Resolved inputs: {"elements": ["a", "b", "c"], "feasible_sets": [[], ["a"], ["a", "b"], ["a", "b", "c"]], "catalyst_arcs": [["a", "a"], ["a", "c"], ["c", "b"]], "minimal_blockers": false, "chain_sizes": [1, 2, 3, 4, 5, 6, 7, 8], "paired_threshold_size": 5, "threshold": 3, "exhaustive_antimatroid_size": 4, "exhaustive_graph_size": 3, "max_ground_size": 8, "max_reaction_enumeration": 16}
{
  "inputs": {
    "elements": [
      "a",
      "b",
      "c"
    ],
    "feasible_sets": [
      [],
      [
        "a"
      ],
      [
        "a",
        "b"
      ],
      [
        "a",
        "b",
        "c"
      ]
    ],
    "catalyst_arcs": [
      [
        "a",
        "a"
      ],
      [
        "a",
        "c"
      ],
      [
        "c",
        "b"
      ]
    ],
    "minimal_blockers": false,
    "chain_sizes": [
      1,
      2,
      3,
      4,
      5,
      6,
      7,
      8
    ],
    "paired_threshold_size": 5,
    "threshold": 3,
    "exhaustive_antimatroid_size": 4,
    "exhaustive_graph_size": 3,
    "max_ground_size": 8,
    "max_reaction_enumeration": 16
  },
  "worked_fixed_sets": [
    "empty",
    "{a}",
    "{a,b,c}"
  ],
  "worked_markers": 5,
  "four_element_threshold_rafs": 5,
  "paired_threshold": {
    "elements": 5,
    "reactions": 10,
    "reaction_subsets_checked": 1024,
    "nonempty_rafs": 16,
    "marker_molecules": 25
  },
  "marker_scaling": [
    {
      "elements": 1,
      "reactions": 1,
      "all_blockers": 0,
      "minimal_blockers": 0
    },
    {
      "elements": 2,
      "reactions": 2,
      "all_blockers": 1,
      "minimal_blockers": 1
    },
    {
      "elements": 3,
      "reactions": 3,
      "all_blockers": 5,
      "minimal_blockers": 3
    },
    {
      "elements": 4,
      "reactions": 4,
      "all_blockers": 17,
      "minimal_blockers": 6
    },
    {
      "elements": 5,
      "reactions": 5,
      "all_blockers": 49,
      "minimal_blockers": 10
    },
    {
      "elements": 6,
      "reactions": 6,
      "all_blockers": 129,
      "minimal_blockers": 15
    },
    {
      "elements": 7,
      "reactions": 7,
      "all_blockers": 321,
      "minimal_blockers": 21
    },
    {
      "elements": 8,
      "reactions": 8,
      "all_blockers": 769,
      "minimal_blockers": 28
    }
  ],
  "exhaustive_checks": [
    {
      "elements": 0,
      "antimatroids": 1,
      "food_comparisons": 1,
      "raf_comparisons": 1
    },
    {
      "elements": 1,
      "antimatroids": 2,
      "food_comparisons": 4,
      "raf_comparisons": 8
    },
    {
      "elements": 2,
      "antimatroids": 6,
      "food_comparisons": 24,
      "raf_comparisons": 384
    },
    {
      "elements": 3,
      "antimatroids": 35,
      "food_comparisons": 280,
      "raf_comparisons": 143360
    },
    {
      "elements": 4,
      "antimatroids": 596,
      "food_comparisons": 9536,
      "raf_comparisons": 0
    }
  ],
  "total_food_comparisons": 9845,
  "total_raf_comparisons": 143753,
  "evidence": "Exact finite constructions and exhaustive subset checks. Five-element same-ground impossibility is the manuscript theorem, not searched here. No Lean compilation."
}