The Vacuum Catastrophe and the Granularity of Hilbert Space

Quantum field theory with a Planckian cutoff predicts a vacuum energy density of 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, and Λ survives there as an integration constant that the horizon fixes. Second, the error in the standard estimate 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 the energy scale of a pixel 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 same L caps a state spread across its Hilbert space at 205 qubits, a third determination with no astronomy in it.