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Claim. For positive integers $a,b$ with $\lfloor b/a\rfloor^3\le a\le\frac{b}{\lfloor b/a\rfloor+1}+1$ the rational $\alpha=2-\frac ab$ is a Turán exponent: there is a single graph $F$ with $\mathrm{ex}(n,F)=\Theta(n^{2-a/b})$. The upper bound is Theorem 8, which verifies the Bukh--Conlon conjecture for every rooted power of the balanced rooted trees $T_{s,t,s'}$ of the paper's Figure 1 (with $t\ge s^3-1$ when $s-s'\ge2$), through the paper's framework of negligible obstructions; the lower bound is Bukh and Conlon's Lemma 6. The statements are recorded on the library's source card.

Covers. The instances $\alpha=2-\frac ab$ with $\lfloor b/a\rfloor^3\le a\le\frac{b}{\lfloor b/a\rfloor+1}+1$, 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, Z. Jiang and J. Ma, Negligible obstructions and Turán exponents, Ann. Appl. Math. 38 (2022), no. 3, 356--384, doi:10.4208/aam.oa-2022-0008, a refereed journal; the site cites the arXiv version. First posting: arXiv:2007.02975, v1 6 July 2020 (the date this page is named by), v3 30 January 2023. 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.