Clock Incompatibility and Loop Consistency as a Diagnostic of Temporal Validity

This Technical Note introduces a methodological diagnostic for assessing when the concept of a global time remains operationally meaningful in cosmology and other frontier regimes. The work does not propose new physics, modify existing dynamical theories, or advance ontological claims about time. Instead, it focuses on the operational compatibility of physically realizable clocks—such as expansion-based, thermal, and kinetic clocks—as a necessary condition for the validity of a global-time description. The diagnostic is formulated in terms of loop consistency among clock translations and a qualitative indicator, the Loop Closure Error (LCE), which signals path dependence and non-integrability in the space of clock descriptions. The approach is calibrated by a quasi-adiabatic, near-equilibrium regime where loop closure holds, and contrasted with non-equilibrium, patchy nucleation regimes where loop consistency can fail. The contribution is methodological rather than foundational. It provides a minimal protocol for clarifying domains of validity of temporal concepts and for avoiding overextension of global-time descriptions beyond their reliable operational range.