{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R334",
  "content_hash": null,
  "slug": "gocb-attempt-universal-permutation",
  "type": "attempt",
  "title": "The universal permutation claim remains open in the sources checked",
  "summary": "OEIS calls A226077 a permutation and lists an inverse, while its record supplies computation without a proof.",
  "relevance": "For Does the greedy one-common-bit sequence visit every positive integer?, record gocb-attempt-universal-permutation (“The universal permutation claim remains open in the sources checked”) documents a concrete method, search boundary, or failed route. The record states: OEIS calls A226077 a permutation and lists an inverse, while its record supplies computation without a proof.",
  "relevance_source": "recorded",
  "body": "A comment added to OEIS A226077 by Reinhard Zumkeller on May 26, 2013 calls the sequence a permutation and points to A226093 as its inverse. A226093 has the title \"Inverse permutation to A226077.\" The accessible records give definitions, generators, and 10,000-term tables. They contain no proof of surjectivity. The source search for this entry found no paper or later proof resolving the universal claim.\n\nThe nearby disjoint-support sequence A109812 has a short surjectivity proof: its first term at least \\(2^k\\) must equal \\(2^k\\), which then forces the least missing value. Exact-one overlap breaks that lemma. In A226077, 6 occurs before 4 and 9 occurs before 8. The A109812 proof therefore cannot be copied into this setting.\n\nThe million-term certificate moves the verified least missing value to 523,263. A resolution still needs a proof that every least missing value is eventually forced, or a positive integer that remains absent forever.",
  "status": "open_strategy",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "universal",
    "statement": "every positive integer occurs somewhere in the infinite sequence"
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://oeis.org/A226077",
      "locator": "OEIS A226077 and A226093, comments and tables; comparison with the proved disjoint-support analogue OEIS A109812; source audit 2026-07-24"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://oeis.org/A226077",
    "locator": "OEIS A226077 and A226093, comments and tables; comparison with the proved disjoint-support analogue OEIS A109812; source audit 2026-07-24"
  },
  "models": [],
  "relations": [
    {
      "slug": "R336",
      "title": "The recurrence always has a next term",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R335",
      "title": "The first million terms cover 1 through 523,262",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R337",
      "title": "The sequence is OEIS A226077",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "greedy-one-common-bit-permutation",
      "title": "greedy one common bit permutation",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}