A Stieltjes Pole-Package Identity for the Prime-Weighted Quantum Operator and the Riemann Hypothesis

This report presents a spectral–analytic framework related to the Riemann Hypothesis. The work introduces a prime-weighted operator construction together with a Stieltjes pole-package identity linking operator-side transforms to zero-side meromorphic structures associated with the Riemann zeta function. The document outlines the analytic architecture of the proposed proof, including the construction of a canonical operator transform on the slit plane Ω = ℂ \ (−∞,0], an independently defined zero-side meromorphic package, and an identification of the two objects through analytic continuation. A rigidity argument is then used to show that the presence of off-critical zeros would force isolated poles incompatible with the analytic structure of the operator transform. The report provides a technical overview intended for mathematical review and discussion and accompanies a manuscript detailing the full construction and analytic framework.