Sharp Near-Critical Conditioning of Independently Jittered Gaussian Double-Grid Collocation Matrices - Order phase law and square-root crossover scaling function

This restricted-access working paper preserves a protected mathematical research record on the conditioning and invertibility of Gaussian collocation operators generated by two independently jittered integer grids. The deposit documents an internally closed theorem-candidate chain for the near-critical boundary regime, including an order-level boundary law and a sharp square-root crossover scaling law. The analytical framework uses exact Gaussian cardinal/Gram factorization, adaptive critical transport models, balanced operator reductions, discrete half-line spectral analysis, and component-level reduction methods. The restricted archive contains the private reviewer manuscript, the chronological proof-chain snapshot, state-transition and provenance records, claim-boundary documentation, and cryptographic integrity manifests. Intermediate hypotheses that were later falsified or superseded are intentionally retained as part of the scientific provenance. The results have not undergone external line-by-line referee validation. No claim of worldwide novelty or priority is made. The record does not claim a general solution of Gröchenig’s Problem 2.4 for arbitrary totally positive matrices, a finite-entry decision algorithm, formal verification, patent validity, or freedom to operate. File access is restricted. Access, if granted, is solely for confidential scholarly or technical evaluation under separately agreed access terms. The deposit itself grants no permission for redistribution, publication, commercial exploitation, software incorporation, or disclosure of the restricted material. RESTRICTED RESEARCH MATERIAL — CONFIDENTIAL EVALUATION ONLY Copyright © 2026 Alexanja Senke. All rights reserved. The files associated with this record contain unpublished and proprietary research material. No copyright license, patent license, know-how license, commercial license, sublicence, right of redistribution, or other exploitation right is granted by the creation of this Zenodo record, assignment of a DOI, submission or approval of an access request, or technical delivery of the files. Access may be granted only to a specifically identified person for the limited purpose of confidential scholarly, mathematical, technical, or due-diligence evaluation. Access is personal and non-transferable. Unless expressly authorized in a separate written agreement signed by the rights holder, the recipient may not reproduce, redistribute, publish, publicly disclose, transmit, sublicense, sell, commercially exploit, translate, adapt, create derivative materials from, incorporate into software or commercial systems, submit as training or evaluation material for machine-learning systems, or use the restricted contents as the basis for filing or asserting intellectual-property rights. Technical access through Zenodo does not constitute publication of the restricted files and does not waive confidentiality, copyright, trade-secret/know-how interests, or any other rights that may exist in the material. Access to the restricted files may be conditioned on execution of a separate Confidential Evaluation Agreement or non-disclosure agreement. Approval of a Zenodo access request constitutes technical access only and does not replace such an agreement. Public Zenodo metadata may be cited in the ordinary scholarly manner. Any quotation, reproduction, disclosure, or dissemination of material contained only in the restricted files requires separate authorization unless otherwise permitted by mandatory applicable law. All rights not expressly granted in a separate written agreement are reserved.