{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1802",
  "content_hash": null,
  "slug": "vp-versus-vnp-claim-status-20260801",
  "type": "claim",
  "title": "Current status and exact unresolved remainder",
  "summary": "OPEN as checked on 2026-08-01. Strongest checked neighboring result: Exponential lower bounds are known for restricted arithmetic models, while unrestricted explicit lower bounds remain far smaller. Exact unresolved remainder: No superpolynomial lower bound for an explicit VNP family in general arithmetic circuits is known.",
  "relevance": "For Is VP equal to VNP?, record vp-versus-vnp-claim-status-20260801 (“Current status and exact unresolved remainder”) records a bound, answer, status fact, or structural consequence. The record states: OPEN as checked on 2026-08-01.",
  "relevance_source": "recorded",
  "body": "The problem was checked as open on 2026-08-01.\n\nThe strongest neighboring result found in the cited sources is: Exponential lower bounds are known for restricted arithmetic models, while unrestricted explicit lower bounds remain far smaller.\n\nThe exact unresolved remainder is: No superpolynomial lower bound for an explicit VNP family in general arithmetic circuits is known.\n\nA complete resolution must meet the following acceptance conditions:\n- Construct polynomial-size circuits for every VNP family, equivalently for a standard VNP-complete family.\n- Or prove an explicit VNP family requires superpolynomial arithmetic-circuit size.",
  "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"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R1801",
      "title": "Strongest checked neighboring result",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R1799",
      "title": "Dated source and duplicate audit",
      "object_type": "attempt",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "R1800",
      "title": "Work at the unresolved boundary",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "vp-versus-vnp",
      "title": "vp versus vnp",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}