{
  "assurance": "Exact DFA invariant closure and finite descriptor checks, without a stack-depth cutoff; the general theorem remains a written proof.",
  "frame_set_pop_obstruction": {
    "certificate": "rejected as required",
    "reason": "X and XX have the same current summary but different summaries after pop",
    "summary": "set of labels present",
    "witness": {
      "group": [
        "q",
        1,
        null
      ],
      "input": "r",
      "kind": "signatures",
      "signatures": [
        [
          [
            [
              "q",
              0
            ],
            "keep"
          ]
        ],
        [
          [
            [
              "q",
              1
            ],
            "keep"
          ]
        ]
      ],
      "witnesses": [
        [
          "q",
          [
            "X"
          ]
        ],
        [
          "q",
          [
            "X",
            "X"
          ]
        ]
      ]
    }
  },
  "missing_bit_repair": {
    "reachable_configurations": 7,
    "summary": "rightmost B0/B1 tag",
    "with_summary": "passed",
    "without_summary": "rejected as required"
  },
  "not_implemented": [
    "general pushdown post* saturation",
    "automatic summary synthesis",
    "minimal summary computation",
    "scaffold generation",
    "proof assistant"
  ],
  "parity_pop_restoration": {
    "abstract_local_groups": 7,
    "closure_obligations": 9,
    "realized_descriptors": 7,
    "regular_invariants": {
      "b_i_and_d_i": "A followed by the corresponding parity language",
      "q0": "(X A)^(even)",
      "q1": "(X A)^(odd)"
    },
    "summary": "parity of X frames",
    "summary_certificate": "passed",
    "without_summary": "rejected as required"
  },
  "status": "passed"
}