Integrated Cosmological Observables and the Limits of Local Inference

Integrated cosmological observables are often combined to strengthen parameter inference and model constraints. In this note, we show that locally consistent fits obtained from individual observable classes may nevertheless lead to residual inconsistencies when integrated globally. Using a minimal diagnostic setup, we illustrate how integrated observables can remain individually informative while failing to uniquely constrain a shared parameter space. The analysis is local and model-agnostic, focusing on limits imposed by the structure of the observational interfaces rather than on extensions of the underlying cosmological framework.