This document serves as a formal public declaration of precedence for a completed theoretical research program developed by the author between 2023 and 2026. The work proposes a first-principles theoretical framework in which a specific class of self-adjoint Hamiltonian operators is constructed on the half-line. The construction of the operator’s potential involves number-theoretic terms derived from the distribution of prime numbers, with the essential self-adjointness of the operator ensured by a linear confining term. The central proposals of this framework are: 1. The discrete spectrum of the constructed Hamiltonian operator is proposed to correspond precisely to the imaginary parts of the non-trivial zeros of the Riemann zeta function. This provides a concrete physical realization of the Hilbert–Pólya conjecture. 2. The mathematical structure derived from this spectral correspondence is shown to have formal connections to specific parameters in modern cosmology. This connection offers a potential theoretical basis for resolving the Hubble Tension from first principles. **Note on Research Development** The author previously uploaded preliminary exploratory drafts to this platform, which were withdrawn on May 6, 2026, upon identification of flaws in the foundational arguments. The present announcement reflects the subsequent, corrected theoretical framework that resolves those foundational issues. This is standard academic practice, and the withdrawal record serves as evidence of the research development timeline. **Purpose and Scope** This announcement contains no mathematical derivations, proofs, data sets, or detailed experimental proposals. Its sole purpose is to establish a timestamped, publicly verifiable record of the core concepts and the completion date of this research program. The full manuscript, containing detailed constructions, proofs of essential self-adjointness, spectral analysis, and cosmological calculations, is complete and remains with the author. It will be submitted for formal peer review to appropriate academic journals in due course. This preprint is released to protect the intellectual priority of the work while the peer-review process is initiated. **Disclaimer** This work is purely theoretical. It does
Ismail Al-alimi (Thu,) studied this question.