The DESI Expansion Anomaly as a Topological Shell Crossing: RP4 Geometry Predicts z = 0.754

DESI DR2 reports a preference for dynamical dark energy over the standard cosmological constant model at between 2.8 and 4.2 standard deviations. The collaboration characterises this as a phantom crossing — dark energy whose equation of state passes through w = −1 — somewhere in the redshift range between 0.4 and 0.8.

We show that this signal is the expected observational signature of a zero-parameter prediction made by Inverted Hypersphere Cosmology (IHC): a discrete localised step in the Hubble expansion rate at redshift z₁ = 0.754, derived entirely from the geometry of the k=1 co-rotating shell at radius R₁ = R_H φ⁻¹. This prediction was in place before DESI DR2 was released.

The phantom crossing is not real. On RP4, the dark energy equation of state is w_Λ = −1 exactly — it cannot evolve. What DESI is seeing is the artefact of fitting a smooth parametric curve to a discrete topological feature. A smooth fitter applied to a sudden step in the expansion rate will always produce an apparent phantom crossing as its best approximation to something it was not designed to model.

Applying the IHC first-shell correction to all 13 DESI DR2 measurements reduces the goodness-of-fit from 1.438 to 0.983 per degree of freedom, with zero parameters adjusted to fit the data. The two most discrepant measurements — the Hubble distance measurements at redshifts 0.51 and 0.71, which sit on either side of the predicted shell crossing — are brought from tensions of −1.80 and −2.14 standard deviations down to −0.31 and −0.91. When the step location is freed and recovered independently from the data, the posterior peaks at z₁ = 0.708 ± 0.188, placing the zero-parameter IHC prediction within 0.25 standard deviations. DESI five-year observations will provide a decisive test at approximately 50 standard deviations of separation between the step model and the cosmological constant.