Unified Brane–Valve Cosmology: A Unified Framework for Non-Singular Bounce Dynamics and Black-Hole-Sourced Dark Energy

Unified Brane-Valve Cosmology (UBVC–Prime): A One-Parameter Unified Geometric Model. This version (March 2026) represents the definitive one-parameter evolution of the Unified Brane-Valve Cosmology (UBVC). Building upon the foundational framework established in Version 5, this update provides a unified geometric mechanism that resolves the Big Bang singularity and the origin of late-time cosmic acceleration through a single 5D curvature scale. STRATEGIC RESEARCH SUITE UBVC–Prime functions as the central hub of a multi-tiered research program, supported by the following peer-accessible assets: * Foundational Geometry: The zero-parameter map of universal expansion is established in SRSC–0P (DOI: 10.5281/zenodo.18911455). * Computational Implementation: The Boltzmann-ready analytic expansion for testing against H0 and S8 data is provided in RVC–1P (DOI: 10.5281/zenodo.18911462). KEY ADVANCEMENTS IN THE PRIME FRAMEWORK * Geometric Unification: Both the non-singular bounce at ρ = 2λ and the late-time valve mechanism are derived from the same five-dimensional action and junction conditions. * Refined Mass Functional: Incorporates an improved ansatz for the cumulative cubic horizon-mass functional, M3(a) = Σ_i M_i^3, driving a precise energy flux across the brane–bulk interface. * Physical Stability: Defines explicit stability conditions and parameter priors that ensure a smooth, non-clustering dark-energy component with a fully determined equation of state: w_DE(a) = -1 - (1/3) d ln M3 / d ln a. This document represents the latest and most complete formulation of the UBVC and serves as the reference version for ongoing review, academic citation, and industrial application.