The Spectral Bridge: Connecting the No-Vacuum Algebraic Theorem to the Riemann Hypothesis: Deficiency Indices, Spectral Zeta Functions, Formal Obstructions, and the Baryon Asymmetry Problem

This is Paper C of the 59-Dimensional Series. It provides the rigorous spectral-theoretic foundation required to bridge the "No-Vacuum" Algebraic Theorem of Paper A with the physical mass predictions of Paper B. Key highlights of this paper include: Resolution of the Baryon Asymmetry: A geometric derivation showing how the 29+1+29 structure breaks matter-antimatter symmetry via a specific spectral phase shift. Deficiency Indices: Formal proof that n+ = n- = 1 for the H₅₉ operator, identifying the Dirichlet extension as the unique physical choice for a stable universe. Formal Obstruction Proof: Demonstration that no standard L² kernel can produce a logarithmic spectral density, addressing long-standing gaps in Hilbert-Pólya constructions. Exact Lower Bound: Calculation of the spectral lower bound at -55/118, offering a testable prediction for quantum cosmology. Spectral Zeta Connection: Derivation of the relation ₇₅₉ (s) = 59^s ₑ (s), linking the 59D Plenum directly to the Riemann Zeta function. References to previous papers (As listed in your document): Paper A: DOI 10. 5281/zenodo. 20076536 Paper B: DOI 10. 5281/zenodo. 20088148