{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1770",
  "content_hash": null,
  "slug": "strong-exponential-time-hypothesis-claim-status-20260801",
  "type": "claim",
  "title": "Current status and exact unresolved remainder",
  "summary": "OPEN as checked on 2026-08-01. Strongest checked neighboring result: Improved algorithms exist for every fixed k, and circuit lower bounds or restricted-model SAT lower bounds give partial evidence. Exact unresolved remainder: The unrestricted quantified lower bound remains unproved and undisproved.",
  "relevance": "This is the dated publication status for the canonical target Strong Exponential Time Hypothesis.",
  "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: Improved algorithms exist for every fixed k, and circuit lower bounds or restricted-model SAT lower bounds give partial evidence.\n\nThe exact unresolved remainder is: The unrestricted quantified lower bound remains unproved and undisproved.\n\nA complete resolution must meet the following acceptance conditions:\n- Prove the quantified lower bound in a standard deterministic machine model.\n- Or give one ε>0 and algorithms solving k-SAT in O((2−ε)^n) for every k.",
  "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": "R1769",
      "title": "Strongest checked neighboring result",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R1767",
      "title": "Dated source and duplicate audit",
      "object_type": "attempt",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "R1768",
      "title": "Work at the unresolved boundary",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "strong-exponential-time-hypothesis",
      "title": "strong exponential time hypothesis",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}