Singularity Regularization and the Emergent Planck Scale in the Logarithmic Superfluid Vacuum

General relativity predicts spacetime singularities where curvature invariants diverge. This paper shows that the logarithmic superfluid vacuum framework regularizes them through the quantum (Bohm) potential — negligible at macroscopic scales, but dominant at the condensate's coherence scale. The healing length ξ = ℏ/ (mₑff c) sets a minimum spatial resolution below which quantum pressure halts gravitational collapse. Requiring self-consistency of the framework's gravitational coupling — combining G ∼ c²/ (ξ²ρ₀) with the healing-length identification and the natural packing density n₀ ∼ 1/ξ³ — uniquely fixes ξ ∼ ℓP (the Planck length), the condensate particle mass mₑff ∼ mP, and the vacuum density ρ₀ at the Planck density. The Planck scale thus emerges as the healing length of the vacuum, not as a fundamental discreteness of spacetime. The temporal singularity is resolved by the same bound on the chemical potential, keeping gravitational time dilation finite.