---

Claim. For positive integers $r,t$ with $t\ge2$ and $r\ge2t+3$ the rational $\alpha=1+\frac{rt-1}{2rt+2r}$, which is $\frac32-\frac{r+1}{2r(t+1)}$ (the site's form with $a=r$ and $b=t$), is a Turán exponent. Theorem 1.7, paged at theorem_1_7, bounds the extremal number of every rooted power of the once-subdivided height-two tree $T'_{r,t}$ by $O(n^{1+(rt-1)/(2rt+2r)})$, verifying the Bukh--Conlon conjecture for these trees; the matching lower bound is Bukh and Conlon's Theorem 1.4, quoted in the paper. The statements are recorded on the library's source card.

Covers. The instances $\alpha=1+\frac{rt-1}{2rt+2r}$ with $t\ge2$ and $r\ge2t+3$, each realized by a single bipartite graph. The statement for every rational $\alpha\in[1,2)$ is settled by the accepted claim page Adamczewski 2026.

Depends on. Nothing in this wiki; the result is the paper's own theorem.

Standing. Claimed, not accepted. arXiv:2607.19607, v1 21 July 2026 (the date this page is named by), 28 pp.; no journal version is known. The site's commentary lists these exponents among the previously known Turán exponents, those known before the 2026 resolution, and credits the paper, but its label credits GPT-6 Astra with the full proof and is not an acceptance of this result; nothing is refereed or formalized.

Read depth. The statements are taken from the paper's abstract and the result list on the library card; no proof was read, and nothing is independently reviewed in this corpus.