{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R641",
  "content_hash": null,
  "slug": "r30n24-claim-functional-graph-inventory",
  "type": "claim",
  "title": "The width-24 graph has 49 components and 194,991 cyclic states",
  "summary": "The exhaustive inventory contains 49 directed cycles, including three fixed points, and its sorted pair list has digest 8bb15c98ca3aeadf.",
  "relevance": "This records a result, observation, or conjecture used to assess the target problem.",
  "relevance_source": "derived",
  "body": "A finite functional graph has one directed cycle in each weak component. The complete width-24 inventory contains 49 cycles, hence 49 weak components. Their lengths sum to 194,991, so that many of the 16,777,216 states are cyclic. Three cycles are fixed points. The maximum global indegree is three.\n\nFor a compact check, each cycle is represented by the least integer on that cycle and its length. Sort these 49 pairs by representative and then length. Serialize each unsigned 32-bit integer as four little-endian bytes, with the representative first, and apply 64-bit FNV-1a starting at `14695981039346656037`. The resulting digest is `8bb15c98ca3aeadf`. Both exhaustive algorithms produce this digest and agree on every pair before it is computed.",
  "status": "reproduced",
  "evidence_grade": "computational",
  "scope": {
    "kind": "bounded",
    "statement": "the complete functional graph of cyclic Rule 30 on 24 binary cells",
    "bounds": {
      "ring_width": {
        "min": 24,
        "max": 24
      },
      "states": {
        "min": 16777216,
        "max": 16777216
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://oeis.org/A334497",
      "locator": "Complete dual traversal in r30n24-artifact-dual-exhaustive-scan, executed on 2026-07-24"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://oeis.org/A334497",
    "locator": "Complete dual traversal in r30n24-artifact-dual-exhaustive-scan, executed on 2026-07-24"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R639",
      "title": "Dual exhaustive C11 verifier for cyclic Rule 30",
      "object_type": "artifact",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "rule-30-cycle-length-24",
      "title": "rule 30 cycle length 24",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}