The WB-Bridge Principle: A Meaning-Preserving Kernel–Spectral Unification (Supplementing the Structural–Axiomatic Proof of the Riemann Hypothesis)
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2025
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| _version_ | 1866901749971812352 |
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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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17545194 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
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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 |