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Claim. Stijn Cambie and Jorik Jooken show that $3$-colorable, hence $K_4$-free, connected graphs of minimum degree $16$ can have diameter at least $\frac{31}{216}n+O(1)$ (Table 1 and the following paragraph on p. 4, the $\delta=16$ block on p. 11 of the preprint; the lower bound $f'(16)\ge31/216$ is stated as unconditional, its exactness as conditional on mild assumptions). Part (i) of the statement of Problem 612 at $r=2$, $\delta=16$, where $8\mid16$ as required, asserts $D\le\frac{16}{7}\frac{n}{16}+O(1)=\frac n7+O(1)$, and $\frac{31}{216}>\frac17$. The instance lies inside the window $8\le\delta\le16$ that Czabarka, Singgih and Székely left open at $r=2$; Cambie and Jooken's data (Table 1) support the conjectured ratio $2/7$ at $\delta=8$, the window's other admissible value.

Covers. Part (i), in full: one false instance refutes it, so this is a second disproof of part (i), beside the refereed one of Czabarka, Singgih and Székely. It does not bear on part (ii).

Standing. A preprint (arXiv v1 of 12 February 2025, 16 pages); no later version and no journal record were found on 2026-09-17. The site's commentary cites the example as a further counterexample to the original conjecture and thanks the first author, and the page's label stays OPEN and the proof-claim tab is empty. The construction's statement is paged on the result page counterexample_p4 at claims checked; the computer search behind the $\delta=16$ block is the authors' own. The claim therefore stays claimed; the standing of part (i) rests on the refereed counterexamples.