{
  "scope": "Exact finite-product compatibility for four supplied transformers; all nested traces through recorded depths; local cover construction on two finite machines; bounded permutation enumeration. Not an unbounded proof or unknown-cover synthesis.",
  "compatibility": {
    "pure_resume": {
      "product_states": 2,
      "induced": {
        "0": "0",
        "1": "1"
      }
    },
    "append_a": {
      "product_states": 2,
      "induced": {
        "0": "1",
        "1": "0"
      }
    },
    "append_b": {
      "product_states": 2,
      "induced": {
        "0": "0",
        "1": "1"
      }
    },
    "last_b_rejected": {
      "product_states": 5,
      "conflicts": {
        "0": [
          "0",
          "1"
        ],
        "1": [
          "0",
          "1"
        ]
      }
    }
  },
  "nested_traces": [
    {
      "mode": "resume",
      "trace_depth": 8,
      "configurations_checked": 11477,
      "maximum_nesting_reached": 8
    },
    {
      "mode": "append",
      "trace_depth": 7,
      "configurations_checked": 4789,
      "maximum_nesting_reached": 7
    }
  ],
  "local_forbidden_merge_rejected": true,
  "local_parity_cover_states": 2,
  "permutation_automata_ends_in_b_search": {
    "1": {
      "candidates": 2,
      "successes": 0,
      "words_used": 127
    },
    "2": {
      "candidates": 16,
      "successes": 0,
      "words_used": 127
    },
    "3": {
      "candidates": 288,
      "successes": 0,
      "words_used": 127
    },
    "4": {
      "candidates": 9216,
      "successes": 0,
      "words_used": 127
    }
  },
  "proof_status": "Proposition 3 for all finite sizes is proved in writing by surjectivity of the b permutation; enumeration only corroborates n<=4."
}