2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/105462We quantify, within mode coupling theory, how changes in the liquid structure affect that of the glass. Apart from the known sensitivity to the structure factor $S(q)$ at wavevectors around the first sharp diffraction peak $q_0$, we find a strong (and inverted) response to structure at wavevectors \emph{below} this peak: an increase in $S(q_0/2)$ {\em lowers} the degree of arrest over a wide $q$-range. This strong sensitivity to `caged cage' packing effects, on length scales of order 2d, is much weaker in attractive glasses where short-range bonding dominates the steric caging effect.4 pages, 5 figures. v2: 3 figures replaced; text rewrittenSoft Condensed MatterStatistical Mechanicstext