Geometric Prediction of Ω_Λ and r_s from ℝP⁴ Topology: BAO Validation with Zero Parameters Fitted to Data

The cosmological constant problem — why the observed dark energy density is ~10^120 times smaller than the naive quantum field theory prediction — has no accepted solution. We present a topological approach: if the pre-collapse state of the universe is invariant under the antipodal map x ~ −x, then by the Euler characteristic theorem the unique compact positive-curvature 4-manifold consistent with this symmetry is RP4 = S4/Z2. The topology is a theorem, not an axiom. The Z2 identification projects out all odd-l spherical harmonics, shifting the spectrally stable Fibonacci mode from l=1 (BAO scale 4.4 times too large on S4) to l=4, where d(S4,4) = 55 = F10. The non-preferential principle that forces RP4 also forces equal distribution of these 55 modes across the 5 embedding directions of R5: M=55/5=11, N=3M=33 nested toroidal shells, and r_s = 153.2 Mpc. The cosmological constant is addressed via a UV–IR Casimir seesaw, giving Ω_Λ = 0.6882. A second independent route via Z3 coherent interference gives Ω_Λ = 0.6889; the 0.10% agreement between two structurally independent derivations is a non-trivial internal consistency check. Against seven BAO surveys (33 measurements, z = 0.106–2.33), IHC achieves χ²/n = 0.916 versus ΛCDM's 1.196 with zero fitted parameters. Bayesian evidence gives ln B = +4.76 (moderate evidence, Jeffreys scale) and a joint four-parameter MCMC places the IHC prediction at Mahalanobis distance 0.70σ from the posterior mean (posterior predictive p-value = 0.61).