{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R70",
  "content_hash": null,
  "slug": "bpe8c-attempt-literature-and-exact-transfer-audit",
  "type": "attempt",
  "title": "The audit found asymptotic theory and no published exact eight-board count",
  "summary": "Classical papers study finite-volume thresholds and internally spanned rectangles; a projected exact row transfer was stopped after its state count grew to 5,968.",
  "relevance": "For Exact spanning-set count for two-neighbor bootstrap percolation on the eight grid, record bpe8c-attempt-literature-and-exact-transfer-audit (“The audit found asymptotic theory and no published exact eight-board count”) documents a concrete method, search boundary, or failed route. The record states: Classical papers study finite-volume thresholds and internally spanned rectangles; a projected exact row transfer was stopped after its state count grew to 5,968.",
  "relevance_source": "recorded",
  "body": "Aizenman and Lebowitz introduced the rigorous finite-volume study of bootstrap percolation and its internally spanned rectangles. Holroyd later obtained the sharp two-dimensional metastability threshold. Morris studied minimal percolating sets on square grids. These sources address structural and asymptotic questions.\n\nThe targeted search found no primary source giving the exact number of spanning subsets of the open \\(8\\times8\\) board. This records the search outcome and does not prove novelty.\n\nAn exact projected row transfer was also tested. Its nondeterministic state records the last two rows of a possible stable vacant fort, then determinizes over each incoming vacancy row. It had 256 projected states after one row and 5,968 after two rows. The computation was stopped at the task's time cap before producing a count. A future exact certificate could continue this transfer with packed bit sets or compile the fort constraints into a decision diagram.",
  "status": "inconclusive",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "a targeted primary-literature search for the exact spanning-set count on the open 8 by 8 grid and a bounded attempt at projected row transfer, completed on 2026-07-25",
    "bounds": {
      "grid_side": {
        "min": 8,
        "max": 8
      },
      "transfer_rows_completed": {
        "min": 2,
        "max": 2
      },
      "distinct_projected_states_after_two_rows": {
        "min": 5968,
        "max": 5968
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.1088/0305-4470/21/19/017",
      "locator": "Aizenman and Lebowitz, Journal of Physics A 21 (1988), 3801-3813; Holroyd, Probability Theory and Related Fields 125 (2003), 195-224; Morris, Electronic Journal of Combinatorics 16 (2009), R2; targeted exact-count search completed 2026-07-25"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1088/0305-4470/21/19/017",
    "locator": "Aizenman and Lebowitz, Journal of Physics A 21 (1988), 3801-3813; Holroyd, Probability Theory and Related Fields 125 (2003), 195-224; Morris, Electronic Journal of Combinatorics 16 (2009), R2; targeted exact-count search completed 2026-07-25"
  },
  "relations": [
    {
      "slug": "R71",
      "title": "The spanning-set count lies between 177,024,301,925,259,284 and 18,161,310,923,858,378,752",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "bootstrap-percolation-eight-count",
      "title": "bootstrap percolation eight count",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}