Falsifiable. The label is the site's (FALSIFIABLE on 2026-10-06; page last edited 1 February 2026), and it is a body note, not a standing: a counterexample would be one forest whose sequence is not unimodal, a finite check. Two claims are recorded, neither accepted: Zhang and Li's manuscript, on its claim page (Zhang and Li, 2026), claims the conjecture for every finite forest, revised on 6 October 2026 with Vallier and a Lean development, its first arXiv submission withdrawn before announcement and the revision posted on arXiv on 6 October 2026; Fang, Lu, Nevo, Yao and Zheng's arXiv preprint, on its claim page (Fang, Lu, Nevo, Yao and Zheng, 2026), claims to prove it for all forests on at least $N_0$ vertices, for an uncomputed $N_0$, with a Lean development. The frontmatter standing is derived from the claim pages: a pending full claim, so claimed.