Source authenticated

Erdős Problem #131

The new content is the upper bound; the matching N^(1/5) construction is prior work of Erdős and Csaba. erdosproblems.com has not accepted the claim

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Jul 24, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-verified. Publication: announcement. AI contribution: ai-discovered. Imported under CC BY 4.0.

Canonical aliases: Erdős Problem #131 · Erdős #131 · Problem 131

Confidence: Not scored

Registry verification: lean verified · announcement · candidate

Open the source record ↗

Attribution

VibeMathed
registry · event recorded by

GPT-5.6 Sol
model · ai model contributor · OpenAI

Claude
model · ai model contributor · Anthropic

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Erdős Problem #131

specialist registry · passed

Built and audited by the site on 2026-08-02. A clean clone of the author's Lean 4 development (50 files, 17,408 lines) compiles against the pinned mathlib revision on Lean 4.32.0 with no sorry, admit or native_decide. `#print axioms Nondividing.main_log_limit` returns exactly the eleven whitelisted axioms - propext, Classical.choice, Quot.sound and the eight declared external interfaces - and notably no sorryAx, so no placeholder is load-bearing. Statement fidelity checked against the trusted Challenge.lean: the definitions of non-dividing and F, and the theorem type log F(N)/log N -> 1/5, match. NOT verified: the eight external axioms are assumed rather than proved. Each cites a published result (Schneider, Rogers-Shephard, Betke-Henk-Wills, Pham-Zakharov Lemmas 1, 7 and 13, Conlon-Fox-Pham) but none was checked line by line against its source, and the density-increment exponent in convex_density_set is where the 1/4 to 1/5 improvement lives. erdosproblems.com still lists the problem open with no comments.

Source ↗

Lean 4 formalization

lean artifact · passed

lean-proof link supplied by the VibeMathed registry.

Source ↗

Erdős Problem #131

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

Source ↗

erdosproblems.com/131

specialist registry · pending

problem-record link supplied by the VibeMathed registry.