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

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}.
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.
This establishes a direct mathematical bridge between the kernel-based and spectral approaches to the Riemann Hypothesis.

The WB-Bridge Principle formalizes, in analytic terms, the meaning-preserving observation structure proposed in the T/F framework.
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.

Acknowledgment: With deep gratitude to Parker Emmerson for his insightful review and inspiration.