Luminary Research Archive
Luminary Research ArchiveIndependent scholarship
Luminary Portal

All Research

Research

29 papers
Browse papers
  1. Audibility of all odd blind modes in rapidly twisted polar-strip tubesScott SchubrEdition 3 · 2026-11-02 Public
  2. Positive Eigenfunctions Above the First Eigenvalue of the Affine 2-LaplacianScott SchubrEdition 4 · 2026-11-02 Public
  3. Sharp all-times heat-content comparison and concentration on compact metric graphsScott SchubrEdition 3 · 2026-11-01 Public
  4. Energy-Filtered Dynamical Localization in Constructive Dirichlet TowersScott SchubrEdition 3 · 2026-11-01 Public
  5. A sharp flatness transition for critical heat traces in twisted tubesScott SchubrEdition 1 · 2026-11-01 Public
  6. Polynomial inertia of signed measures with negative intervalsScott SchubrEdition 3 · 2026-11-01 Public
  7. Unrestricted Half-Power Obstruction and Polynomial Certificates for the Vámos QuarticScott SchubrEdition 5 · 2026-10-31 Public
  8. Source-Resolved Resolvent Growth under Reciprocal-Theta ConfinementScott SchubrEdition 1 · 2026-10-27 Public
  9. Distributional traces and central moment tests for Vámos quarticsScott SchubrEdition 1 · 2026-10-27 Public
  10. Certified resolvent detection of the third Weyl-blind twisting harmonicScott SchubrEdition 2 · 2026-10-27 Public
  11. Finite positivity and correction inertia for the Riemann theta formScott SchubrEdition 2 · 2026-10-27 Public
  12. Collision and cancellation spectra for concentrated energy formsScott SchubrEdition 2 · 2026-10-27 Public
  13. Finite-spectral recovery of Weyl-blind twisting modesScott SchubrEdition 2 · 2026-10-27 Public
  14. Frequency Localization for Weil Operator CertificatesScott SchubrEdition 3 · 2026-10-27 Public
  15. Joint Cutoffs and Negative-Spectrum Decay for Weighted Weil OperatorsScott SchubrEdition 3 · 2026-10-27 Public
  16. Positive heat-flow observations on spherical shells: cutoffs, optimal preparation and concentrationScott SchubrEdition 2 · 2026-10-27 Public
  17. Phase transitions and effective curvature bounds in Fourier density modelsScott SchubrEdition 2 · 2026-10-27 Public
  18. Finite-order positivity and growing negative inertia for averaged Riemann theta productsScott SchubrEdition 2 · 2026-10-27 Public
  19. A Weyl Law for Rapidly Twisted Polar-Strip TubesScott SchubrEdition 2 · 2026-10-27 Public
  20. Weyl Laws and Angular Stability for Rapidly Twisted TubesScott SchubrEdition 2 · 2026-10-27 Public
  21. Pure-Point Dirichlet Spectrum in an Enlarging Cube TowerScott SchubrEdition 2 · 2026-10-27 Public
  22. Geometric Blind Modes in the Weyl Asymptotics of Twisted TubesScott SchubrEdition 2 · 2026-10-27 Public
  23. Heat-Trace Recovery of a Weyl-Blind Twisting ModeScott SchubrEdition 2 · 2026-10-27 Public
  24. Left-Sector Mellin Certification of a Weyl-Blind Twisting ModeScott SchubrEdition 2 · 2026-10-27 Public
PublicEdition 3

Audibility of all odd blind modes in rapidly twisted polar-strip tubes

Scott Schubr

Original PDF · First-page preview

Loading original first page…

Abstract

For a fixed connected polar section, the leading Weyl profile of a rapidly twisted Euclidean tube is independent of every odd logarithmic harmonic of inverse twisting speed. We prove that the next heat profile detects the entire odd lattice. A finite positive-root matrix lemma and two controlled aperture limits represent the full connected relative heat trace as the Laplace transform of a positive measure. An analytic mass bound and Euler-product domination then give a strict, frequency-dependent lower bound for every odd Mellin multiplier. Together with the established actual-tube heat expansion, this determines each admissible pure amplitude and every smooth admissible odd Fourier profile from the complete spectrum. A matching upper multiplier bound identifies exponential smoothing and rules out a local Hölder inverse from the lower heat profile alone, even with fixed finite-order smoothness control on the geometry. The argument is analytic.

Read the full paper in the original PDF.