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Claim. On 2026-06-21 Kenta Kitamura (forum name KentaKitamura) posted in the thread of Problem 346 a Lean 4 development for the reading of the question in which the limit of $a_{n+1}/a_n$ is assumed to exist. Its theorems main_expanded and main_valueDeletion_expanded state: if $A=\{a_0<a_1<\cdots\}$ is a strictly increasing sequence of positive integers such that $A$ minus any finite set of terms is complete, $A$ minus any infinite set of terms is not complete, $a_{n+1}/a_n\ge1+\epsilon$ for some $\epsilon>0$ and all $n$, and $a_{n+1}/a_n\to L$ for some $L>1$, then $a_{n+1}/a_n\to\varphi=(1+\sqrt5)/2$. The two versions delete indices and values respectively, and the repository proves them equivalent for strictly increasing sequences. Its README reports that #print axioms lists only propext, Classical.choice and Quot.sound for both theorems, with no sorryAx; the post discloses that the formalization and its write-up were prepared with assistance from Codex and ChatGPT.

Covers. Sequences satisfying the problem's hypotheses whose consecutive ratios converge: for them the limit is $\varphi$, as the question asks. It settles nothing for sequences whose ratios do not converge, where Price's counterexample shows that the hypotheses do not force convergence; so the Statement, with convergence part of the conclusion, is disproved, while for the variant in which the limit is assumed to exist this development claims the answer yes.

Standing. Claimed. Nat Sothanaphan wrote in the thread on 2026-06-21 that the Lean proof correctly shows that a limit $L\ne\varphi$ is impossible, that the case $L>\varphi$ is also handled by Burr and Erdős (1981), and gave an informal argument for the remaining case $L<\varphi$, crediting GPT-5.5 Thinking for the check and discussion. The site's curator labels Problem 346 solved and credits Price's counterexample; the label does not credit this result, so the thread check is recorded here in prose and no reviewed evidence is listed. Nothing was built or audited here, so no formalized evidence is listed.

Depends on. Nothing in this wiki.