Finite-spectral recovery of Weyl-blind twisting modes
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Abstract
Odd logarithmic twisting modes in a fixed polar-strip tube are invisible to the leading Weyl profile but detectable in the next heat profile. This paper gives a quantitative continuation of that complete-spectrum result. An estimate on the actual curved normal cap yields a heat remainder O(T¹⁷⁄⁶) and normalized bias O(T⁻¹⁄⁶). A complete finite spectral prefix, certified uncertainties, a counting envelope and a certified complex multiplier enclosure give a deterministic recovery disk. With exact inputs, the fixed-mode cutoff rate is O((log Λ/Λ)¹⁄¹²); the relative-noise balance is O(σ¹⁄⁷) before heat-multiplier inversion. A long-straight-core construction shows why a uniform geometric prior is necessary, and two-sided multiplier bounds quantify exponential conditioning. The concrete fundamental-mode interval execution is valid and returns the unchanged amplitude prior.
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Research details
- Subjects
- Mathematics · Analysis and Spectral Theory
- Keywords
- inverse spectrum, twisted tubes, finite spectral data, deterministic error bounds, geometric priors
- Manuscript date
- 2026-10-23
- Reader reuse
- No additional permission granted
Scope
Conditional certified finite-prefix recovery bounds with controlled geometric priors and numerical-input hypotheses. The supplied concrete interval example leaves the amplitude prior unchanged.
Disclosures
Author-posted preprint. AI-assisted internal research and verification were used.
Reproduction
The eleven-member package includes complete LaTeX, both unchanged mathematical predecessors and three reproduction scripts. check_conditioning.py uses standard Python for exact scalar bounds. The deliberately noninformative interval example uses Python 3.12 and python-flint 0.9.0 through concrete_spectral.py and concrete_recovery.py. It reproduces the unchanged amplitude prior.
References and related resources
- S. Schubr, Heat-Trace Recovery of a Weyl-Blind Twisting Mode , edition 1 (2026), companion manuscript supplied with this paper.
- S. Schubr, Audibility of all odd blind modes in rapidly twisted polar-strip tubes , edition 1 (2026), companion manuscript supplied with this paper.
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