{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1488",
  "content_hash": null,
  "slug": "deterministic-logspace-versus-nondeterministic-logspace-attempt-dated-source-audit",
  "type": "attempt",
  "title": "Dated source and duplicate audit",
  "summary": "The exact target, equivalent terminology, and 2025-2026 status evidence were checked on 2026-08-01. Strongest checked result: NL=coNL, undirected reachability is in L, and directed reachability has sublinear-space algorithms with larger time or other tradeoffs. Unresolved remainder: Deterministic logarithmic space for directed reachability remains unknown.",
  "relevance": "Documents why Is L equal to NL? was treated as a distinct open target on 2026-08-01.",
  "relevance_source": "recorded",
  "body": "The audit ran on 2026-08-01 across the cited primary literature and problem collections, Crossref, arXiv, and stable publisher records, TheoremDB published, prospecting, packet, formal, and retired corpus. It checked the exact statement, its named or normalized variants, recent status evidence, and the controlled TheoremDB corpus.\n\nQueries included:\n- L versus NL open problem current\n- directed reachability deterministic logspace open\n\nThe exact target, equivalent terminology, and 2025-2026 status evidence were checked on 2026-08-01. Strongest checked result: NL=coNL, undirected reachability is in L, and directed reachability has sublinear-space algorithms with larger time or other tradeoffs. Unresolved remainder: Deterministic logarithmic space for directed reachability remains unknown.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.1137/0217058",
      "locator": "N. Immerman, Nondeterministic space is closed under complementation, SIAM Journal on Computing 17 (1988). NL=coNL theorem"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1137/0217058",
    "locator": "N. Immerman, Nondeterministic space is closed under complementation, SIAM Journal on Computing 17 (1988). NL=coNL theorem"
  },
  "relations": [
    {
      "slug": "R1491",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "deterministic-logspace-versus-nondeterministic-logspace",
      "title": "deterministic logspace versus nondeterministic logspace",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}