Hello, I'd like to present a part of my currently ongoing project

This is Paper 1 of a larger series. 

My model is based on an inversion principle that forces the universe into a self measuring RP4 topology 

Everything has been tested by myself and my research partner, all python scripts have been provided in the upload for openness and transparency and reproducibility.

Anthropic Claude ai was used for latex compilation, writing, and result analysis, The conceptual idea, framework, and methodology is the work of the author's 

Abstract 

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 = 0.6882 from the RP⁴ UV–IR Casimir seesaw (ρ\_Λ² = ½ρ\_UV|ρ\_IR|, with exact rational Casimir coefficient Z\^reg(−1) = −631/30, no free parameters). A second independent derivation via the RP⁴ β-chain gives Ω\_Λ = 0.6889 ± 0.0006; the 0.10% agreement between the two derivations constitutes a non-trivial internal consistency check. The BAO sound horizon r\_s\^IHC = 153.2 Mpc is derived from real projective 4-space (RP⁴) topology; neither Ω\_Λ nor r\_s is fitted to BAO or CMB data. 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 β\_coh = 6cos(π/23) derived from the Dirac spectrum on RP⁴. The ratio ξ = r\_s\^IHC / r\_s\^CAMB = 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 D\_H 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/n = 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.

https://zenodo.org/records/19139368

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