The Vacuum Catastrophe and the Granularity of Hilbert Space

Quantum field theory with a Planckian cutoff predicts a vacuum energy density of order the Planck density, 4.6×10¹¹³ J m⁻³, 123 orders of magnitude above what the observed cosmological constant allows. This paper resolves the discrepancy in two steps, within a framework in which every quantum state carries the same finite budget of L bits and gravity follows from that limit. First, the zero-point energy does not gravitate: a stress tensor proportional to the metric has no flux through any null surface, so it never enters the thermodynamic derivation of Einstein's equations, whatever its magnitude, and Λ survives as an integration constant that the horizon fixes. Second, the standard estimate's error is in the state count. The energy Λ carries inside the horizon is the horizon entropy times the horizon temperature, which gives ρ_Λ = 3πρ_Planck/2L², with L = 6.4×10⁶¹ the number of Planck lengths around the horizon: one factor of L because the count is of a boundary and not of a volume, and one because a pixel's energy scale is E_P/L and not E_P. The acceleration scale of galactic rotation curves, a₀ = (1.20 ± 0.24)×10⁻¹⁰ m s⁻², fixes L independently at (4.6 ± 0.9)×10⁶¹ and gives ρ_Λ = (1.0 ± 0.4)×10⁻⁹ J m⁻³, against the observed 5.2×10⁻¹⁰; in the measured variable a₀ the two agree at 1.4σ, the residual being the order-unity coefficient the framework has yet to derive. The same L caps a state spread across its Hilbert space at 205 qubits, a ceiling whose measurement would be a third determination with no astronomy in it.

v2: Sec. III states the conservation step that restricts the decoupling to the spacetime-constant vacuum energy and answers the radiative-stability objection to an integration-constant Λ; Sec. IV credits the E = TS identity (Padmanabhan 2002) and holographic dark energy (Hsu 2004, Li 2004) and assigns the galactic test to the coefficient of Axiom 2 and the qubit ceiling to the exponent; Sec. V adds Milgrom's own form of the a₀–Λ relation, Verlinde's coefficient evaluated at the de Sitter radius, and the tighter a₀ calibration of Desmond 2023; Sec. VI adds the DESI DR2 Lyman-α result and the reported redshift evolution of a₀ (MUSE-DARK III) as a test. Seventeen references added; companion citations moved to concept DOIs. Claims unchanged. v1 (10 Sep 2026) remains the priority record.