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

We present the Inverted Hypersphere Cosmology (IHC) framework, in which information-theoretic constraints imposed by the RP4 antipodal identification — a topological self-measurement operator that couples UV and IR vacuum modes — determine the cosmological constant and baryon acoustic oscillation (BAO) scale without parameters fitted to data. Specifically, IHC predicts the dark energy density parameter Ω_Λ = 0. 6889 ± 0. 0006 and the BAO sound horizon rₛIHC = 153. 2 Mpc from real projective 4-space (RP4) topology; neither quantity is fitted to BAO or CMB data. A second independent derivation via the RP4 UV–IR Casimir seesaw gives Ω_Λ = √ (1262/ (270π²) ) = 0. 6882 with no free parameters; the 0. 10% agreement between the two derivations constitutes a non-trivial internal consistency check. The universe is modelled as RP4 containing N = 33 nested toroidal structures scaling by the golden ratio φ = (1 + √5) /2, generating a geometric suppression factor β = 1345 ± 50 with coherence amplitude βcoh = 6cos (π/23) derived from the Dirac spectrum on RP4. The ratio ξ = rₛIHC / rₛCAMB = 1. 0367 is a topological invariant that cancels exactly in all dimensionless CMB and BAO observables, but is observable only through the H (z) step at z₁ = 0. 754, where the amplitude ξ−1 enters DH additively rather than as a ratio, breaking the ratio degeneracy. Against seven independent BAO surveys (33 measurements, z = 0. 106–2. 33), IHC achieves χ²/n = 0. 916 versus ΛCDM's 1. 196 (Δχ² = +9. 22) with zero parameters fitted to BAO data. DESI DR2 (13 observables) gives χ²/dof = 0. 98, matching ΛCDM with two fewer fitted parameters. Exact Bayesian evidence computed via dynesty nested sampling gives ln B (IHC/ΛCDM) = +4. 76 (moderate evidence on the Jeffreys scale). A joint four-parameter MCMC places the IHC zero-parameter prediction at Mahalanobis distance 0. 70σ from the posterior mean, within the joint 68% credible region. Survey consistency tests show all six pairwise tensions below 1. 1σ; a posterior predictive check yields p-value = 0. 61, confirming model adequacy.