Vacuum Phase Selection and Single-Spectral-Scale Constraints for the Observable Universe

We formulate a low-energy description of the observable universe in which vacuum-phase selection precedes numerical calibration. The sole foundational input is an unbranched fundamental vacuum layer generating candidate vacuum configurations; spacetime, particle content, interactions, constants, effective scales, and vacuum energy are defined only on stable branches. The branch coupled to present laboratory and cosmological observations is denoted by \(V_0\). For branches admitting a continuum limit and a quantum spectral representation, one finds a common origin, a decomposition into \(V_0\) and \(Vi≠0\), covariant variational dynamics, and long-time stable spectral selection. Within \(V_0\), general relativity, local quantum field theory, the effective Standard Model structure, and dark-sector sources appear as low-energy structures. Calibration by the CODATA 2022 fine-structure constant gives \(N_=1.037111×10¹³\). In the stable spectral representation used here, residual decoupling and four-dimensional spectral-level normalization produce an \(N⁻⁹\) vacuum-energy suppression, yielding \(Λₜₕ=1.10560×10⁻⁵²\,m⁻²\), \(ρΛ,th=5.324×10⁻¹⁰\,{J\,m⁻³}\), \(ωΛ,th=0.31537\), and \(S8,th=0.762±0.015\). The same scale constrains post-calibration microscopic residuals, including the electron-sector profile and precision-QED channels. Consistency is required across background expansion, structure growth, dark-sector phenomenology, and microscopic low-energy residuals.