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Research Article · Preprint Mathematics

Finite-spectral recovery of Weyl-blind twisting modes

Scott Schubr

Luminary Oddities

  • Mathematics
  • Analysis and Spectral Theory
Primary subject
Mathematics
Paper type
Research Article
Manuscript stage
Preprint
Manuscript
Archived
Edition
2 · 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. We give a quantitative continuation of this complete-spectrum result. An estimate on the actual curved normal cap yields heat remainder O(T^(17/6)), and hence normalized bias O(T^(-1/6)). A complete finite spectral prefix, certified spectral uncertainties, a counting envelope and a certified complex multiplier enclosure then give a deterministic recovery disk. With exact spectral inputs its fixed-mode cutoff rate is O((logΛ/Λ)^(1/12)); the relative-noise balance is O(σ^(1/7)) before inversion of the heat multiplier. A long-straight-core construction proves why a uniform geometric prior is necessary. Two-sided multiplier bounds quantify exponential conditioning of the ideal lower heat profile. The geometric remainder constants exist but are not fully evaluated numerically. A concrete fundamental-mode interval execution is valid and noninformative.

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

Scope of the work

Certified finite-spectral recovery disks and sufficient cutoff/noise rates for fixed Weyl-blind twist modes under controlled geometry, with multiplier conditioning and a necessary geometric prior.

Reproduction notes

10-page manuscript and 11 source-package members. Compile main.tex; the two included nine-page predecessor PDFs supply the cited heat expansion and all-odd noncancellation dependencies. Standard-library check_conditioning.py checks exact scalar bounds. With Python 3.12 and python-flint 0.9.0, run concrete_spectral.py in a writable extracted copy, then concrete_recovery.py --output recovery.json to reproduce the valid noninformative interval example and unchanged prior.

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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 2). Luminary Research Archive. https://research.luminaryoddities.com/finite-spectral-recovery-weyl-blind-twisting-modes/v/2

BibTeX
@techreport{luminary_finite_spectral_recovery_weyl_blind_twisting_modes_v2,
  title = {Finite-spectral recovery of Weyl-blind twisting modes},
  author = {Scott Schubr},
  year = {2026},
  institution = {Luminary Research Archive},
  type = {Research Article},
  note = {Version 2},
  url = {https://research.luminaryoddities.com/finite-spectral-recovery-weyl-blind-twisting-modes/v/2}
}

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