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 m_p (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) = ρ_vac, analogous to the Gibbs surface excess in non-equilibrium thermodynamics. A critical dimensionless parameter f ≡ m_p c²/(k_B T) governs the transition from continuous interface dynamics to discrete particle formation, and admits three equivalent representations: geometric (R/δ), thermodynamic (m_p c²/k_B 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