{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1099",
  "content_hash": null,
  "slug": "lonely-runner-conjecture-attempt-resolution-route",
  "type": "attempt",
  "title": "Resolve the stated acceptance condition",
  "summary": "Prove the separation assertion for every n and every set of distinct constant speeds, or give explicit distinct speeds and prove that at least one runner never attains the required distance from all others.",
  "relevance": "For Lonely runner conjecture, record lonely-runner-conjecture-attempt-resolution-route (“Resolve the stated acceptance condition”) documents a concrete method, search boundary, or failed route. The record states: Prove the separation assertion for every n and every set of distinct constant speeds, or give explicit distinct speeds and prove that at least one runner never attains the required distance from all others.",
  "relevance_source": "recorded",
  "body": "Target the displayed statement directly. Prove the separation assertion for every n and every set of distinct constant speeds, or give explicit distinct speeds and prove that at least one runner never attains the required distance from all others. Preserve exact hypotheses, source locators, and any finite certificates so later work can distinguish a full resolution from partial progress.",
  "status": "open_strategy",
  "evidence_grade": "self_reported",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://arxiv.org/abs/2409.20160",
      "locator": "Editorial research route recorded 2026-07-31"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2409.20160",
    "locator": "Editorial research route recorded 2026-07-31"
  },
  "relations": [
    {
      "slug": "R1100",
      "title": "Current status and unresolved remainder",
      "object_type": "claim",
      "relation": "addresses",
      "direction": "outgoing"
    },
    {
      "slug": "lonely-runner-conjecture",
      "title": "lonely runner conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}