A Single-Parameter Physical Framework: Casimir Effect, Cosmological Constant, and Hubble Tension

This paper presents a single-parameter arithmetic-geometric framework for jointly studying the cosmological constant, the Casimir effect, the Lamb shift, the electron-mass hierarchy, and the Hubble tension. The construction is rooted in absolute-vacuum symmetry breaking and is organized by a dimensionless topological parameter N within a noncommutative spectral-geometric setting. From the closed chain alpha -> N -> Lambda, the framework fixes N = 1.037111 x 10^13 and yields quantitative outputs for the dark-energy baseline, Lamb shift, electroweak vacuum expectation value, effective electron Yukawa coupling, and global Hubble rate. It further interprets the Casimir effect as a topological differential response of finite pure-point spectra and the Hubble tension as a combination of a global baseline with local-void dynamics. Core algebraic structures and physical mappings are formally checked in Lean 4 and cross-validated with 80-bit high-precision floating-point computations, providing a unified and empirically delimited cross-scale framework.