Emergent Spacetime from Computational Hydrodynamics Resolution of the Quantum-Gravity Interface via Acoustic Metric Formalism

We propose Hydrodynamic Quantum Cosmology (HQC), a framework positing that spacetimeis an emergent acoustic metric arising from a scale-dependent, superfluid vacuum state. Wedemonstrate that General Relativity (GR) emerges as the hydrodynamic limit of a discrete quantumcomputational substrate (Rule 30 lattice) on a Chiral 3-Torus (T3) topology. We resolve three criticalphenomenological challenges: (1) We derive the Fine Structure Constant (α−1 ≈ 137.0363) as theinfrared fixed point of the renormalization group flow determined by the topological invariants of theunit cell; (2) We demonstrate that Lorentz Invariance is an emergent symmetry for low-energy excitations(λ ≫ ℓPlanck); and (3) We distinguish between dissipationless geodesic motion in the superfluidregime (Standard GR) and viscous drag effects manifest in the dark sector (Dark Matter).