{
  "date": "2026-09-17",
  "scope": "FDE reference; finite set realization of Nanty's NOT/AND/OR fragment; explicitly chosen extensions of NR20 complementation. No recovered complete UMMO logic.",
  "order": [
    "T",
    "F",
    "B",
    "N"
  ],
  "bits": {
    "T": [
      1,
      0
    ],
    "F": [
      0,
      1
    ],
    "B": [
      1,
      1
    ],
    "N": [
      0,
      0
    ]
  },
  "fde": {
    "not": [
      "F",
      "T",
      "B",
      "N"
    ],
    "and": [
      [
        "T",
        "F",
        "B",
        "N"
      ],
      [
        "F",
        "F",
        "F",
        "F"
      ],
      [
        "B",
        "F",
        "B",
        "F"
      ],
      [
        "N",
        "F",
        "F",
        "N"
      ]
    ],
    "or": [
      [
        "T",
        "T",
        "T",
        "T"
      ],
      [
        "T",
        "F",
        "B",
        "N"
      ],
      [
        "T",
        "B",
        "B",
        "T"
      ],
      [
        "T",
        "N",
        "T",
        "N"
      ]
    ],
    "designated": [
      "T",
      "B"
    ],
    "excluded_middle": [
      "T",
      "T",
      "B",
      "N"
    ],
    "explosion_countermodels": [
      {
        "p": "B",
        "q": "F"
      },
      {
        "p": "B",
        "q": "N"
      }
    ],
    "and_elimination_countermodels": [],
    "disjunctive_syllogism_countermodels": [
      {
        "p": "B",
        "q": "F"
      },
      {
        "p": "B",
        "q": "N"
      }
    ]
  },
  "nanty": {
    "sets": {
      "T": 5,
      "F": 6,
      "B": 4,
      "N": 8
    },
    "not": [
      10,
      9,
      11,
      7
    ],
    "and": [
      [
        5,
        4,
        4,
        0
      ],
      [
        4,
        6,
        4,
        0
      ],
      [
        4,
        4,
        4,
        0
      ],
      [
        0,
        0,
        0,
        8
      ]
    ],
    "or": [
      [
        5,
        7,
        5,
        13
      ],
      [
        7,
        6,
        6,
        14
      ],
      [
        5,
        6,
        4,
        12
      ],
      [
        13,
        14,
        12,
        8
      ]
    ],
    "closure_size": 16,
    "closure_masks": [
      0,
      1,
      2,
      3,
      4,
      5,
      6,
      7,
      8,
      9,
      10,
      11,
      12,
      13,
      14,
      15
    ],
    "text_discrepancies": [
      {
        "expression": "T ∨ N = ¬F",
        "left": 13,
        "right": 9,
        "correction": "T ∨ N = ¬f"
      },
      {
        "expression": "F ∨ N = ¬T",
        "left": 14,
        "right": 10,
        "correction": "F ∨ N = ¬t"
      },
      {
        "expression": "N ∨ B = N",
        "left": 12,
        "right": 8,
        "correction": "N ∨ B = ¬(t ∨ f)"
      },
      {
        "expression": "F ↔ F = N",
        "left": 7,
        "right": 8,
        "correction": "F ↔ F = ¬N, given the stated axiom F → F = ¬N"
      }
    ]
  },
  "nr20_complement": [
    {
      "input": 1,
      "once": 14,
      "set_twice": 1,
      "relation_twice": 15
    },
    {
      "input": 2,
      "once": 13,
      "set_twice": 2,
      "relation_twice": 15
    },
    {
      "input": 4,
      "once": 11,
      "set_twice": 4,
      "relation_twice": 15
    },
    {
      "input": 8,
      "once": 7,
      "set_twice": 8,
      "relation_twice": 15
    }
  ],
  "checks": [
    {
      "name": "FDE: double negation",
      "assignments": 4,
      "passed": true
    },
    {
      "name": "FDE: idempotence AND and OR",
      "assignments": 4,
      "passed": true
    },
    {
      "name": "FDE: two De Morgan laws",
      "assignments": 16,
      "passed": true
    },
    {
      "name": "FDE: two distributivity laws",
      "assignments": 64,
      "passed": true
    },
    {
      "name": "FDE: 32 cells of published AND/OR tables",
      "assignments": 32,
      "passed": true
    },
    {
      "name": "Set complement: involution",
      "assignments": 16,
      "passed": true
    },
    {
      "name": "Sets: absorption and De Morgan",
      "assignments": 256,
      "passed": true
    },
    {
      "name": "Nanty: 36 cells of published NOT/AND/OR tables",
      "assignments": 36,
      "passed": true
    }
  ]
}