A null test of the Hubble tension

The origin of the Hubble tension remains one of the central open problems in modern cosmology, with competing explanations invoking either early-Universe physics, late-time modifications of cosmic expansion, or unresolved observational systematics. In this Letter we propose a new, purely geometric null test of the late-time expansion history that is exactly independent of the Hubble constant. By combining strong-lensing time-delay distances with gravitational-wave standard-siren luminosity distances, we construct a dimensionless ratio that depends only on the redshift dependence of the expansion rate and can be both predicted from early-Universe data and measured directly at late times, without relying on the cosmic distance ladder or the sound horizon. We show that the comparison between the early- and late-time determinations of this ratio provides a transparent consistency test of the standard cosmological expansion. When combined with an independent standard-siren measurement of $H_{0}$, this framework allows one to unambiguously distinguish between early- and late-time origins of the Hubble tension. With the forthcoming detection of lensed gravitational-wave standard sirens, the proposed test provides a timely and robust framework for probing this long-standing cosmological puzzle.