  The Hubble tension, if not caused by any systematics, could be relieved or
even resolved from modifying either the early-time or late-time Universe. The
early-time modifications are usually in tension with either galaxy clustering
or galaxy lensing constraints. The late-time modifications are also in conflict
with the constraint from the inverse distance ladder, which, however, is
weakened by the dependence on a sound-horizon prior and some particular
approximation for the late-time expansion history. To achieve a more general
no-go argument for the late-time scenarios, we propose to use a global
parametrizationbased on the cosmic age (PAge) to consistently use the cosmic
chronometers data beyond the Taylor expansion domain and without the input of a
sound-horizon prior. Both the early-time and late-time scenarios are therefore
largely ruled out, indicating the possible ways out of the Hubble tension from
either exotic modifications of our concordance Universe or some unaccounted
systematics.
