Left-Sector Mellin Certification of a Weyl-Blind Twisting Mode
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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.
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- Left_Sector_Mellin_Certification.pdf137.5 KiB · pdf
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d29ca701b725831272230eccea2b4deecb5d9614c428a806e0fea5fd3b0b22e8 - Left_Sector_Mellin_Certification_Package.zip174.2 KiB · package
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9ce03ed9079ce20b1ee6adf8aeda8b868a614cc5685083ae36fa9e3ac7814a68
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Research details
- Subjects
- Mathematics · Analysis and Spectral Theory
- Keywords
- relative heat trace, Mellin transform, sectorial resolvent, twisted tubes, validated computation, inverse spectrum
- Manuscript date
- 2026-10-23
- Reader reuse
- No additional permission granted
Scope
Original fifth-harmonic separation for the fixed connected geometry, under the stated arithmetic contract. The sector propagation mechanism is classical.
Disclosures
Author-posted preprint. AI-assisted internal research and verification were used.
Reproduction
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 with --recompute regenerates the supplied aperture disks; default assembly reuses them. The manuscript states the floating-point implementation contract.
References and related resources
- S. Schubr, Heat-Trace Recovery of a Weyl-Blind Twisting Mode , first edition, Luminary Oddities, 2026. https://luminaryoddities.com/researcharchive/ heat-trace-recovery-weyl-blind-twisting-mode/v/1 .
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- L. N. Trefethen and J. A. C. Weideman, The exponentially convergent trapezoidal rule, SIAM Review 56 (2014), 385–458. doi:10.1137/130932132.
- 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.
- 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.
- S. Schubr, Certified Resolvent Detection of a Third Weyl-Blind Twisting Mode , prepared companion manuscript, Luminary Oddities, 2026.
- 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.
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