Erdős problems frontier

{
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  "text": "Erdős Problem #41 remains OPEN. Statement: Let `A ⊆ ℕ` be an infinite set such that the triple sums `a + b + c` are all distinct for `a, b, c` in `A` (aside from the trivial coincidences). Is it true that `liminf n → ∞ |A ∩ {1, …, N}| / N^(1/3) = 0`? Topics: number theory, sidon sets, additive combinatorics. Erdős prize: $500. 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."
 },
 "confidence": {
  "basis": "agent-imported candidate claim; reviewer acceptance required",
  "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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  "evidence_spans": [
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    "artifact_id": "va_9bc926d75e4e3881",
    "artifact_packet_id": "cap_61973ee16b553d57",
    "candidate_claim_id": "vc_0bd9cabd429a45df"
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  "model_system": "agent artifact packet",
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  "replicated": false,
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  "type": "computational"
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  "retracted": false
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 "id": "vf_e98c39e418546862",
 "links": [],
 "previous_version": null,
 "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",
   "extractor_version": "vela/0.691.0",
   "method": "artifact_to_state_import",
   "model": "agent:erdos-spine-ingest",
   "model_version": null
  },
  "journal": null,
  "openalex_id": null,
  "pmc": null,
  "pmid": null,
  "publisher": "artifact packet",
  "review": {
   "corrections": [],
   "reviewed": false,
   "reviewed_at": null,
   "reviewer": null
  },
  "source_type": "model_output",
  "title": "cap_61973ee16b553d57 · vc_0bd9cabd429a45df",
  "url": "https://www.erdosproblems.com/41",
  "year": null
 },
 "updated": null,
 "version": 1
}