{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1769",
  "content_hash": null,
  "slug": "strong-exponential-time-hypothesis-claim-literature-frontier",
  "type": "claim",
  "title": "Strongest checked neighboring result",
  "summary": "Improved algorithms exist for every fixed k, and circuit lower bounds or restricted-model SAT lower bounds give partial evidence.",
  "relevance": "Locates the present research frontier immediately below Strong Exponential Time Hypothesis.",
  "relevance_source": "recorded",
  "body": "Improved algorithms exist for every fixed k, and circuit lower bounds or restricted-model SAT lower bounds give partial evidence.\n\nThis leaves the following boundary unresolved: The unrestricted quantified lower bound remains unproved and undisproved. 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/10.1006/jcss.2000.1727",
      "locator": "R. Impagliazzo and R. Paturi, On the complexity of k-SAT, Journal of Computer and System Sciences 62 (2001). definition and consequences"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1006/jcss.2000.1727",
    "locator": "R. Impagliazzo and R. Paturi, On the complexity of k-SAT, Journal of Computer and System Sciences 62 (2001). definition and consequences"
  },
  "relations": [
    {
      "slug": "R1770",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "strong-exponential-time-hypothesis",
      "title": "strong exponential time hypothesis",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}