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Claim. In the notation of Problem 561, with $\ell_k=\max\{n_i+m_j-1:i+j=k\}$,

$$\hat R(F_1,F_2)\ge\sum_{k=2}^{s+t}\ell_k-\sum_{k=2}^{s+t-1}\eta_k,$$

where $\eta_k\in\{0,1\}$ is $0$ exactly when some pair $(n_i,m_j)$ with $i+j=k$ attaining $\ell_k$ has both entries odd or one entry equal to $1$. That is, the conjectured value is a lower bound up to a deficit of at most one edge on each diagonal but the last, and a diagonal attained by two odd star sizes or by a single-edge star carries no deficit. The argument, as the problem page records it, deletes a vertex of large degree and repeats, with a splitting fact proved through Vizing's theorem and $2$-factorizations. On a pair of star forests for which every $\eta_k$ is $0$ the bound is the conjectured formula, since the matching upper bound is immediate; the case of all star sizes odd is one such family, and Theorem 2.5 of Davoodi, Javadi, Kamranian and Raeisi already proves it.

Submission note. Posted to erdosproblems.com as a proof claim by Ricky Cipollini (account rickyc) on 7 August 2026, giving "Qwen 3.8 Max" as the AI used:

We prove the following lower bound:

$$\widehat R(F_1,F_2)\ge > \sum_{k=2}^{s+t}\ell_k-\sum_{k=2}^{s+t-1}\eta_k.$$

Notes: The 3 page paper

was written by me with LaTeX assistance and minor polishing by GPT-5.6 Sol. I'll note that this is AI-assisted by Qwen 3.8 Max (this is a nice new model, but it tends to make up theorems).

Covers. The formula $\hat R(F_1,F_2)=\sum_kl_k$ for every pair of star forests with $\eta_k=0$ for all $2\le k<s+t$, that is, every diagonal maximum before the last is attained by a pair of odd sizes or by a pair containing a single-edge star (for example when $F_1$ or $F_2$ is a matching); for other pairs, a lower bound within $\sum\eta_k\le s+t-2$ edges of the formula. The formula for all star forests is not claimed.

Depends on. Nothing in this wiki; the argument is the author's own.

Standing. Claimed. The claimant, Ricky Cipollini, posting as rickyc, placed the argument as a comment of 6 August 2026 in the site's discussion thread, the date the page is named by, and submitted it as a partial proof claim on 7 August 2026 with the manuscript linked from the claim tab. The tab names Qwen 3.8 Max as the AI system used in the mathematics, and the claimant's notes say that the claimant wrote the three-page note and used GPT-5.6 Sol only for typesetting help and light editing. The claim page states the bound from the comment's three-page argument, which was not checked; the linked manuscript is not its basis, and no evidence kind is listed. The claim had no comments on the tab (2026-10-06); the site's label is OPEN and its commentary does not mention the claim (page last edited 1 February 2026); no arXiv version, journal record or independent review was found. The later partial claim tienxion 2026 credits its framework to this author and reproves the deletion lemma.