Proof of the Riemann Hypothesis via Trace-Class Regularisation of the Prime Field and Spectral Stability of the Mehler-Zeta Operator

Citing:- Please cite the DOI for the specific Zenodo version you consulted.- The Concept DOI points to the latest version. Linking request:- Please link to the Zenodo record rather than rehosting files elsewhere.License: CC BY-NC-ND 4.0 (attribution required; non-commercial use; no distributed derivatives).Title: Trace-Class Regularisation of the Prime Field and Spectral Stability of the Mehler-Zeta Operator Abstract:This manuscript presents a complete, closed-form spectral proof of the Riemann Hypothesis. The argument is exhaustive and relies on a "Capacity vs. Demand" conflict governing the spectrum of the Riemann zeta function. The proof establishes that the Archimedean geometry of the Mehler-regularised operator imposes a strictly sub-exponential capacity on spectral growth. Conversely, any zero off the critical line necessitates an exponential spectral demand that exceeds this capacity. This analytic incompatibility forces the spectrum to be confined to the critical line $\Re(s) = 1/2$. Methodological Key:Principle I: Local Negativity / Vacuum Capacity.Principle II: Global Equivalence (Weil Criterion).Principle III: Two-Stage Renormalisation. Call for Review:This work operates strictly within $L^2(\mathbb{R})$ using standard functional-analytic tools. The logic is closed. I invite specialists in Spectral Theory and Analytic Number Theory to review this construction. Correspondence:I welcome direct correspondence from researchers regarding the verification of this result.Email: 859963392@protonmail.com