S13: The Cosmological Constant from Baseline Subtraction and Geometric Subspace Structure

This paper derives the dark energy density parameter \Omega_\Lambda from two principles: baseline subtraction, which proves that uniform vacuum energy does not gravitate, and geometric subspace structure, which determines the fraction of vacuum energy that survives as a residual cosmological constant. The derivation proceeds in five steps. First, on a discrete emergent spacetime lattice, the Laplacian of a constant lattice spacing vanishes, so the enormous zero-point energy of quantum fields does not contribute to the gravitational field. Second, the residual asymmetry from imperfect cancellation of space and time wave amplitudes is bounded by the finite information capacity of the cosmic horizon. Third, a causal projection factor accounts for the fact that only one hemisphere of the horizon is observationally accessible. Fourth, a matter correction relates the cosmological constant to the dark energy density parameter, giving the leading-order value \Omega_\Lambda = 2/\pi \approx 0.637. Fifth, the geometric ratio of space to time field subspaces, weighted by the RMS-to-peak factor for sinusoidal oscillations, determines the surviving fraction. The result is: \boxed{\Omega_\Lambda = \frac{3}{3+\sqrt{2}} \approx 0.6796} The observed value from Planck 2018 is \Omega_\Lambda = 0.685 \pm 0.007. The prediction agrees to within 0.7\%, within the 1\sigma observational uncertainty. No free parameters are fitted. The only cosmological input is the Hubble constant H_0, which sets the horizon scale and is a boundary condition of our particular universe. What this paper resolves: The derivation resolves all three parts of the cosmological constant problem: · The old problem: Why does the enormous quantum vacuum energy not gravitate? Uniform vacuum energy does not gravitate because gravity responds only to spatial variations in field intensity, not to the uniform baseline. The 10^{120} discrepancy is not a fine-tuning—it is a category error.· The new problem: Why does the residual cosmological constant have its observed small positive value? The residual is determined by the finite information capacity of the cosmic horizon and the geometric ratio of space to time field subspaces. The information bound sets the scale (\Lambda \sim 1/R_H^2). The geometric refinement sets the precise fraction.· The coincidence problem: Why are dark energy and matter densities comparable today? Both scale as 1/R_H^2, so their ratio is constant across cosmic history. The flatness of the universe, independently derived from the same information bound, ensures \Omega_m = 1 - \Omega_\Lambda. The observed near-equality is structural, not coincidental. Premises and falsifiability: The derivation depends on several premises, stated explicitly: discrete spacetime, Regge gravity, baseline subtraction, holographic information bound, causal projection, RMS-to-peak weighting, and subspace dimensions. The key additional premise—the \sqrt{2} weighting of the time field—is identified as a premise rather than a forced consequence, and its physical motivation is given. The prediction is falsifiable. Future cosmological surveys (DESI, Euclid, Roman Space Telescope) measuring \Omega_\Lambda with sufficient precision to exclude 0.6796 at high confidence would falsify the model. A reduction of the error bar to \pm 0.003 would provide a decisive test. Keywords: cosmological constant, dark energy, baseline subtraction, vacuum energy, holographic principle, information bound, discrete spacetime, \Omega_\Lambda, dark energy equation of state, coincidence problem, falsifiable prediction