Positive lattice amphichirality barrier for cubic lattice knots

Let $K$ be an amphichiral knot type and let $\omega$ be a minimal simple cubic lattice representative of $K$. Consider the minimal BFACF graph and the reflected mirror seed of $\omega$. Positive lattice amphichirality barrier. There exist amphichiral knot types $K$ and minimal simple cubic lattice representatives $\omega$ such that $\omega$ and its reflected mirror seed are not connected in the minimal BFACF graph, but merge at a strictly higher level. The figure-eight and $6_3$ computations give seed-generated evidence with barriers $32-30=2$ and $44-40=4$, respectively. This conjecture proposes that amphichirality need not be realized within the birth-level component structure of the lattice move graph, and that a positive merge barrier can occur. The reported computations are experimental evidence rather than a proof.