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In two-centre structured Gaussian traps, effective-depth obstructions in multipole Gram certification arise from inter-centre leakage and dictionary conditioning, requiring a distinction between numerical threshold validity and theorem-level block certification. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

June 7, 20260 citationsOpen Access

Two-Centre Multipole Gram Certification in Structured Gaussian Traps: Block Stability, Effective-Depth Obstructions, and Nonseparable Stress Tests

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DPDmytro Panasenko

Key Points

This study aims to explore finite-depth multipole Gram certification for structured Gaussian traps.
Analyzed block stability using a finite-dimensional theorem up to depth L=3.
Performed threshold-sensitivity tests and nonseparable perturbation stress tests.
Combined numerical diagnostics with theoretical frameworks.
Identified effective-depth obstructions due to inter-centre leakage.
Distinguished between numerical threshold validity and theorem-level certification.
Documented outcomes of stress tests indicating weaknesses in current methodologies.

Abstract

This preprint studies finite-depth multipole Gram certification for a two-centre structured Gaussian trap. It combines a finite-dimensional block-stability theorem with reproducible numerical diagnostics up to depth L=3, threshold-sensitivity tests, and weak nonseparable perturbation stress tests. The manuscript distinguishes numerical threshold validity from theorem-level block certification and documents effective-depth obstructions arising from inter-centre leakage and dictionary conditioning.

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Two-Centre Multipole Gram Certification in Structured Gaussian Traps: Block Stability, Effective-Depth Obstructions, and Nonseparable Stress Tests

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