{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R45",
  "content_hash": null,
  "slug": "b2z100-attempt-bounded-search",
  "type": "attempt",
  "title": "Bounded local searches reached one circular-distance violation",
  "summary": "The searches found near-feasible 14-sets but supplied no existence or nonexistence certificate.",
  "relevance": "For Existence of a fourteen-point two-fold difference packing modulo 100, record b2z100-attempt-bounded-search (“Bounded local searches reached one circular-distance violation”) documents a concrete method, search boundary, or failed route. The record states: The searches found near-feasible 14-sets but supplied no existence or nonexistence certificate.",
  "relevance_source": "recorded",
  "body": "A seeded one-swap simulated-annealing run evaluated 600,000,000 proposals. A separate conflict-directed tabu run was capped after reaching the same best score. Neither run found a feasible 14-set. The best retained near miss was\n\\[\n\\{0,5,7,31,43,58,61,62,63,72,80,84,91,97\\}.\n\\]\nIts only overloaded ordered residues are 19 and 81, each with multiplicity three. These are the two orientations of one overloaded circular distance class.\n\nThis evidence explains why simple greedy searches may stall one step short. It carries no upper-bound force. The exact continuation is the binary model in the artifact. Solving it with proof logging, followed by independent proof checking, would settle the candidate.",
  "status": "inconclusive",
  "evidence_grade": "computational",
  "scope": {
    "kind": "bounded",
    "statement": "heuristic searches for a 14-element set in Z/100Z, with exact checking of every visited incumbent",
    "bounds": {
      "target_size": {
        "min": 14,
        "max": 14
      },
      "recorded_one_swap_proposals": {
        "min": 600000000,
        "max": 600000000
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.1109/18.30982",
      "locator": "Seeded local computations performed and capped on 2026-07-25; near-miss multiplicities rechecked by b2z100-artifact-verifier-and-ilp"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1109/18.30982",
    "locator": "Seeded local computations performed and capped on 2026-07-25; near-miss multiplicities rechecked by b2z100-artifact-verifier-and-ilp"
  },
  "models": [],
  "relations": [
    {
      "slug": "R47",
      "title": "The certified maximum lies between 13 and 14",
      "object_type": "claim",
      "relation": "tests",
      "direction": "outgoing"
    },
    {
      "slug": "R44",
      "title": "Exact difference verifier and complete size-14 feasibility model",
      "object_type": "artifact",
      "relation": "uses",
      "direction": "outgoing"
    },
    {
      "slug": "b2-two-set-z100",
      "title": "b2 two set z100",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}