No semistability at infinity for Calabi-Yau metrics asymptotic to cones

We discover a "no semistability at infinity" phenomenon for complete Calabi-Yau metrics asymptotic to cones, by eliminating the possible appearance of an intermediate K-semistable cone in 2-step degeneration theory developed Donaldson and first author. It is sharp contrast setting local singularities K\"ahler-Einstein metrics. A byproduct proof polynomial convergence rate such manifolds, which bridges gap between general Colding-Minicozzi classification results Conlon-Hein.