We present a unified, mathematically closed geometric framework in which dark energy arises from the pressure of an inflating fourth spatial dimension acting on our three-dimensional brane. Starting from the 5D Einstein-scalar system, we derive — without free parameters — that the potential slope satisfies λ² = 2/n from the G55 consistency condition, yielding the geometric baseline w (0) = −0. 75. The Israel junction conditions are solved explicitly to derive the (1+τ) ⁻¹ suppression factor from first principles. We derive V0 from the bulk self-tuning condition Λ4 = 0, closing the second observational input functionally. The geometric coupling ξgeom = 1/33 is obtained in closed form from the exact warp-factor integrals ∫A⁴dy = 1/31 and ∫A⁴ (φ') ²dy = 8/33. The meV-scale of the boundary coupling σ is explained as a geometric consequence of the dark energy scale through σ = τρ_φ/n. The structural prediction wa = − (1+w0) ², testable by Euclid in October 2026, is the primary falsifiable test. With one observational input (τ = 0. 445 from DESI) the framework is overconstrained: two genuine independent predictions (Δχ² < 1 vs ΛCDM; σ ≈ (1. 30 meV) ⁴) are satisfied without adjustment.
Anamaria Moritz (Fri,) studied this question.