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Research Article · Preprint Mathematics

Finite-spectral recovery of Weyl-blind twisting modes

Scott Schubr

Luminary Oddities LLC

  • Mathematics
  • Analysis and Spectral Theory
Primary subject
Mathematics
Subject subfields
Analysis and Spectral Theory
Paper type
Research Article
Manuscript stage
Preprint
Manuscript
Archived
Edition
1 · Permanent link
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Overview

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 geometric remainder constants are not fully evaluated numerically in this manuscript. The concrete fundamental-mode interval execution is valid but noninformative; practical numerical reconstruction is not claimed.

Keywords inverse spectrum · twisted tubes · finite spectral data · deterministic error bounds · geometric priors

Scope of the work

Conditional certified finite-prefix recovery bounds with controlled geometric priors and numerical-input hypotheses. The supplied concrete interval example leaves the amplitude prior unchanged. No successful practical reconstruction or unrestricted-core stability is claimed.

Reproduction notes

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 an unchanged amplitude prior, not a successful inverse reconstruction.

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Author disclosures

Author-posted preprint. AI-assisted internal research and verification do not constitute external human peer review or proof-assistant formalization.

References and related publications

  1. S. Schubr, Heat-Trace Recovery of a Weyl-Blind Twisting Mode , edition 1 (2026), companion manuscript supplied with this paper.
  2. S. Schubr, Audibility of all odd blind modes in rapidly twisted polar-strip tubes , edition 1 (2026), companion manuscript supplied with this paper.
  3. D. Krejčiřík, Waveguides with asymptotically diverging twisting , Applied Mathematics Letters 46 (2015), 7–10. arXiv:1407.4028.
  4. T. Coulhon and A. Sikora, Gaussian heat kernel upper bounds via the Phragmén–Lindelöf theorem , Proceedings of the London Mathematical Society (3) 96 (2008), 507–544. arXiv:math/0609429.
  5. R. L. Frank and S. Larson, Uniform bounds for Neumann heat kernels and their traces in convex sets , preprint (2026). arXiv:2601.07341v1.
  6. L. Li and A. Strohmaier, Heat kernel estimates for general boundary problems , Journal of Spectral Theory 6 (2016), 903–919. arXiv:1604.00784.
  7. R. R. Lederman and S. Steinerberger, Stability estimates for truncated Fourier and Laplace transforms , Integral Equations and Operator Theory 87 (2017), 529–543. arXiv:1605.03866.
  8. M. Choulli and E. Soccorsi, An inverse anisotropic conductivity problem induced by twisting a homogeneous cylindrical domain , Journal of Spectral Theory 5 (2015), 295–329. doi:10.4171/JST/99. Preprint title: Recovering the twisting function in a twisted waveguide from the DN map , arXiv:1209.5662v3.
  9. O. Kavian, Y. Kian and E. Soccorsi, Uniqueness and stability results for an inverse spectral problem in a periodic waveguide, preprint (2015). arXiv:1504.04267v1.
  10. E. Sultanow, A. Hatziiliou, C. May and N. Kratzke, Hearing the Edges: Recovering a 3D Rectangular Box from Dirichlet Eigenvalues , Axioms 15 (2026), 284. doi:10.3390/axioms15040284.

A stable scholarly record

Cite this edition

Scott Schubr. (2026). Finite-spectral recovery of Weyl-blind twisting modes (Version 1). Luminary Research Archive. https://research.luminaryoddities.com/finite-spectral-recovery-weyl-blind-twisting-modes/v/1

BibTeX
@techreport{luminary_finite_spectral_recovery_weyl_blind_twisting_modes_v1,
  title = {Finite-spectral recovery of Weyl-blind twisting modes},
  author = {Scott Schubr},
  year = {2026},
  institution = {Luminary Research Archive},
  type = {Research Article},
  note = {Version 1},
  url = {https://research.luminaryoddities.com/finite-spectral-recovery-weyl-blind-twisting-modes/v/1}
}

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