Formalization of the distinction between operational noise and signal

This paper proposes a formal framework, based on Distributed Informational Determinism (DID), for distinguishing between operational noise and signal in the analysis of complex systems. The central idea is that an observable event should not be considered only as an isolated local outcome, but as part of a broader informational trajectory. Within this perspective, the same piece of information may be irrelevant in one domain of analysis and relevant in another.

The paper introduces the concepts of local event, informational trajectory, domain of analysis, ontological relevance, operational relevance, admissible counterfactual variation, distance between trajectories, and threshold of relevance. Signal is defined as information whose admissible counterfactual variation modifies the trajectory beyond a relevance threshold with respect to a given domain. Operational noise is defined as information that is present within the trajectory but does not produce a relevant modification within that domain.

The proposed formalization does not claim universal empirical validation of DID. Rather, it provides a coherent formal criterion for organizing the noise/signal distinction in relation to a specified analytical domain. An industrial quality-control example is used to show how the same temperature variation may be operational noise with respect to final component conformity, but signal with respect to process stability or predictive maintenance.