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.
Boris Kulangiev (Mon,) studied this question.