Erdős problems frontier

{
 "assertion": {
  "direction": null,
  "entities": [],
  "relation": null,
  "text": "Erdős Problem #488 has status 'falsifiable'. Statement: Let $A$ be a finite set and $$B=\\{ n \\geq 1 : a\\mid n\\textrm{ for some }a\\in A\\}.$$ Is it true that, for every $m>n\\geq \\max(A)$, $$\\frac{\\lvert B\\cap [1,m]\\rvert }{m}< 2\\frac{\\lvert B\\cap [1,n]\\rvert}{n}?$$ Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.",
  "type": "open_question"
 },
 "conditions": {
  "age_group": null,
  "cell_type": null,
  "clinical_trial": false,
  "concentration_range": null,
  "duration": null,
  "human_data": false,
  "in_vitro": false,
  "in_vivo": false,
  "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
 },
 "created": "2026-05-30T00:42:06.826507+00:00",
 "evidence": {
  "effect_size": null,
  "evidence_spans": [
   {
    "artifact_id": "va_9bc926d75e4e3881",
    "artifact_packet_id": "cap_61973ee16b553d57",
    "candidate_claim_id": "vc_2af409e77728f93f"
   }
  ],
  "method": "ScienceClaw-shaped artifact packet import",
  "model_system": "agent artifact packet",
  "p_value": null,
  "replicated": false,
  "replication_count": null,
  "sample_size": null,
  "species": null,
  "type": "computational"
 },
 "flags": {
  "contested": false,
  "declining": false,
  "gap": false,
  "gravity_well": false,
  "negative_space": false,
  "retracted": false
 },
 "id": "vf_29c8b747d0aa12af",
 "links": [
  {
   "created_at": "2026-06-10T06:44:20Z",
   "inferred_by": "reviewer",
   "note": "open obligation for #488",
   "target": "vf_ef7066987d658f0e",
   "type": "depends"
  }
 ],
 "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_2af409e77728f93f",
  "url": "https://www.erdosproblems.com/488",
  "year": null
 },
 "updated": null,
 "version": 1
}