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The claim. For every $\eta>0$ there is a finite 3-regular bipartite graph $H$ with $\mathrm{ex}(n,H)=O(n^{4/3+\eta})$ (Theorem 1.4 of O. Janzer, Disproof of a conjecture of Erdős and Simonovits on the Turán number of graphs with minimum degree 3, Int. Math. Res. Not. IMRN 2023, no. 10, 8478--8494; arXiv:2109.06110, first posted 13 September 2021). Such an $H$ is bipartite with minimum degree $r=3$, for which Problem 147 asks for $\mathrm{ex}(n,H)\gg n^{3/2+\epsilon(H)}$ with some $\epsilon(H)>0$. Taking $\eta<1/6$ makes the two exponents incompatible, so the universal statement of the problem is false already at $r=3$. The paper's own target is the Erdős--Simonovits conjecture that a bipartite graph has extremal number $O(n^{3/2})$ exactly when it is 2-degenerate; the same construction refutes the lower bound asked here.

What the corpus holds. The complete same-paper proof chain, following arXiv v2 of 8 November 2021, is compiled on the source card, with the exponent transfer on the result page and two compilation-supplied qualifications (a constant in Lemma 2.5, a restricted form of Lemma 2.19), neither an author-issued correction, each passed by a bounded independent review recorded under the card's evidence. Locators refer to arXiv v2; the IMRN version may differ.

Acceptance. Refereed: International Mathematics Research Notices, first published online 26 April 2022, issue 2023(10). Reviewed: the site's curator, Thomas Bloom, credits this paper with the disproof of the case $r=3$ in the problem's commentary (erdosproblems.com/147, linked above, page last edited 18 January 2026, label DISPROVED (LEAN)). No formalization of this theorem is recorded in the corpus; the site's label DISPROVED (LEAN) refers to an external Lean proof that refutes the statement through the minimum-degree-$4$ witness $C_{12}[2]$, linked on the blow-up page, and formalized is not listed.

Depends on. Theorem 1.4 and its exponent transfer, whose same-paper proof chain the source card compiles.