Erdős problems frontier

{
 "assertion": {
  "direction": null,
  "entities": [],
  "relation": null,
  "text": "Erdős Problem #347 has status 'proved (lean)'. Statement: Is there a sequence $A=\\{a_1\\leq a_2\\leq \\cdots\\}$ of integers with $$\\lim \\frac{a_{n+1}}{a_n}=2$$ such that $$P(A')= \\left\\{\\sum_{n\\in B}n : B\\subseteq A'\\textrm{ finite }\\right\\}$$ has density $1$ for every cofinite subsequence $A'$ of $A$? This has been solved in the affirmative by ebarschkis in the comments (based on idea of Tao and van Doorn, also in the comments). Thos was formalized in Lean by Barschkis using Aristotle. Topics: number theory, complete sequences. 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_2e4ad5ecf784b675"
   }
  ],
  "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_3bdeedd439e228be",
 "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_2e4ad5ecf784b675",
  "url": "https://www.erdosproblems.com/347",
  "year": null
 },
 "updated": null,
 "version": 1
}