Wavebasis Crack — Better Fix

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This study examines the "wavebasis crack" problem — a class of numerical/analytical instabilities that arise when representing wavefields (e.g., acoustics, elastodynamics, electromagnetics) using basis functions that produce discontinuities, poor conditioning, or spurious solutions near cracks, interfaces, or boundaries. It presents diagnosis, mathematical formulation, improved basis choices, stabilization techniques, implementation notes, and examples.