The weak Pach-Tardos conjecture for acyclic matrix patterns

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This event attributed to Lior Gishboliner

Pettie and Tardos, the 2024 refutation of the original form evidence for this event

Proved, in the weak form: for every acyclic pattern $P$, $\mathrm{Ex}(n,P) \le n^{1+O_P(1/\log\log n)}$, hence $n^{1+o(1)}$. Stated as Theorem 1 in the language of ordered bipartite graphs: for all $s,t \ge 1$ and $\varepsilon>0$ there is $n_0$ such that every $n \times n$ ordered bipartite graph with $n \ge n_0$ and at least $n^{1+\varepsilon}$ edges contains a copy of every $s \times t$ ordered bipartite tree. The paper does NOT restore the original polylog conjecture, which stays refuted. parent of this event

This event attributed to ChatGPT-6 Astra

VibeMathed record: The weak Pach-Tardos conjecture for acyclic matrix patterns evidence for this event

The weak Pach-Tardos conjecture for acyclic matrix patterns parent of this event

This event attributed to Xiangyu Li

The weak Pach-Tardos conjecture for acyclic matrix patterns evidence for this event