Projection by Admissibility Constraints and Sparse Spectral Support in Wave Systems

We study wave reports (data products) under dimension reduction (e.g. 3D → 2D) asan interface-level projection constrained by admissibility rather than as a purely geometricmetaphor. Our central aim is operational: to certify when a reported low-dimensional, sparsemode family is stable under finite reporting depth and finite resolution, and to flag when thesame situation is better modeled as broadband (crowded) reporting.We formalize (i) a certification rule that requires any “Gaussian” or “normal” reportto declare its aggregation depth n together with an explicit error bound, and (ii) a modecrowdingcriterion in which the Berry–Esseen scale