Inverted Hypersphere Cosmology: The Cosmological Framework, From a Single Axiom, Validated Against BAO, SNe Ia, and CMB Data

This paper develops the cosmological sector of Inverted Hypersphere Cosmology (IHC), a framework that begins from a single axiom, that a state of non-existence is not self-consistent, and asks what minimal structure a self-referential reality must possess. Consistency is argued to force a non-preferential superposition whose natural geometric carrier is the real projective space RP^4 = S^4/Z_2. A chain of uniqueness arguments then fixes, with no adjustable parameters, a sequence of structural quantities: the spatial dimension n = 4, a self-similarity constant for the collapse hierarchy equal to the golden ratio φ, a shell count N = 33 = 3M with M = 11 from Fibonacci spectral stability on RP^4, and a Z_3 triality structure. From this geometry, parameter-free values are derived for the dark-energy equation of state w = -1, the dark-energy fraction Ω_Λ = (5 - √5)/4, the coherence coefficient β_coh = 6cos(π/23), and the sound horizon r_s^IHC = R_H·φ^-7.

Beyond this derivation, the paper's central contribution is a validation programme testing these predictions against published data. The full Planck 2018 CMB power spectrum (613 bandpowers, full covariance), 33 BAO distance measurements from seven surveys, and 40 Pantheon Type Ia supernova distances are used, together with a rigorous Bayesian Information Criterion comparison against re-optimised ΛCDM and wCDM. IHC achieves strong evidence on the standard Jeffreys scale against both alternatives across 73 BAO+SNe data points. A specific, advance prediction, a discrete step in the expansion rate at redshift z_1 = 0.754, made before the DESI DR2 data that subsequently reported a dark-energy anomaly in exactly this range, is tested directly against all 13 DESI measurements and found to explain the anomaly's location and magnitude with zero adjustable parameters.

Throughout, an explicit separation is maintained between quantities genuinely derived from the axiom, external inputs (Planck's baryon and cold dark matter densities, used identically to how any theoretical CMB calculation requires them), and results that are reported honestly as mixed or as open tensions rather than omitted. The dark-energy equation of state carries the one genuine, unresolved tension found in this programme, traced by a leave-one-survey-out test to a single dataset with an independently-documented anomaly, and the CMB comparison is reported as a mixed result: a clear win against the standard comparison value, and a narrow loss on BIC against the single best-fit value the data alone permit.