Research Article · Preprint Mathematics
Heat-Trace Recovery of a Weyl-Blind Twisting Mode
- Primary subject
- Mathematics
- Subject subfield
- Analysis and Spectral Theory
- Paper type
- Research Article
- Manuscript stage
- Preprint
- Manuscript
- Archived
- Edition
- 1 · Permanent link
Overview
Abstract
A fixed connected polar section can hide every odd logarithmic harmonic of inverse twisting speed from the leading Weyl profile. We show that its original pure cosine perturbation is nevertheless audible in the next heat-trace term. The second coefficient contains the relative heat trace of a connected step strip; replacing the exposed radial face by an independent angular channel gives the wrong model. We derive a uniform momentum-integrated radial expansion and use an exact angular clock, a small real shear and weighted Dirichlet–Neumann bracketing to obtain an actual two-term heat expansion for the Euclidean tube. A positive corner-loop remainder is nonincreasing in heat time. Its Stieltjes representation controls the complex Mellin transform sharply enough to prove noncancellation at the original fundamental frequency. Thus a parameter invisible in the leading Weyl law is determined by the lower-order heat profile, without adding any lower-homogeneity perturbation. Higher odd frequencies and a two-term unsmoothed counting law are left open.
Keywords twisted tube · heat trace · spectral asymptotics · relative heat invariant · Mellin transform · inverse spectral problem
Scope of the work
The actual second heat coefficient and pure fundamental mode k = ±1 on the fixed connected geometry, under the explicit normalized swept-core hypothesis. No noncancellation result for k = 3 or all higher odd modes, two-term unsmoothed counting law, or finite-spectrum recovery is claimed. This is a distinct follow-up to Geometric Blind Modes in the Weyl Asymptotics of Twisted Tubes; the predecessor remains unchanged.
Reproduction notes
The seven-member publication package contains the nine-page manuscript PDF, self-contained main.tex, a standard-library Python rational certificate, reader README, citation file, manifest and checksums. Compile with Tectonic or run pdflatex twice. Run python -B nonzero_certificate.py to check the finite rational inequalities; the operator proof is analytic and appears in the manuscript.
The manuscript
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The complete manuscript, as published in this edition.
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Author disclosures
AI-assisted exploration, internal verification and manuscript preparation are disclosed in the paper. Internal reviews are not external human refereeing or formal proof-assistant verification.
A stable scholarly record
Cite this edition
Scott Schubr. (2026). Heat-Trace Recovery of a Weyl-Blind Twisting Mode (Version 1). Luminary Research Archive. https://research.luminaryoddities.com/heat-trace-recovery-weyl-blind-twisting-mode/v/1
BibTeX
@techreport{luminary_heat_trace_recovery_weyl_blind_twisting_mode_v1,
title = {Heat-Trace Recovery of a Weyl-Blind Twisting Mode},
author = {Scott Schubr},
year = {2026},
institution = {Luminary Research Archive},
type = {Research Article},
note = {Version 1},
url = {https://research.luminaryoddities.com/heat-trace-recovery-weyl-blind-twisting-mode/v/1}
}Loading discussion…