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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- Heat_Trace_Recovery_Weyl_Blind_Mode.pdf124.9 KiB · pdf
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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
The actual second heat coefficient and pure fundamental mode k = ±1 on the fixed connected geometry, under the explicit normalized swept-core hypothesis. This is a distinct follow-up to Geometric Blind Modes in the Weyl Asymptotics of Twisted Tubes; the predecessor remains unchanged.
Disclosures
AI-assisted exploration, internal verification and manuscript preparation are disclosed in the paper.
Reproduction
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.