A No-Go Theorem for Clock Universality from the Hubble Constant Bifurcation

We establish a no-go theorem: under minimal assumptions—metric propagation, local Lorentz invariance, emission locality, and universal clocks—all measurements of the Hubble constant must yield the same value. Recent meta-analyses of sound-horizon-independent data instead demonstrate a persistent, synchronous bifurcation in H0: distance-ladder techniques cluster near H0 ~73 km/s/Mpc, while geometric, gravitational-wave, and early-universe one-step probes converge near H0 ~67 km/s/Mpc (Fig. 1). This discrepancy exceeds 6 sigma significance and cannot be attributed to temporal evolution, calibration systematics, or early-universe physics.