Researchers used a simple mathematical trick to show that the new low-redshift distance data from DESI and three Type Ia supernova compilations mostly probe a single combination of cosmological parameters. That combination, measured by the leading data direction they call V0 (with amplitude c0), is essentially the physical matter density Ωm h^2 — a product of the matter fraction and the square of the reduced Hubble constant. Baryon acoustic oscillation (BAO) distances from DESI prefer a value of c0 that is about +2.2 standard deviations higher than the prediction from cosmic microwave background (CMB) data, while the three supernova data sets are individually mild and inconsistent with confirming that BAO signal.

The authors performed a singular value decomposition (SVD) of the low-redshift distance measurements. SVD is a way to find the main linear patterns in a set of numbers. They applied it to 13 BAO observables spanning redshift z≈0.295 to 2.33 and to supernova distance compilations, anchoring their comparison with CMB chains from ACT DR6 and Planck 2018. For BAO, the first singular value was about 25 times larger than the next, which means the data effectively select one dominant direction, V0. To translate BAO measurements into distances they used a fiducial drag-epoch sound horizon rd = 147.09 Mpc. Importantly, the dominance of V0 follows from the CMB parameter uncertainties together with the low-redshift measurement covariance — not from the particular low-redshift data values.

Because V0 is, to high accuracy, a measurement of Ωm h^2, most of the reported tension between DESI BAO and the CMB shows up there. The paper quotes +2.2σ for BAO’s c0 versus the CMB prediction. The three supernova compilations give c0 tensions of −0.8σ (DES‑Dovekie), −1.1σ (Pantheon+), and −1.7σ (Union3), but the supernova sets do not have enough precision on c0 to confirm or refute the BAO signal. When the authors allow a common dark‑energy extension (the w0–wa parameterization), a second direction V1 becomes measurable and acts as an independent test of evolving dark energy; V1 shows no significant departure from a cosmological constant (+1.2σ for BAO). Spatial curvature is the only other extension that opens a genuinely new measurable direction for BAO, and in their estimate both measurable directions then mildly prefer positive curvature, though the second direction is poorly constrained.