A Causal Solution to the BTFR and the Cosmological Constant: The Finite-Capacity Vacuum Bridge

This work introduces a finite-capacity vacuum framework in which the physical vacuum is modeled as a causal response medium characterized by a single universal relaxation time $\tau$. An explicit effective action (“Lagrangian bridge”) is constructed by dressing kinetic and geometric operators with a causal response kernel, linking microscopic precision physics to macroscopic sustained regimes without introducing new particles or phenomenological interpolation functions. The same $\tau$ jointly constrains electroweak and leptonic observables, the baryonic Tully–Fisher relation (BTFR), and cosmological scales. Using SPARC-based BTFR data, the framework reproduces galactic scaling relations with a mean bias below observational uncertainties. The macroscopic acceleration scale $a_*$ and the effective cosmological constant $\Lambda_{\rm eff}$ emerge directly from $\tau$, yielding a closed micro–macro chain: $\tau \rightarrow a_* \rightarrow \Lambda_{\rm eff}$. No additional free parameters are introduced. The theory is presented with explicit binary falsifiability conditions: failure in any sector collapses the single-constant hypothesis. This manuscript provides the macroscopic and action-level closure of the program, to be read in conjunction with the companion micro-precision work. Born in Argentina, created for humanity.