Holographic Subtraction: Derivation of 3D Space, Time, and Einstein's Equations from Quantum Fields on the Cosmological Horizon

We propose a thermodynamic framework in which three spatial dimensions, time, andEinstein’s field equations emerge sequentially from a holographic information principle appliedto a quantum oscillator field on the cosmological horizon S2∞ (hereafter simply S2). Startingfrom a latent D-dimensional information manifold (where D is not postulated), we derive thatobservable space has precisely d = 3 dimensions via thermodynamic free-energy minimization.The optimal configuration is D = 4 with suppression vector (ε1, ε2, ε3, ε4) = (1, 1, 1, ε∗),where ε∗(N) = (0.052 ± 0.008) N −(0.57±0.03) (R2 = 0.998). For N = (2.26 ± 0.03) × 10122(cosmological holographic bound), extrapolation gives ε∗ ∼ 10−70, rendering the fourthdimension unobservable. The discrepancy between non-interacting UV theory (γUV = 0.74)and observed scaling (γobs = 0.57) arises from vortex screening in the interacting IR theory,characterized by a screening anomalous dimension ηscr = 0.34 ± 0.06 (distinct from the XYspin exponent; see the mapping box below). Numerical simulation of NBH = 104 black-holepositions modeled as vortex defects on S2 yields w(θ) ∝ θ−(0.47±0.08) for θ < 10◦(p = 0.003).Chandra CSC 2.0 (Nsrc = 317,167) gives w(θ) = (0.019 ± 0.006) θ−(0.48±0.11), consistent at2σ (preliminary).PACS: 04.60.-m, 04.60.Bc, 98.80.Qc, 95.30.Sf