Resolved inputs: {"universe_size": 3, "sets": [[0, 1], [1, 2], [2]], "block_length": 2, "amplification_sweep": [1, 2, 3, 6, 12], "gap_sizes": [2, 3, 4, 5, 6, 7, 8], "exhaustive_reaction_cap": 18, "exhaustive_set_cap": 18}
{
  "inputs": {
    "universe_size": 3,
    "sets": [
      [
        0,
        1
      ],
      [
        1,
        2
      ],
      [
        2
      ]
    ],
    "block_length": 2,
    "amplification_sweep": [
      1,
      2,
      3,
      6,
      12
    ],
    "gap_sizes": [
      2,
      3,
      4,
      5,
      6,
      7,
      8
    ],
    "exhaustive_reaction_cap": 18,
    "exhaustive_set_cap": 18
  },
  "exhaustive_audit": {
    "reaction_subsets_checked": 512,
    "raf_count": 3,
    "minimum_cover_size": 2,
    "minimum_raf_size": 7
  },
  "covers": [
    {
      "set_indices": "0 1",
      "cover_size": 2,
      "raf_size": 7,
      "inclusion_minimal": true,
      "reaction_ids": "b0:0 b0:1 b1:0 b1:1 g0 g1 g2",
      "closure_depth": 5
    },
    {
      "set_indices": "0 2",
      "cover_size": 2,
      "raf_size": 7,
      "inclusion_minimal": true,
      "reaction_ids": "b0:0 b0:1 b2:0 b2:1 g0 g1 g2",
      "closure_depth": 5
    },
    {
      "set_indices": "0 1 2",
      "cover_size": 3,
      "raf_size": 9,
      "inclusion_minimal": false,
      "reaction_ids": "b0:0 b0:1 b1:0 b1:1 b2:0 b2:1 g0 g1 g2",
      "closure_depth": 5
    }
  ],
  "amplification": [
    {
      "block_length": 1,
      "raf_ratio": "8/5",
      "cover_ratio": "4",
      "transferred_bound": null,
      "bound_applicable": false,
      "bound_holds": null
    },
    {
      "block_length": 2,
      "raf_ratio": "2",
      "cover_ratio": "4",
      "transferred_bound": null,
      "bound_applicable": false,
      "bound_holds": null
    },
    {
      "block_length": 3,
      "raf_ratio": "16/7",
      "cover_ratio": "4",
      "transferred_bound": null,
      "bound_applicable": false,
      "bound_holds": null
    },
    {
      "block_length": 6,
      "raf_ratio": "14/5",
      "cover_ratio": "4",
      "transferred_bound": "23/5",
      "bound_applicable": true,
      "bound_holds": true
    },
    {
      "block_length": 12,
      "raf_ratio": "13/4",
      "cover_ratio": "4",
      "transferred_bound": "11/2",
      "bound_applicable": true,
      "bound_holds": true
    }
  ],
  "irreducible_gap": [
    {
      "universe_size": 2,
      "block_length": 2,
      "reactions": 8,
      "small_irraf": 4,
      "large_irraf": 6,
      "ratio": "3/2"
    },
    {
      "universe_size": 3,
      "block_length": 3,
      "reactions": 15,
      "small_irraf": 6,
      "large_irraf": 12,
      "ratio": "2"
    },
    {
      "universe_size": 4,
      "block_length": 4,
      "reactions": 24,
      "small_irraf": 8,
      "large_irraf": 20,
      "ratio": "5/2"
    },
    {
      "universe_size": 5,
      "block_length": 5,
      "reactions": 35,
      "small_irraf": 10,
      "large_irraf": 30,
      "ratio": "3"
    },
    {
      "universe_size": 6,
      "block_length": 6,
      "reactions": 48,
      "small_irraf": 12,
      "large_irraf": 42,
      "ratio": "7/2"
    },
    {
      "universe_size": 7,
      "block_length": 7,
      "reactions": 63,
      "small_irraf": 14,
      "large_irraf": 56,
      "ratio": "4"
    },
    {
      "universe_size": 8,
      "block_length": 8,
      "reactions": 80,
      "small_irraf": 16,
      "large_irraf": 72,
      "ratio": "9/2"
    }
  ],
  "evidence": "Exact finite incidence/closure/subset calculations and rational ratio arithmetic. Complexity hardness remains the manuscript theorem under P != NP; no Lean compilation."
}