{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R510",
  "content_hash": null,
  "slug": "mgpc-attempt-full-vertex-flood-fill",
  "type": "attempt",
  "title": "Full-vertex flood fill has quadratic state cost",
  "summary": "The route gives complete component and path certificates at small p, while its state count prevents it from crossing the unresolved effective interval.",
  "relevance": "For Prime exceptions to connectivity of the Markoff graph, record mgpc-attempt-full-vertex-flood-fill (“Full-vertex flood fill has quadratic state cost”) documents a concrete method, search boundary, or failed route. The record states: The route gives complete component and path certificates at small p, while its state count prevents it from crossing the unresolved effective interval.",
  "relevance_source": "recorded",
  "body": "The direct program processed 1,169,185,984 vertices through \\(p=3001\\) in 114.7 seconds of recorded chunk runtime. Its arrays use fewer than \\(31p^2\\) payload bytes at the largest prime, before allocator overhead. The surface itself has \\(p^2+O(p)\\) vertices. Any explicit visited bitmap therefore needs at least \\(p^2\\) bits. At \\(p=10^6\\), that lower bound is 125 GB, while this implementation's array layout would approach 30 TB.\n\nThis route remains useful for small-prime reproduction, shortest paths, component certificates, and independent checks of stronger algorithms. The quadratic state count makes it inconclusive as a plan for the finite interval left by current theorems.",
  "status": "inconclusive",
  "evidence_grade": "computational",
  "scope": {
    "kind": "family",
    "statement": "explicit full-vertex breadth-first search for coefficient-one Markoff graphs at growing prime parameters",
    "family": "direct surface enumeration and breadth-first component search"
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.1007/s40993-024-00592-9",
      "locator": "Brown, Introduction, comparison with O(p^2) flood fill; packet artifact gives measured small-p execution"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1007/s40993-024-00592-9",
    "locator": "Brown, Introduction, comparison with O(p^2) flood fill; packet artifact gives measured small-p execution"
  },
  "models": [],
  "relations": [
    {
      "slug": "R508",
      "title": "Exact Vieta-component enumerator",
      "object_type": "artifact",
      "relation": "uses",
      "direction": "outgoing"
    },
    {
      "slug": "R511",
      "title": "Shard the criterion scan, then route failures to the almost-linear test",
      "object_type": "attempt",
      "relation": "constrains",
      "direction": "outgoing"
    },
    {
      "slug": "markoff-graph-prime-connectivity-exceptions",
      "title": "markoff graph prime connectivity exceptions",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}