Structural Compatibility as a Derived Condition The Non-Primitive Ontological Status of C in Field-Network Theory

Abstract

Description This paper develops the ontological foundations of Field-Network Theory by examining the status of structural compatibility. Earlier formulations represented compatibility as a separate operator constraining possible events. The present work argues that no independent compatibility operator is required. Instead, structural compatibility is shown to arise from the relation between realised structural memory (D) and the open possibility structure (𝒬) under candidate event realisation. The paper distinguishes clearly between ontological concepts and mathematical representations. Realised structural memory, open possibility structure and irreducible event realisation constitute the minimal ontology. Compatibility functions, dominance relations, continuation scores and stochastic selection models are interpreted as optional mathematical representations rather than additional constituents of reality. This work builds directly upon the earlier papers Field-Network Theory – Logical Core Structure and A Formal Mathematical Research Program for Field-Network Theory, refining the ontology while remaining fully compatible with the existing mathematical framework. It proposes an ontological reduction rather than a modification of the mathematical research programme.