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Claim. For every integer $s\ge2$ the rational $\alpha=2-\frac2{2s+1}$, and also $\alpha=\frac75$, is a Turán exponent: Theorem 1.2 gives a single bipartite graph $H$ with $\mathrm{ex}(n,H)=\Theta(n^\alpha)$ for each. The exponents $2-\frac2{2s+1}$ are realized by generalized cubes, which also answers a question of Pinchasi and Sharir; the exponent $\frac75$ comes from an upper bound on theta graphs in an asymmetric setting applied to a comb-pasting graph. Before this paper only the families $1+1/s$ and $2-1/s$ were known. The statements are recorded on the library's source card.

Covers. The instances $\alpha=2-\frac2{2s+1}$ for $s\ge2$ and $\alpha=\frac75$, 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.

Acceptance. Refereed: T. Jiang, J. Ma and L. Yepremyan, On Turán exponents of bipartite graphs, Combin. Probab. Comput. 31 (2022), no. 2, 333--344, doi:10.1017/S0963548321000341, a refereed journal. First posting: arXiv:1806.02838, v1 7 June 2018 (the date this page is named by). No reviewed evidence is listed: the site's commentary lists these exponents among the Turán exponents known before 2026 and credits the paper, but its label credits GPT-6 Astra with the full proof and is not an acceptance of this result.

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.