PulsumSpace: A Necessary Consistency Constraint Linking Gravitation and Clock Rates

Independent measurements of gravitational acceleration and local clock rates constitute two of the most precise operational probes in modern physics. Any consistent physical description must ensure mutual compatibility between such independently accessible observables.In this work, we derive a necessary consistency constraint linking gravitational acceleration to the spatial gradient of clock frequencies, without invoking spacetime geometry, field equations, or model-specific assumptions.We show that if gravitation and time do not originate from a common underlying physical cause, their measured relation cannot remain invariant across locations, heights, or experimental realizations. Conversely, the experimental observation of an invariant relation imposes a strict structural requirement on any viable framework describing gravitation and temporal rates.This result establishes a model-independent no-go condition: either gravitation and clock rates share a common origin, or the empirical consistency of measurements is violated. The derived constraint is directly falsifiable using existing gravimetric and precision timekeeping technologies.