{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R325",
  "content_hash": null,
  "slug": "gct45-attempt-literature-and-state-space-audit",
  "type": "attempt",
  "title": "Literature and finite-state audit",
  "summary": "General cover-time theory certifies the interval, and the exact connected-set recurrence reduces the finite computation to 116,166 systems.",
  "relevance": "For Largest expected cover time on the four by five grid, record gct45-attempt-literature-and-state-space-audit (“Literature and finite-state audit”) documents a concrete method, search boundary, or failed route. The record states: General cover-time theory certifies the interval, and the exact connected-set recurrence reduces the finite computation to 116,166 systems.",
  "relevance_source": "recorded",
  "body": "Matthews proves the harmonic-factor comparison between cover time and maximal hitting time. Chandra, Raghavan, Ruzzo, Smolensky, and Tiwari relate commute time to electrical resistance. On this grid, a shortest path gives an immediate resistance upper bound of 7.\n\nThe finite-state audit enumerated 116,166 connected nonempty subsets. Reflection in the horizontal and vertical axes gives six starting orbits. Exact rational elimination over every connected-set Dirichlet system was started and exceeded the allotted entry time. No exact value or maximizing orbit is claimed here.",
  "status": "in_progress",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "connected visited sets and starting symmetry orbits for simple random walk on P_4 square P_5",
    "bounds": {
      "rows": {
        "min": 4,
        "max": 4
      },
      "columns": {
        "min": 5,
        "max": 5
      },
      "connected_nonempty_subsets": {
        "min": 116166,
        "max": 116166
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.1214/aop/1176991686",
      "locator": "Peter Matthews, Covering problems for Markov chains, Annals of Probability 16 (1988), 1215-1228; A. Chandra et al., The electrical resistance of a graph captures its commute and cover times, STOC 1989, 574-586"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1214/aop/1176991686",
    "locator": "Peter Matthews, Covering problems for Markov chains, Annals of Probability 16 (1988), 1215-1228; A. Chandra et al., The electrical resistance of a graph captures its commute and cover times, STOC 1989, 574-586"
  },
  "models": [],
  "relations": [
    {
      "slug": "R326",
      "title": "The maximum expected cover time lies in a certified rational interval",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "grid-cover-time-four-by-five",
      "title": "grid cover time four by five",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}