Baxter onset defect conjecture for Miura-ori boundary corrections

Let $E_d(m,n)$ be the count and let $p_d(m,n)$ denote its closed-form polynomial in the threshold regime. For $s=\min(m,n)<d-1$, define the boundary correction, with the other variable denoted by $n$, by

$$B_d^{(s)}(n):=E_d(s,n)-p_d(s,n).$$

Let $\operatorname{Bax}(k)$ be the $k$-th Baxter number. Baxter onset defect conjecture. For every $d\ge4$, the correction $B_d^{(d-2)}(n)$ is linear in $n$ with leading coefficient $-4\operatorname{Bax}(d-3)$. The observed coefficients agree with the first Baxter numbers, and transfer-matrix computations extend the agreement through $d=11$; a proof remains open and would show that the threshold $d-1$ is sharp.