{
  "scope": "Exact free-word equations and handwritten indexed branch closure for pop_left_green, only_of_right, and the Pair arm of pop_green, reusing the previously certified sequence-preserving view conversions. Source files are hash-pinned. This is not OCaml extraction, buffer verification, or a Rocq rerun.",
  "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": "17c38506a568113452f5c50965266bab4d85c5c8b7ad09da79f556f9e656a587",
  "level_quantifier": "every natural nesting level l; erased at runtime",
  "word_quantifier": "every symbol names an arbitrary word block; X0,X1 jointly represent one stored entry rather than two payload letters",
  "branch_counts": {
    "pop_left_green_typed_subcases": 7,
    "only_of_right_typed_subcases": 6,
    "pop_pair_green_result_arms": 2
  },
  "pop_left_green": [
    {
      "case": "GT/EN/exact4",
      "input_coloring": "GT/EN",
      "child_shape": "Empty",
      "result_kind": "Six_elements",
      "prefix_min_before": 5,
      "prefix_min_after": 4,
      "normal_form": [
        "X0",
        "X1",
        "B",
        "D",
        "E",
        "F",
        "G",
        "H"
      ]
    },
    {
      "case": "GT/EN/at_least5",
      "input_coloring": "GT/EN",
      "child_shape": "Empty",
      "result_kind": "Ok_pt",
      "prefix_min_before": 6,
      "prefix_min_after": 5,
      "normal_form": [
        "X0",
        "X1",
        "P",
        "G",
        "H"
      ]
    },
    {
      "case": "GT/GN",
      "input_coloring": "GT/GN",
      "child_shape": "Nonempty",
      "result_kind": "Ok_pt/YT-YN",
      "prefix_min_before": 8,
      "prefix_min_after": 7,
      "normal_form": [
        "X0",
        "X1",
        "P",
        "C",
        "G",
        "H"
      ]
    },
    {
      "case": "YT/YN/Single",
      "input_coloring": "YT/YN",
      "child_shape": "Single",
      "result_kind": "Ok_pt/OST-ON",
      "prefix_min_before": 7,
      "prefix_min_after": 6,
      "normal_form": [
        "X0",
        "X1",
        "P",
        "C",
        "G",
        "H"
      ]
    },
    {
      "case": "YT/YN/Pair",
      "input_coloring": "YT/YN",
      "child_shape": "Pair",
      "result_kind": "Ok_pt/OPT-ON",
      "prefix_min_before": 7,
      "prefix_min_after": 6,
      "normal_form": [
        "X0",
        "X1",
        "P",
        "C",
        "G",
        "H"
      ]
    },
    {
      "case": "OST/ON",
      "input_coloring": "OST/ON",
      "child_shape": "Single",
      "result_kind": "Ok_pt/RT-RN",
      "prefix_min_before": 6,
      "prefix_min_after": 5,
      "normal_form": [
        "X0",
        "X1",
        "P",
        "C",
        "G",
        "H"
      ]
    },
    {
      "case": "OPT/ON",
      "input_coloring": "OPT/ON",
      "child_shape": "Pair",
      "result_kind": "Ok_pt/RT-RN",
      "prefix_min_before": 6,
      "prefix_min_after": 5,
      "normal_form": [
        "X0",
        "X1",
        "P",
        "C",
        "G",
        "H"
      ]
    }
  ],
  "only_of_right": [
    {
      "case": "GT/EN",
      "child_shape": "Empty",
      "output_shape": "Only_end",
      "prefix_entries_constructed": 8,
      "normal_form": [
        "B",
        "D",
        "E",
        "F",
        "G",
        "H",
        "I",
        "J",
        "S"
      ]
    },
    {
      "case": "GT/GN",
      "child_shape": "Nonempty",
      "output_shape": "Only/GN",
      "prefix_entries_constructed": 8,
      "normal_form": [
        "B",
        "D",
        "E",
        "F",
        "G",
        "H",
        "I",
        "J",
        "R",
        "S"
      ]
    },
    {
      "case": "YT/YN/Single",
      "child_shape": "Single",
      "output_shape": "Only/YN",
      "prefix_entries_constructed": 8,
      "normal_form": [
        "B",
        "D",
        "E",
        "F",
        "G",
        "H",
        "I",
        "J",
        "R",
        "S"
      ]
    },
    {
      "case": "YT/YN/Pair",
      "child_shape": "Pair",
      "output_shape": "Only/YN",
      "prefix_entries_constructed": 8,
      "normal_form": [
        "B",
        "D",
        "E",
        "F",
        "G",
        "H",
        "I",
        "J",
        "R",
        "S"
      ]
    },
    {
      "case": "OST/ON",
      "child_shape": "Single",
      "output_shape": "Only/ON",
      "prefix_entries_constructed": 8,
      "normal_form": [
        "B",
        "D",
        "E",
        "F",
        "G",
        "H",
        "I",
        "J",
        "R",
        "S"
      ]
    },
    {
      "case": "OPT/ON",
      "child_shape": "Pair",
      "output_shape": "Only/ON",
      "prefix_entries_constructed": 8,
      "normal_form": [
        "B",
        "D",
        "E",
        "F",
        "G",
        "H",
        "I",
        "J",
        "R",
        "S"
      ]
    }
  ],
  "pop_pair_green": [
    {
      "case": "Six_elements_then_only_of_right",
      "normal_form": [
        "X0",
        "X1",
        "B",
        "D",
        "E",
        "F",
        "G",
        "H",
        "I",
        "J",
        "R",
        "S"
      ],
      "returned_head_block": [
        "X0",
        "X1"
      ],
      "residual_chain_block": [
        "B",
        "D",
        "E",
        "F",
        "G",
        "H",
        "I",
        "J",
        "R",
        "S"
      ]
    },
    {
      "case": "Ok_pt_then_Pair",
      "normal_form": [
        "X0",
        "X1",
        "L0",
        "L1",
        "I",
        "J",
        "R",
        "S"
      ],
      "returned_head_block": [
        "X0",
        "X1"
      ],
      "residual_chain_block": [
        "L0",
        "L1",
        "I",
        "J",
        "R",
        "S"
      ]
    }
  ],
  "negative_controls": [
    {
      "mutation": "right_before_six",
      "reason": "word normal forms differ"
    },
    {
      "mutation": "reverse_six",
      "reason": "word normal forms differ"
    },
    {
      "mutation": "swap_residual_left_and_right",
      "reason": "word normal forms differ"
    },
    {
      "mutation": "retain_popped_head",
      "reason": "word normal forms differ"
    },
    {
      "mutation": "keep_Left_EN_after_exact4",
      "reason": "residual prefix has 4 entries, below the Left minimum 5"
    },
    {
      "mutation": "omit_adapt_to_prefix",
      "reason": "the constructed Only prefix has 8 entries, but an arbitrary Right-node phantom prefix index is not evidence for that size"
    }
  ]
}