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The aim is to establish a theoretical approach to determining the critical line in composite domains.

March 3, 2026Open Access

CDRH–Theorem II

Key Points

The aim is to establish a theoretical approach to determining the critical line in composite domains.
Develop a zero-free composite explicit formula with a Weil-compatible test class.
Introduce a W-scaling lemma to ensure window-stable line shapes at β= 1/2.
Utilize a Mellin-Fourier representation of the transfer function with symbolic derivations.
Identify the composite spectral measure with the zeta-zero measure.
Demonstrate resonance stability leading to a Riemann Hypothesis conclusion.

Abstract

We give a purely theoretical path to the critical line coming from the composite domain: (1) a zero–free composite explicit formula in windowed cpw (cycles-per-window) coordinates with a Weil–compatible test class; (2) a W–scaling lemma which forces window–stable line shapes precisely at β= 1/2 ; (3) a Mellin–Fourier representation of the transfer T= JMΠW with symbolic derivations of mirror antiphase, ratio2f /1f and ∆AIC invariance. With uniqueness of the test class we identify the composite spectral measure with the zeta–zero measure and obtain an RH conclusion from resonance stability.

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Stephen Steiner (Mon,) studied this question.

www.synapsesocial.com/papers/69a67f4af353c071a6f0b2fa — DOI: https://doi.org/10.5281/zenodo.18826590

CDRH–Theorem II

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