Unification of Fundamental Forces as Hierarchy of Informational Stability

This paper presents an exploratory operator-based framework examining fundamental interactions from an informational standpoint. A single functional on a relational substrate combines local, non-local, and hierarchical contributions with an irreversible cost. It investigates whether interaction sectors correspond to stability properties, rather than taking gauge symmetries as fundamental. The physical content is analysed through the Hessian's spectral properties. Eigenvalue organisation diagnoses potential interaction hierarchies, without deriving specific gauge groups. Computational toy models test internal consistency via comparison to null constructions, using spectral entropy and gap measures. Results show non-trivial hierarchies emerge only from the complete informational structure and are robust across scales. This pre-unificatory work clarifies how interaction-like structures can emerge from a single, information-theoretic operator.