Problem detail · source-aware
VibeMathed reports this item as candidate. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Let $A=\{1\leq a_1< a_2<\cdots\}$ be a set of integers such that $A\backslash B$ is complete for any finite subset $B$ and not complete for any infinite subset $B$. If $a_{n+1}/a_n \geq 1+\epsilon$ for all $n$, must $\lim_n a_{n+1}/a_n=(1+\sqrt{5})/2$? Under the reading where the ratio limit is assumed to exist, a Lean-verified argument forces the limit to be the golden ratio; a separate construction disproves the literal statement where convergence is not assumed.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
Kitamura's affirmative Lean 4 formalization of the limit-exists reading was produced with ChatGPT and Codex; days earlier, GPT Pro with Codex had produced a Lean-checked disproof of the literal reading (Liam Price), which the forum classes as solving a variant with precursors in Burr-Erdős 1981.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
A community screening found the Lean of the variant disproof correct and corresponding to its paper (one typo); the affirmative limit-exists formalization reports standard axioms only. erdosproblems.com still lists the problem open.
Correctness: supported · statement fidelity: audited · peer review: none
The problem statement is ambiguous: the limit-exists reading is claimed proved (Lean), while the convergence-from-hypotheses reading was disproved by a Lean-checked construction of Price that the community classes as a variant
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.