{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R511",
  "content_hash": null,
  "slug": "mgpc-attempt-sharded-criterion-and-libbgs",
  "type": "attempt",
  "title": "Shard the criterion scan, then route failures to the almost-linear test",
  "summary": "Scan every prime with 20,000,000 < p <= 100,000,000 in ten-million shards, preserve exact violating thresholds, and send criterion failures to Brown's stronger algorithm.",
  "relevance": "For Prime exceptions to connectivity of the Markoff graph, record mgpc-attempt-sharded-criterion-and-libbgs (“Shard the criterion scan, then route failures to the almost-linear test”) documents a concrete method, search boundary, or failed route. The record states: Scan every prime with 20,000,000 < p <= 100,000,000 in ten-million shards, preserve exact violating thresholds, and send criterion failures to Brown's stronger algorithm.",
  "relevance_source": "recorded",
  "body": "Run the embedded maximal-divisor artifact on eight disjoint ten-million intervals covering \\(20{,}000{,}000<p\\leq100{,}000{,}000\\). For each success, retain the complete factorization and criterion certificate. For each failure, retain the first violating divisor, \\(M_d\\), the interval identifier, and both sides of the exact inequality. Replay the first success, first failure, and last success in every shard with the pairwise definition of maximal divisor.\n\nNext, install Rust 1.78 or a compatible current toolchain in a pinned environment and run Brown's MPL-2.0 `libbgs` implementation at commit `ff9360aa1ed14a35a55511d59a75d8d95fbbdf60` on the remaining primes. Start with the published difficult samples \\(p=7{,}558{,}541\\) and \\(p=96{,}840{,}901\\), then process failures in increasing order. Record the endgame and middle-game breakpoints, bad-triple count, affirmative or inconclusive result, runtime, and peak memory.",
  "status": "next_experiment",
  "evidence_grade": "self_reported",
  "scope": {
    "kind": "bounded",
    "statement": "calibration at p=7,558,541 plus planned two-stage tests for every prime 20,000,000 < p <= 100,000,000",
    "bounds": {
      "p": {
        "min": 7558541,
        "max": 100000000
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.1007/s40993-024-00592-9",
      "locator": "Brown, Algorithm 3, Section 4, and the libbgs repository at the pinned commit"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1007/s40993-024-00592-9",
    "locator": "Brown, Algorithm 3, Section 4, and the libbgs repository at the pinned commit"
  },
  "models": [],
  "relations": [
    {
      "slug": "R510",
      "title": "Full-vertex flood fill has quadratic state cost",
      "object_type": "attempt",
      "relation": "constrains",
      "direction": "incoming"
    },
    {
      "slug": "R509",
      "title": "Exact maximal-divisor criterion scan",
      "object_type": "artifact",
      "relation": "uses",
      "direction": "outgoing"
    },
    {
      "slug": "R512",
      "title": "Dated source and convention audit",
      "object_type": "attempt",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "markoff-graph-prime-connectivity-exceptions",
      "title": "markoff graph prime connectivity exceptions",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}