{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R672",
  "content_hash": null,
  "slug": "rr8gc-attempt-seeded-local-search",
  "type": "attempt",
  "title": "Seeded local search raises the incumbent from 807 to 1,282",
  "summary": "Single-rotor mutations found a long-lived state concentrated around the lower-left start, while leaving a large certified gap.",
  "relevance": "For Longest rotor-router cover time on the eight by eight grid, record rr8gc-attempt-seeded-local-search (“Seeded local search raises the incumbent from 807 to 1,282”) documents a concrete method, search boundary, or failed route. The record states: Single-rotor mutations found a long-lived state concentrated around the lower-left start, while leaving a large certified gap.",
  "relevance_source": "recorded",
  "body": "A deterministic C++ search began with the candidate's 807-move state and used `mt19937_64` seed 2026072508. Each proposal changed one rotor. One proposal in 64 changed two rotors, one in 1,024 changed four, and one in 2,048 also changed the start vertex. Nondecreasing moves were accepted, with a rare random escape. Random restarts were interleaved with restarts at the incumbent. The run produced the 1,282-move configuration preserved in the replay record.\n\nThis search certifies only the lower bound supplied by its saved state. The raw search space has\n\\[\n64\\cdot2^4\\cdot3^{24}\\cdot4^{36}\n=1{,}365{,}745{,}435{,}494{,}690{,}943{,}435{,}859{,}428{,}192{,}026{,}624\n\\]\nstart-and-rotor states. A complete computation can quotient the four rotations of the square, branch on the exit sequences actually used before a proposed deadline, and prune at 3,136 using the excursion bound. Per-target rotor-potential bounds may lower that deadline before branching.",
  "status": "in_progress",
  "evidence_grade": "computational",
  "scope": {
    "kind": "bounded",
    "statement": "the capped deterministic local-search run with seed 2026072508 on the 8 by 8 grid",
    "bounds": {
      "rows": {
        "min": 8,
        "max": 8
      },
      "columns": {
        "min": 8,
        "max": 8
      },
      "seed": {
        "min": 2026072508,
        "max": 2026072508
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.4169/amer.math.monthly.123.7.627",
      "locator": "Deterministic local search and exact saved-state replay, 2026-07-25"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.4169/amer.math.monthly.123.7.627",
    "locator": "Deterministic local search and exact saved-state replay, 2026-07-25"
  },
  "models": [],
  "continuation": "rotation quotient, exit-sequence branching, and rotor-potential upper bounds",
  "relations": [
    {
      "slug": "R670",
      "title": "Exact replay of the 1,282-move initial state",
      "object_type": "artifact",
      "relation": "produces",
      "direction": "outgoing"
    },
    {
      "slug": "rotor-router-eight-grid-cover",
      "title": "rotor router eight grid cover",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}