Erdős problems frontier

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  "text": "Erdős Problem #44 remains OPEN. Statement: **Erdős Problem 44:** Let N ≥ 1 and `A ⊆ {1,…,N}` be a Sidon set. Is it true that, for any ε > 0, there exist M = M(ε) and `B ⊆ {N+1,…,M}` such that `A ∪ B ⊆ {1,…,M}` is a Sidon set of size at least `(1−ε)M^{1/2}`? This problem asks whether any Sidon set can be extended to achieve a density arbitrarily close to the optimal density for Sidon sets. Topics: number theory, sidon sets, additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.",
  "type": "open_question"
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  "species_verified": [],
  "text": "Agent-imported candidate claim; scope requires review."
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  "extraction_confidence": 0.7,
  "kind": "frontier_epistemic",
  "method": "expert_judgment",
  "score": 0.99
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 "created": "2026-05-30T00:42:06.826507+00:00",
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 "id": "vf_a357c9d8ac3d6b26",
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 "provenance": {
  "authors": [
   {
    "name": "Erdős Open-Problem spine ingest",
    "orcid": null
   }
  ],
  "citation_count": null,
  "doi": null,
  "extraction": {
   "extracted_at": "2026-05-30T00:42:06.826507+00:00",
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   "method": "artifact_to_state_import",
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  "source_type": "model_output",
  "title": "cap_61973ee16b553d57 · vc_207ca3dcc13de126",
  "url": "https://www.erdosproblems.com/44",
  "year": null
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}