Null Space, Integrated Observables, and Interface Stress Tests Subtitle: A Diagnostic Analysis of Non-Invertible Observational Interfaces

This technical note presents a set of domain-independent stress tests aimed at isolating a structural constraint common to heterogeneous observational and inferential systems: the emergence of null informational spaces due to non-invertible, capacity-limited interfaces. The analysis shows that, under minimal and operationally realistic assumptions, the absence of local signal does not imply absence of underlying structure, but reflects intrinsic limits of access imposed by the observational interface. Across multiple domains—including cosmological integrated observables, classical inverse problems, and algorithmic diagnostics—the residual information generated by non-invertibility cannot be eliminated, but only redistributed, typically toward integrated or global observables. The work is purely diagnostic and methodological. It introduces no new physical entities, mechanisms, or ontological commitments. Its purpose is to clarify why persistent residuals and apparent failures of local closure recur across otherwise unrelated systems, and to delineate the structural limits within which such phenomena arise.