evidence boundary
supportsfrontiers / frontier
Erdős problems frontier
- id
- vfr_37aec80d874a0239
- license
- CC-BY-4.0
- findings
- 1,256
- accepted core
- 6
- contested
- 0
- links
- 17
- sources
- 1,234
- evidence
- 1,256
- avg conf
- 0.98
e1271/1271 · statement.attested · reviewer:will-blair · 2026-06-10 · null→null
Evidence atom
back to sources{"artifact_id":"va_9bc926d75e4e3881","artifact_packet_id":"cap_61973ee16b553d57","candidate_claim_id":"vc_cc4fc15311b97749"}
- id
- vea_1d361737d2e832fd
- frontier
- Erdős problems frontier
- source
- vs_ef2303ee158e5d7f
- finding
- vf_548d85ccc6d3d37c
finding binding
boundopen_question
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.
source binding
source-boundcap_61973ee16b553d57 · vc_cc4fc15311b97749
vs_ef2303ee158e5d7f
review context
unverified1 events
1 reviewable changes and 0 evaluation records target this atom or its bound objects.
statement
{"artifact_id":"va_9bc926d75e4e3881","artifact_packet_id":"cap_61973ee16b553d57","candidate_claim_id":"vc_cc4fc15311b97749"}
locator
span:0
extraction method
artifact_to_state_import
support relation
supports
condition refs
vcnd_a44664cb66191d03
caveats
No caveats recorded.
Review, event, and evaluation records
2events
vev_90e1ae49a2d6683dfinding.assertedCandidate claim vc_cc4fc15311b97749 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30
reviewable changes
vpr_d110170198daf7dafinding.addCandidate claim vc_cc4fc15311b97749 imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30
evaluations
No evaluation rows are attached.