{
  "assurance": "Exact minimization and injectivity checks for the finite examples; bounded exhaustive corroboration of common-pop collapse through four states.",
  "common_untyped_pop": [
    {
      "down_tables_times_permutations_checked": 1,
      "ordered_two_push_solutions": 1,
      "states": 1,
      "unequal_push_solutions": 0
    },
    {
      "down_tables_times_permutations_checked": 8,
      "ordered_two_push_solutions": 2,
      "states": 2,
      "unequal_push_solutions": 0
    },
    {
      "down_tables_times_permutations_checked": 162,
      "ordered_two_push_solutions": 6,
      "states": 3,
      "unequal_push_solutions": 0
    },
    {
      "down_tables_times_permutations_checked": 6144,
      "ordered_two_push_solutions": 24,
      "states": 4,
      "unequal_push_solutions": 0
    }
  ],
  "not_verified": [
    "the general residual theorem",
    "unrestricted pushdown reachability",
    "automatic synthesis from source programs",
    "scaffold generation",
    "proof assistant formalization"
  ],
  "residual_examples": [
    {
      "failures": [],
      "minimal_states": 2,
      "name": "parity of hidden height",
      "permutation_summary": true,
      "transitions": {
        "X": {
          "image": [
            1,
            0
          ],
          "injective": true
        }
      }
    },
    {
      "failures": [],
      "minimal_states": 3,
      "name": "hidden height modulo three",
      "permutation_summary": true,
      "transitions": {
        "A": {
          "image": [
            1,
            2,
            0
          ],
          "injective": true
        }
      }
    },
    {
      "failures": [
        {
          "letter": "X",
          "merge": [
            0,
            1,
            1
          ]
        }
      ],
      "minimal_states": 2,
      "name": "presence of X",
      "permutation_summary": false,
      "transitions": {
        "A": {
          "image": [
            0,
            1
          ],
          "injective": true
        },
        "X": {
          "image": [
            1,
            1
          ],
          "injective": false
        }
      }
    },
    {
      "failures": [
        {
          "letter": "X",
          "merge": [
            0,
            1,
            1
          ]
        }
      ],
      "minimal_states": 2,
      "name": "exact emptiness",
      "permutation_summary": false,
      "transitions": {
        "X": {
          "image": [
            1,
            1
          ],
          "injective": false
        }
      }
    },
    {
      "failures": [
        {
          "letter": "B0",
          "merge": [
            1,
            2,
            1
          ]
        },
        {
          "letter": "B1",
          "merge": [
            0,
            2,
            0
          ]
        }
      ],
      "minimal_states": 3,
      "name": "rightmost B0/B1 tag",
      "permutation_summary": false,
      "transitions": {
        "A": {
          "image": [
            0,
            1,
            2
          ],
          "injective": true
        },
        "B0": {
          "image": [
            0,
            1,
            1
          ],
          "injective": false
        },
        "B1": {
          "image": [
            0,
            1,
            0
          ],
          "injective": false
        }
      }
    }
  ],
  "status": "passed"
}