{
  "scope": "Exact symbolic word equations and handwritten indexed branch closure for triple_of_chain, pop_only_green, chain_of_triple, and the Single arm of pop_green. Source files are hash-pinned. This is not OCaml extraction, buffer verification, a Rocq rerun, or a certificate for pop_pair_green.",
  "source_commit": "503c5d3ff7f9a20bad1cd7a8f8d7abf4e635d3a0",
  "checked_source_hashes": {
    "lib/cadeque_core.ml": "2a7e36a50e9cec5f3cc06226922ab26e039e1fa0dc1188e879e594f320ae003e",
    "theory/Cadeque/Core.v": "32340da1cedd75eddee2e3205fee4ae4d99f71e347e807b993d528f3e6f1875f",
    "theory/Cadeque/Types.v": "4beb995bd9634c6cc275aa053e009065a7ff699e2ad7b04fd2821df97bcd9e23",
    "theory/Cadeque/Models.v": "d19612a21f4e506aedb31657393c437a07d1f2f8e5ed4ebcea4e408d6b05402f"
  },
  "checker_sha256": "34c2d3daa852d1ebb586e9a9b919eea0662262bd499a6af30dce722bf5d56c56",
  "word_quantifier": "formal blocks admit arbitrary word substitutions; X0,X1 jointly represent one stored value and need not be one payload letter",
  "level_quantifier": "every natural nesting level l; erased at runtime",
  "branch_counts": {
    "triple_of_chain": 7,
    "pop_only_green_typed_subcases": 7,
    "chain_of_triple": 6,
    "composed_single_pop": 7
  },
  "triple_of_chain": [
    {
      "case": "G/Hole",
      "normal_form": [
        "TL",
        "R",
        "TR"
      ]
    },
    {
      "case": "Single_child",
      "normal_form": [
        "HL",
        "BL",
        "TL",
        "R",
        "TR",
        "BR",
        "HR"
      ]
    },
    {
      "case": "Pair_yellow",
      "normal_form": [
        "HL",
        "BL",
        "TL",
        "R",
        "TR",
        "BR",
        "Q",
        "HR"
      ]
    },
    {
      "case": "Pair_orange",
      "normal_form": [
        "HL",
        "L",
        "BL",
        "TL",
        "R",
        "TR",
        "BR",
        "HR"
      ]
    },
    {
      "case": "R/Hole/Only",
      "normal_form": [
        "TL",
        "R",
        "TR"
      ]
    },
    {
      "case": "R/Hole/Left",
      "normal_form": [
        "TL",
        "R",
        "TR"
      ]
    },
    {
      "case": "R/Hole/Right",
      "normal_form": [
        "TL",
        "R",
        "TR"
      ]
    }
  ],
  "pop_only_green": [
    {
      "case": "GT/Only_end/empty",
      "input_coloring": "GT/Only_end",
      "child_shape": "Empty",
      "output_shape": "empty",
      "prefix_min_before": 1,
      "prefix_min_after": 0,
      "normal_form": [
        "X0",
        "X1"
      ]
    },
    {
      "case": "GT/Only_end/nonempty",
      "input_coloring": "GT/Only_end",
      "child_shape": "Empty",
      "output_shape": "Only_end",
      "prefix_min_before": 2,
      "prefix_min_after": 1,
      "normal_form": [
        "X0",
        "X1",
        "P"
      ]
    },
    {
      "case": "GT/GN",
      "input_coloring": "GT/GN",
      "child_shape": "Nonempty",
      "output_shape": "YN",
      "prefix_min_before": 8,
      "prefix_min_after": 7,
      "normal_form": [
        "X0",
        "X1",
        "P",
        "C",
        "S"
      ]
    },
    {
      "case": "YT/YN/Single",
      "input_coloring": "YT/YN",
      "child_shape": "Single",
      "output_shape": "ON/OST",
      "prefix_min_before": 7,
      "prefix_min_after": 6,
      "normal_form": [
        "X0",
        "X1",
        "P",
        "C",
        "S"
      ]
    },
    {
      "case": "YT/YN/Pair",
      "input_coloring": "YT/YN",
      "child_shape": "Pair",
      "output_shape": "ON/OPT",
      "prefix_min_before": 7,
      "prefix_min_after": 6,
      "normal_form": [
        "X0",
        "X1",
        "P",
        "C",
        "S"
      ]
    },
    {
      "case": "OST/ON",
      "input_coloring": "OST/ON",
      "child_shape": "Single",
      "output_shape": "RN/RT",
      "prefix_min_before": 6,
      "prefix_min_after": 5,
      "normal_form": [
        "X0",
        "X1",
        "P",
        "C",
        "S"
      ]
    },
    {
      "case": "OPT/ON",
      "input_coloring": "OPT/ON",
      "child_shape": "Pair",
      "output_shape": "RN/RT",
      "prefix_min_before": 6,
      "prefix_min_after": 5,
      "normal_form": [
        "X0",
        "X1",
        "P",
        "C",
        "S"
      ]
    }
  ],
  "chain_of_triple": [
    {
      "case": "GT",
      "normal_form": [
        "TL",
        "R",
        "TR"
      ]
    },
    {
      "case": "YT/Single",
      "normal_form": [
        "HL",
        "BL",
        "TL",
        "R",
        "TR",
        "BR",
        "HR"
      ]
    },
    {
      "case": "YT/Pair",
      "normal_form": [
        "HL",
        "BL",
        "TL",
        "R",
        "TR",
        "BR",
        "Q",
        "HR"
      ]
    },
    {
      "case": "OST",
      "normal_form": [
        "HL",
        "BL",
        "TL",
        "R",
        "TR",
        "BR",
        "HR"
      ]
    },
    {
      "case": "OPT",
      "normal_form": [
        "HL",
        "L",
        "BL",
        "TL",
        "R",
        "TR",
        "BR",
        "HR"
      ]
    },
    {
      "case": "RT",
      "normal_form": [
        "TL",
        "R",
        "TR"
      ]
    }
  ],
  "composed_single_pop": [
    {
      "case": "GT/Only_end/empty",
      "chain_equation": [
        "X0",
        "X1"
      ],
      "returned_head_block": [
        "X0",
        "X1"
      ],
      "residual_chain_block": []
    },
    {
      "case": "GT/Only_end/nonempty",
      "chain_equation": [
        "X0",
        "X1",
        "P"
      ],
      "returned_head_block": [
        "X0",
        "X1"
      ],
      "residual_chain_block": [
        "P"
      ]
    },
    {
      "case": "GT/GN",
      "chain_equation": [
        "X0",
        "X1",
        "P",
        "C",
        "S"
      ],
      "returned_head_block": [
        "X0",
        "X1"
      ],
      "residual_chain_block": [
        "P",
        "C",
        "S"
      ]
    },
    {
      "case": "YT/YN/Single",
      "chain_equation": [
        "X0",
        "X1",
        "P",
        "C",
        "S"
      ],
      "returned_head_block": [
        "X0",
        "X1"
      ],
      "residual_chain_block": [
        "P",
        "C",
        "S"
      ]
    },
    {
      "case": "YT/YN/Pair",
      "chain_equation": [
        "X0",
        "X1",
        "P",
        "C",
        "S"
      ],
      "returned_head_block": [
        "X0",
        "X1"
      ],
      "residual_chain_block": [
        "P",
        "C",
        "S"
      ]
    },
    {
      "case": "OST/ON",
      "chain_equation": [
        "X0",
        "X1",
        "P",
        "C",
        "S"
      ],
      "returned_head_block": [
        "X0",
        "X1"
      ],
      "residual_chain_block": [
        "P",
        "C",
        "S"
      ]
    },
    {
      "case": "OPT/ON",
      "chain_equation": [
        "X0",
        "X1",
        "P",
        "C",
        "S"
      ],
      "returned_head_block": [
        "X0",
        "X1"
      ],
      "residual_chain_block": [
        "P",
        "C",
        "S"
      ]
    }
  ],
  "negative_controls": [
    {
      "mutation": "retain_popped_head",
      "reason": "word normal forms differ"
    },
    {
      "mutation": "swap_child_suffix",
      "reason": "word normal forms differ"
    },
    {
      "mutation": "reverse_pair_yellow_children",
      "reason": "word normal forms differ"
    },
    {
      "mutation": "keep_GN_after_pop",
      "reason": "word may agree, but GN requires a prefix of at least 8 entries"
    }
  ]
}