Dimensional analysis applied to physical constants: A theoretical framework for analyzing constant variations

The stability of fundamental physical constants underpins modern physics, yet distinguishing their intrinsic time variation from systemic drifts in measurement reference frames remains a critical metrological challenge, particularly following the 2019 redefinition of the SI base units. This work establishes a generalized dimensional analysis framework to categorize constant variations into three mathematically constrained scenarios. First, we demonstrate that if dimensionless constants remain invariant, a rigid algebraic constraint binds the co-variation of dimensionful parameters, preserving the structure of physical laws. Second, we formalize the standard scenario where an observed variation in a single dimensionless constant maps directly to its corresponding non-reference dimensionful counterpart. Crucially, our third scenario reveals that a drift in a defined SI reference standard (e.g., c, h, or e) cannot occur in isolation; instead, it triggers a predictable, correlated "cascading" variation pattern across multiple dimensionless observables. By deriving specific sensitivity exponents for these covariant patterns, this framework provides a diagnostic metrological signature. This signature enables the discrimination between a localized experimental anomaly in a non-reference parameter and a systemic shift originating from the foundational reference standards themselves.