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Claim. Theorem 1.2 (p. 1): $f(n)=U(n)$ for all sufficiently large $n$, where $U(n)=m+1,m+2,m+2,m+4$ for $n=4m,4m+1,4m+2,4m+3$, so van Doorn's upper bound $\lfloor n/4\rfloor+d$ is attained and van Doorn's conjecture holds for large $n$. Theorem 1.3, computer-assisted: for every $n\ge4$, $f(n)=U(n)$ except on van Doorn's fifteen exceptional $n<92$, where $f(n)=U(n)-1$, or $U(n)-2$ for $n\in\{15,27\}$, by program checks over $5000\le n\le5504797$ and an analytic estimate beyond. The tab entry sketches the route: a badly ordered pair is first reduced to a canonical interval; small denominators are handled by Dress's discrepancy theorem; the pairs that remain, those near the extremal size, are cut down by a balanced Dirichlet approximation and by signed counts over determinant layers until only two central configurations are left, and those two are counted exactly. The entry says that the argument gives no explicit threshold, so by itself it does not reach the conjectured $n\ge92$. The exact formula implies the asymptotic $f(n)=(\frac14+o(1))n$, so the claim is a full claim on Problem 1005, stronger than the question asks. Read depth: the statements of Theorems 1.2 and 1.3 (p. 1), compiled on the result page theorem_1_2; the digest is on the card wang_2026_exact_formula_erdos_problem_1005; the proofs and the tab entry's comment are not covered.

Submission note. Posted to erdosproblems.com as a proof claim by Yanmohan Wang (account dct) on 28 July 2026, giving "GPT 5.6" as the AI used:

Building on van Doorn’s residue-class upper bounds and Cipollini’s theorem $f(n)=(1/4+o(1))n$, this proof obtains, for all sufficiently large $m$,

$$> f(4m)=m+1,\quad f(4m+1)=m+2,\quad f(4m+2)=m+2,\quad f(4m+3)=m+4.$$

The proof

reduces bad pairs to canonical intervals. Dress’s discrepancy theorem handles small denominators, while a balanced Dirichlet approximation and signed determinant-layer counts reduce the remaining near-extremal pairs to two central configurations, which are counted exactly. The argument does not determine $n_0$, so it does not prove the conjectured threshold $n\ge92$. Notes: This proposed proof has not yet been peer reviewed. Comments, corrections, and counterexamples are welcome.

Standing. The claim was filed on the site's proof-claims tab on 28 July 2026 by the first author, Y. Wang, with a link to the manuscript in the authors' repository, committed the same day; the preprint, by Wang, Xie and Zhao, was posted to arXiv on 16 August 2026, the only version, with the computation's code in the same repository (listed, not run). The tab entry names GPT 5.6 as the system used, and the paper's AI-use declaration (p. 9) says that the authors used ChatGPT-5.6 to assist in generating candidate proof strategies and verified and refined every suggestion. The entry itself notes that the proof is not peer reviewed. The site has not accepted the claim (its commentary rests on Cipollini's lower bound), no refereed publication, no formalization and no outside review was found (2026-09-18). The claim stays claimed.

Depends on. Cipollini's page, whose theorem the entry says the argument builds on, and van Doorn's page, whose residue-class upper bounds it uses.