{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R246",
  "content_hash": null,
  "slug": "fcptp-attempt-four-cube-transfer-and-status-audit",
  "type": "attempt",
  "title": "The four-cube exact numerator remains open in this entry",
  "summary": "The rank-free topology reduction is complete, while the first straightforward frontier ordering grew beyond the capped computation.",
  "relevance": "For Exact tunnel probability for site percolation on a four by four by four cubical box, record fcptp-attempt-four-cube-transfer-and-status-audit (“The four-cube exact numerator remains open in this entry”) documents a concrete method, search boundary, or failed route. The record states: The rank-free topology reduction is complete, while the first straightforward frontier ordering grew beyond the capped computation.",
  "relevance_source": "recorded",
  "body": "A direct extension of the certified transfer to side length four reached 7,916,922 distinct states after the 27th voxel. The run was capped before completing all 64 variables, so it supplies no count for the requested event. The exact four-cube numerator remains undetermined here.\n\nThe literature search located general studies of Bernoulli site-percolation cubical unions, limit theorems for random cubical Betti numbers, and algorithms for cubical homology. No source found in this focused search tabulates the finite \\(4\\times4\\times4\\), \\(p=1/2\\), closed-union probability. A practical continuation can improve the variable ordering, use a slice-based connectivity transfer, or compile the same canonical state recurrence with a compact packed representation.",
  "status": "incomplete",
  "evidence_grade": "computational",
  "scope": {
    "kind": "bounded",
    "statement": "the requested 4 by 4 by 4 box at site probability 1/2",
    "bounds": {
      "side_length": {
        "min": 4,
        "max": 4
      },
      "unit_cubes": {
        "min": 64,
        "max": 64
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://arxiv.org/abs/1910.12803",
      "locator": "Kenneth Dowling and Erik Lundberg, Homotopy Types of Random Cubical Complexes, for the site-percolation cubical-union model"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1910.12803",
    "locator": "Kenneth Dowling and Erik Lundberg, Homotopy Types of Random Cubical Complexes, for the site-percolation cubical-union model"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R245",
      "title": "Exact two-connectivity frontier transfer for the three-cube box",
      "object_type": "artifact",
      "relation": "uses",
      "direction": "outgoing"
    },
    {
      "slug": "four-cube-site-percolation-tunnel-probability",
      "title": "four cube site percolation tunnel probability",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}