Erdős problems frontier

{
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  "text": "Erdős Problem #694 has status 'solved (lean)'. Statement: Let $f_\\max(n)$ be the largest $m$ such that $\\phi(m) = n$, and $f_\\min(n)$ be the smallest such $m$, where $\\phi$ is Euler's totient function. Investigate $$ \\max_{n\\leq x}\\frac{f_\\max(n)}{f_\\min(n)}. $$ GPT-5.5 Pro (prompted by Price) has proved (see also the comments for a summary) that $$ \\max_{n\\leq x}\\frac{f_{\\max}(n)}{f_{\\min}(n)}=(e^\\gamma+o(1))\\log\\log x. $$ A Lean formalisation of the reduction exists, conditional on Mertens' product theorem and Linnik's theorem; see the [formal proof](https://github.com/Shashi456/erdos-formalizations/blob/main/Erdos/P694/Proof.lean). Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible.",
  "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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    "artifact_packet_id": "cap_61973ee16b553d57",
    "candidate_claim_id": "vc_cc4fc15311b97749"
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  "method": "ScienceClaw-shaped artifact packet import",
  "model_system": "agent artifact packet",
  "p_value": null,
  "replicated": false,
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  "type": "computational"
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 "id": "vf_548d85ccc6d3d37c",
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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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  "source_type": "model_output",
  "title": "cap_61973ee16b553d57 · vc_cc4fc15311b97749",
  "url": "https://www.erdosproblems.com/694",
  "year": null
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 "version": 1
}