Substrate Hydrodynamics: Emergent Fundamental Constants, Dispersive Cutoffs, and Action-Limited Spacetime

We formulate a hydrodynamic vacuum framework in which fundamental natural constants—the speed of light c, Newton's gravitational constant G, and Planck's constant ħ—emerge as constitutive mechanical properties of a phase-coherent elastic substrate. The mesoscopic correlation scale σ_cut ≈ 100 nm is derived non-anthropocentrically as the geometric mean of the Planck length and the Hubble horizon, σ_cut = √(l_P · R_H), representing a topological freeze-in scale from the early universe. By imposing a finite action density bound and momentum dispersion cutoff at σ_cut, the zero-point vacuum energy density is regulated to ρ_vac ≈ 1.06 × 10^-2 J/m^3, naturally solving the 120-order-of-magnitude vacuum catastrophe without fine-tuning.