What question did this study set out to answer?

To certify the stability of low-dimensional, sparse mode families in wave reports under certain conditions.

February 13, 20260 citationsOpen Access

Projection by Admissibility Constraints and Sparse Spectral Support in Wave Systems

Key Points

To certify the stability of low-dimensional, sparse mode families in wave reports under certain conditions.
Examined dimension reduction from 3D to 2D in wave reports.
Developed a certification rule for Gaussian reports with aggregation depth and error bounds.
Created a mode crowding criterion using the Berry–Esseen scale.
Established conditions for when low-dimensional modes remain stable under finite reporting depth.
Identified scenarios that are better represented by broadband reporting rather than sparse modes.

Abstract

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

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