Erdős problems frontier

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  "text": "Erdős Problem #501 remains OPEN. Statement: For every $x \\in \\mathbb{R}$ let $A_x \\subset \\mathbb{R}$ be a bounded set with outer measure $< 1$. Must there exist an infinite independent set, that is, some infinite $X \\subseteq \\mathbb{R}$ such that $x \\notin A_y$ for all $x \\neq y \\in X$? If the sets $A_x$ are closed and have measure $< 1$, then must there exist an independent set of size $3$? Known results: Erdős–Hajnal [ErHa60] proved the existence of arbitrarily large finite independent sets. Hechler [He72] showed the answer is **no** assuming the continuum hypothesis. Topics: combinatorics, set theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.",
  "type": "open_question"
 },
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  "species_unverified": [],
  "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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    "artifact_packet_id": "cap_61973ee16b553d57",
    "candidate_claim_id": "vc_d11ea0453b020966"
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  "type": "computational"
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 "id": "vf_fccad3dc897074b9",
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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",
   "model": "agent:erdos-spine-ingest",
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  "publisher": "artifact packet",
  "review": {
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  "source_type": "model_output",
  "title": "cap_61973ee16b553d57 · vc_d11ea0453b020966",
  "url": "https://www.erdosproblems.com/501",
  "year": null
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 "version": 1
}