SISSI Information Theory And Theorem

This work presents a unified framework that connects a spectral coherence–based method (SISSI/SGCI) with a formal proposal for defining information in dynamical systems. The manuscript introduces: (1) a generalized coherence index for time-varying signals; (2) a theoretical formulation of “Harmonic Information” defined as the loss of coherence across time-lags; and (3) a mathematical theorem establishing sufficient conditions under which information can be expressed as the average decrease in coherence. The theory aims to provide an interpretable bridge between classical signal analysis, stochastic processes, and information theory. While inspired by established concepts (spectral similarity, autocorrelation, Shannon entropy), the proposed formulation emphasizes dynamical coherence rather than probabilistic uncertainty. The manuscript includes a preliminary proof, discussion of assumptions, limitations, and potential implications for physics, computation, and complex systems. The contribution is exploratory and does not claim to replace or generalize Shannon’s framework; instead, it proposes an alternative viewpoint that may be useful for systems where information manifests primarily through structural coherence rather than statistical entropy. The document is intended as a conceptual and mathematical starting point for future peer-reviewed validation, refinement, and critique.