arXiv:2611.05686v1 Announce Type: new Abstract: We translate the spectral gap-closing criterion for multi-dimensional monotone quasiperiodic Schr\"odinger operators into a concrete dynamical protocol and verify it by large-scale numerics. For a non-principal label we construct a sampling function whose leading eigenfunction weight at the origin vanishes; a local bump then drives the residual weight through zero. The height of a weighted oscillatory time average of the origin-to-localization-center correlator exhibits a deep minimum precisely at the closing, while the site-control label remains featureless and orders of magnitude larger. The signature is robust and maps directly onto superconducting-circuit and photonic platforms.
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