Interface Precipitation Cosmology: A Two-Constant Framework Linking Cosmological and Hadronic Scales

We present a minimal two-constant framework for cosmology based on interface dynamics, characterized by a vacuum surface tension γ and a discrete mass scale mₚ (the proton mass, reinterpreted as the minimum stable fragmentation unit of the vacuum interface). We derive a scale-invariant interface invariant R (T) ·ρ (T) = ρᵥac, analogous to the Gibbs surface excess in non-equilibrium thermodynamics. A critical dimensionless parameter f ≡ mₚ c²/ (kB T) governs the transition from continuous interface dynamics to discrete particle formation, and admits three equivalent representations: geometric (R/δ), thermodynamic (mₚ c²/kB T), and cosmological (cH₀/a₀). Calibrating f from the observed MOND acceleration scale a₀ yields a critical temperature T* ≈ 172 MeV, consistent with the QCD crossover temperature within ~0. 2%. No QCD scale is introduced as an input; this agreement is interpreted as suggestive rather than derived. This is Volume III of the IPU (Interface Precipitation Universe) series. Related works: - IPU 8. 0 + SGWB: 10. 5281/zenodo. 19427118 - IPU Vol. II (Void Scale): 10. 5281/zenodo. 19883101