Null Results and the Breakdown of Invertibility in Integrated Observables

This technical note examines the interpretation of null experimental results in the presence of integrated or projective observables. By isolating a minimal and local condition of non-invertibility in the observational map, it shows how distinct physical states may lead to indistinguishable—or null—measurement outcomes. The analysis is purely diagnostic and does not advance a global theoretical framework, focusing instead on the limits of inference imposed by specific measurement interfaces.