The WB-Bridge Principle: A Meaning-Preserving Kernel–Spectral Unification (Supplementing the Structural–Axiomatic Proof of the Riemann Hypothesis)

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Main Author: Takahashi, Takashi
Format: Recurso digital
Published: Zenodo 2025
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author Takahashi, Takashi
author_facet Takahashi, Takashi
contents <p>This short paper presents the WB-Bridge Principle, a concise analytic formulation unifying the Weil–Bochner kernel positivity and spectral L² nonnegativity under a single meaning-preserving window W_B(\xi)=e^{-\xi^2/B^2}.<br>Through the self-dual log-Gaussian window W_B, both analytic paradigms are shown to represent the same nonnegative quadratic form under the Mellin–Plancherel duality.<br>This establishes a direct mathematical bridge between the kernel-based and spectral approaches to the Riemann Hypothesis.</p> <p>The WB-Bridge Principle formalizes, in analytic terms, the meaning-preserving observation structure proposed in the T/F framework.<br>It completes the sequence of works beginning with The Structural–Axiomatic Proof of the Riemann Hypothesis, and serves as the short “front statement” for further analytical studies.</p> <p>Acknowledgment: With deep gratitude to Parker Emmerson for his insightful review and inspiration.</p>
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spellingShingle The WB-Bridge Principle: A Meaning-Preserving Kernel–Spectral Unification (Supplementing the Structural–Axiomatic Proof of the Riemann Hypothesis)
Takahashi, Takashi
Riemann Hypothesis
Bochner kernel
spectral L²
Mellin–Plancherel duality
positivity
T/F Theory
analytic number theory
meaning-preserving principle
<p>This short paper presents the WB-Bridge Principle, a concise analytic formulation unifying the Weil–Bochner kernel positivity and spectral L² nonnegativity under a single meaning-preserving window W_B(\xi)=e^{-\xi^2/B^2}.<br>Through the self-dual log-Gaussian window W_B, both analytic paradigms are shown to represent the same nonnegative quadratic form under the Mellin–Plancherel duality.<br>This establishes a direct mathematical bridge between the kernel-based and spectral approaches to the Riemann Hypothesis.</p> <p>The WB-Bridge Principle formalizes, in analytic terms, the meaning-preserving observation structure proposed in the T/F framework.<br>It completes the sequence of works beginning with The Structural–Axiomatic Proof of the Riemann Hypothesis, and serves as the short “front statement” for further analytical studies.</p> <p>Acknowledgment: With deep gratitude to Parker Emmerson for his insightful review and inspiration.</p>
title The WB-Bridge Principle: A Meaning-Preserving Kernel–Spectral Unification (Supplementing the Structural–Axiomatic Proof of the Riemann Hypothesis)
topic Riemann Hypothesis
Bochner kernel
spectral L²
Mellin–Plancherel duality
positivity
T/F Theory
analytic number theory
meaning-preserving principle
url https://doi.org/10.5281/zenodo.17545194