Gaussian Double-Grid Collocation: Near-Critical Aperiodic Invertibility and a Bounded-Variation Extension
Year: 2026
Type: article
Abstract: INTERLINK BRIDGE / MATHEMATICAL RESEARCH Gaussian Double-Grid Collocation:Near-Critical Aperiodic Invertibility and a Bounded-Variation Extension This restricted-file mathematical research record preserves a near-critical theorem and a new unified analytic extension for Gaussian collocation between independently perturbed integer grids. The WSC-02 result, supported by a standalone exact-rational certificate, proves invertibility for arbitrary aperiodic perturbations under a,b <= 0.3994 and a+b <= 0.4994. The strengthened bounded-variation theorem candidate treats the full strict threshold a+b < 1/2 when one grid has finite total variation and the other grid is unrestricted within its displacement bound. This subsumes the previously separate monotone and summable-nonmonotone-defect candidates and explicitly includes finite-variation sequences that are not summably close to any monotone sequence. The proof uses published one-grid Gaussian interpolation, de Boor–Jia–Pinkus stable-main-diagonal theory, a trace-class analytic Fredholm determinant, and log-concavity of noncolliding Brownian-bridge probabilities. Crucial source transfers remain subject to independent mathematical review; no priority or novelty is asserted. The two-arbitrary-grid conjecture and Gröchenig's unrestricted Problem 2.4 remain open. A short engineering note outlines conditional mathematical relevance to ISAC/6G sensing and Gaussian-kernel imaging, not demonstrated technology or performance. All rights reserved, file access restricted; no redistribution without permission. DOI 10.5281/zenodo.23442996 STATUS Suggested: Restricted Files / Publication Working Paper / version v0.2. NO UPLOAD PERFORMED. Reserved Zenodo DOI: 10.5281/zenodo.23442996Access / rights: Restricted files; all rights reserved; no redistribution or citationwithout written authorization.Scientific status: One internally rationally certified theorem (WSC-02); one strength-ened bounded-variation theorem candidate at the full strict threshold. Monotone andsummable-defect classes follow as special cases. No external line-by-line referee approvalor novelty/priority claim
Author: Senke, Alexanja
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222881080
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