
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            1
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        },
        {
          "prefix": 58,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
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            0,
            0,
            1,
            1,
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            1,
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            0,
            1,
            1,
            1,
            1
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        },
        {
          "prefix": 59,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
            1,
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            0,
            1,
            1,
            0,
            0,
            1,
            1,
            0,
            0,
            1,
            1,
            1,
            1
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        },
        {
          "prefix": 60,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
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            1,
            1,
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            0,
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            1,
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            0,
            1,
            1,
            1,
            1
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        },
        {
          "prefix": 61,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
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            0,
            0,
            1,
            1,
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            0,
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            1,
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            0,
            1,
            1,
            1,
            1
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        },
        {
          "prefix": 62,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
            1,
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            0,
            0,
            1,
            1,
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            0,
            1,
            1,
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            0,
            1,
            1,
            1,
            1
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        },
        {
          "prefix": 63,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
            1,
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            0,
            0,
            1,
            1,
            0,
            0,
            1,
            1,
            0,
            0,
            1,
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            1,
            1
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        },
        {
          "prefix": 64,
          "solver_status": "OPTIMAL",
          "wall_seconds": 0.000124,
          "status": "SAT",
          "basis": "checked_assignment",
          "assignment": [
            0,
            0,
            1,
            1,
            1,
            1,
            0,
            1,
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            0,
            0,
            0,
            1,
            1,
            0,
            1
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        },
        {
          "prefix": 65,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
            0,
            0,
            1,
            1,
            1,
            1,
            0,
            1,
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            0,
            0,
            0,
            1,
            1,
            0,
            1
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        },
        {
          "prefix": 66,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
            0,
            0,
            1,
            1,
            1,
            1,
            0,
            1,
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            0,
            0,
            0,
            1,
            1,
            0,
            1
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        },
        {
          "prefix": 67,
          "status": "SAT",
          "basis": "checked_assignment_reused",
          "assignment": [
            0,
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            1,
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            1,
            1,
            0,
            1,
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            0,
            0,
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            0,
            1
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        },
        {
          "prefix": 68,
          "solver_status": "INFEASIBLE",
          "wall_seconds": 9.2e-05,
          "status": "UNSAT",
          "basis": "solver_status_only"
        }
      ],
      "run": {
        "stop": "solver_unsat",
        "solver": "OR-Tools CP-SAT",
        "version": "9.15.6755",
        "calls": 13,
        "per_call_seconds": 0.05,
        "total_seconds": 10,
        "elapsed_seconds": 0.0015054160030558705,
        "independent_unsat_proof_checked": false,
        "note": "Model retained, but each solve is a fresh CP-SAT call; no retained learned state. Time limits are not a hard process watchdog."
      },
      "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"
    },
    "exact_H": 68
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  {
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    },
    "report": {
      "schema": "random-sat-audit-v1",
      "backend": "ortools",
      "n": 40,
      "k": 3,
      "declared_law": "iid_proper_with_replacement",
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      "source_proof_verified": false,
      "asymptotic_threshold_estimated": false,
      "duplicate_clause_count": 0,
      "clause_type_count": 79040,
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      "summary": {
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        "independent_H_upper": null,
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]
