{
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  "ref": "R1677",
  "content_hash": null,
  "slug": "one-way-functions-exist-claim-status-20260801",
  "type": "claim",
  "title": "Current status and exact unresolved remainder",
  "summary": "OPEN as checked on 2026-08-01. Strongest checked neighboring result: Candidate constructions follow from factoring, lattice, coding, and other assumptions; black-box and structural equivalences connect OWFs to cryptographic primitives. Exact unresolved remainder: No unconditional construction or impossibility theorem is known.",
  "relevance": "This is the dated publication status for the canonical target Do one-way functions exist?.",
  "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: Candidate constructions follow from factoring, lattice, coding, and other assumptions; black-box and structural equivalences connect OWFs to cryptographic primitives.\n\nThe exact unresolved remainder is: No unconditional construction or impossibility theorem is known.\n\nA complete resolution must meet the following acceptance conditions:\n- Construct such a family and prove security unconditionally.\n- Or prove every polynomial-time computable function family can be inverted with nonnegligible probability in probabilistic polynomial time.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://doi.org/10.1109/SFCS.1989.63483",
      "locator": "R. Impagliazzo and M. Luby, One-way functions are essential for complexity based cryptography, FOCS 1989. main equivalence theorems"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1109/SFCS.1989.63483",
    "locator": "R. Impagliazzo and M. Luby, One-way functions are essential for complexity based cryptography, FOCS 1989. main equivalence theorems"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R1676",
      "title": "Strongest checked neighboring result",
      "object_type": "claim",
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      "direction": "incoming"
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    {
      "slug": "R1674",
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    },
    {
      "slug": "R1675",
      "title": "Work at the unresolved boundary",
      "object_type": "attempt",
      "relation": "addresses",
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    },
    {
      "slug": "one-way-functions-exist",
      "title": "one way functions exist",
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}