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Research Article · Preprint Mathematics

Left-Sector Mellin Certification of a Weyl-Blind Twisting Mode

Scott Schubr

Luminary Oddities LLC

  • Mathematics
  • Analysis and Spectral Theory
Primary subject
Mathematics
Subject subfield
Analysis and Spectral Theory
Paper type
Research Article
Manuscript stage
Preprint
Manuscript
Archived
Edition
1 · Permanent link
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Overview

Abstract

A complex Mellin invariant of a fixed connected step junction is certified on a ray with negative real part. Positive-axis exponential flatness is propagated through an exterior sector using a classical Phragmén–Lindelöf multiplier with explicit constants. A left-sector contour suppresses reciprocal-Gamma conditioning and detects the original fifth inverse-speed harmonic, which is invisible to the leading Weyl profile of the same Euclidean tube. Complete residual bounds retain the noncommuting aperture inverse and infinite input tails. The certificate includes 67 complex nodes, the endpoint calculation, infinite quadrature tails and stated arithmetic errors. The junction Mellin modulus is below 3.198 × 10⁻⁹, while cancellation requires a modulus above 1.18 × 10⁻⁸; the fifth heat multiplier therefore has modulus greater than 2.16 × 10⁻⁷. Higher modes and finite-data stability are outside this certificate.

Keywords relative heat trace · Mellin transform · sectorial resolvent · twisted tubes · validated computation · inverse spectrum

Scope of the work

Original fifth-harmonic separation for the fixed connected geometry, under the stated arithmetic contract. The sector propagation mechanism is classical. No higher-mode theorem or stable finite-spectrum inversion is claimed.

Reproduction notes

The eleven-member package contains editable LaTeX, the aperture solver, directed interval arithmetic, certificate assembly, an independent checker and reader instructions. Full node reconstruction uses Python 3.12 and NumPy 2.3.5: python -B certify.py --recompute --output reproduced_certificate.json. Assembly without --recompute reuses supplied aperture disks; it does not regenerate them. The manuscript states the floating-point implementation contract.

The manuscript

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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 , first edition, Luminary Oddities LLC, 2026. https://luminaryoddities.com/researcharchive/ heat-trace-recovery-weyl-blind-twisting-mode/v/1 .
  2. M. van den Berg and S. Srisatkunarajah, Heat equation for a region in R2 with a polygonal boundary, J. London Math. Soc. (2) 37 (1988), 119–127. doi:10.1112/jlms/s2-37.121.119.
  3. J. Behrndt, F. Gesztesy and S. Nakamura, Spectral shift functions and Dirichlet-to-Neumann maps , arXiv:1609.08292. https://arxiv.org/abs/1609.08292.
  4. L. N. Trefethen and J. A. C. Weideman, The exponentially convergent trapezoidal rule, SIAM Review 56 (2014), 385–458. doi:10.1137/130932132.
  5. NumPy developers, NumPy 2.3.5 source: einsumfunc.py, einsum_sumprod.c.src, and loops_umath_fp.dispatch.c.src. https://github.com/numpy/numpy/tree/v2.3.5/numpy/ _core.
  6. E. Anderson et al., LAPACK Users’ Guide, third edition, SIAM, 1999, “Error Bounds for Fast Level 3 BLAS. ” https://netlib.org/lapack/lug/node108.html.
  7. S. Schubr, Certified Resolvent Detection of a Third Weyl-Blind Twisting Mode , prepared companion manuscript, Luminary Oddities LLC, 2026.
  8. L. G. Rogers, Estimates for the resolvent kernel of the Laplacian on p.c.f. self similar fractals and blowups, arXiv:1009.5334, Section8, Corollary8.2 and its proof. https://arxiv.org/abs/1009. 5334.
  9. T. Coulhon and A. Sikora, Gaussian heat kernel upper bounds via the Phragmén–Lindelöf theorem, Proc. London Math. Soc. 96 (2008), 507–544. doi:10.1112/plms/pdm050.

A stable scholarly record

Cite this edition

Scott Schubr. (2026). Left-Sector Mellin Certification of a Weyl-Blind Twisting Mode (Version 1). Luminary Research Archive. https://research.luminaryoddities.com/left-sector-mellin-certification-weyl-blind-twisting-mode/v/1

BibTeX
@techreport{luminary_left_sector_mellin_certification_weyl_blind_twisting_mode_v1,
  title = {Left-Sector Mellin Certification 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/left-sector-mellin-certification-weyl-blind-twisting-mode/v/1}
}

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