Heat-Trace Recovery of a Weyl-Blind Twisting Mode
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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.
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Research details
- Subjects
- Mathematics · Analysis and Spectral Theory
- Keywords
- twisted tube, heat trace, spectral asymptotics, relative heat invariant, Mellin transform, inverse spectral problem
- Manuscript date
- 2026-10-22
- Reader reuse
- No additional permission granted
Scope
An actual two-term heat expansion and analytic noncancellation recover the original fundamental cosine twisting amplitude hidden from the leading Weyl profile on the fixed connected geometry.
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.
Reproduction
The paper has 9 pages. The editable-source archive contains 7 files. Compile main.tex. The optional standard-library nonzero_certificate.py checks the exact fundamental-mode scalar inequalities.