The polynomial removal conjecture for ordered binary matrices

Lineage and corrections

Theorem 1.1: there is a fixed binary $66\times66$ matrix $H$ such that for every $h\ge1$, with $n_h=(386h+2)2^h$ and $\epsilon_h=(386h+2)^{-2}$, some $A_h$ is $\epsilon_h$-far from $H$-free yet $N_H(A_h)\le\epsilon_h2^{-h}n_h^{132}$; hence no polynomial removal bound holds for this $H$, and the finite-family question fails for one square pattern. Corollary: canonical row-column sampling testers need $\exp(\Omega(\epsilon^{-1/2}))$ samples along this sequence. Not shown: which patterns do admit polynomial removal, or a counterexample smaller than $66\times66$. parent of this event

The polynomial removal conjecture for ordered binary matrices evidence for this event

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The polynomial removal conjecture for ordered binary matrices parent of this event

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Lean challenge statement: MatrixRemoval.lean evidence for this event

Alon-Ben-Eliezer, Efficient removal lemmas for matrices (Problem 1.4) evidence for this event

Gishboliner-Shapira, Polynomial property testing (Conjecture 4.5 in arXiv v1) evidence for this event

Lean solution module: OAI/Combinatorics/MatrixRemoval/Main.lean evidence for this event