{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1801",
  "content_hash": null,
  "slug": "vp-versus-vnp-claim-literature-frontier",
  "type": "claim",
  "title": "Strongest checked neighboring result",
  "summary": "Exponential lower bounds are known for restricted arithmetic models, while unrestricted explicit lower bounds remain far smaller.",
  "relevance": "For Is VP equal to VNP?, record vp-versus-vnp-claim-literature-frontier (“Strongest checked neighboring result”) records a bound, answer, status fact, or structural consequence. The record states: Exponential lower bounds are known for restricted arithmetic models, while unrestricted explicit lower bounds remain far smaller.",
  "relevance_source": "recorded",
  "body": "Exponential lower bounds are known for restricted arithmetic models, while unrestricted explicit lower bounds remain far smaller.\n\nThis leaves the following boundary unresolved: No superpolynomial lower bound for an explicit VNP family in general arithmetic circuits is known. The distinction is retained here so a restricted theorem, finite computation, or neighboring case is not presented as a solution of the full target.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://doi.org/10.1145/800135.804419",
      "locator": "L. Valiant, Completeness classes in algebra, STOC 1979. VP, VNP, and permanent completeness"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1145/800135.804419",
    "locator": "L. Valiant, Completeness classes in algebra, STOC 1979. VP, VNP, and permanent completeness"
  },
  "relations": [
    {
      "slug": "R1802",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "vp-versus-vnp",
      "title": "vp versus vnp",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}