Field-Network Theory – Reality Happens Through Events, Not Objects: A Mathematical Exposition and Research Program

Field-Network Theory (FNT) presents a mathematical framework in which the future is understood as event formation rather than as a collection of objects—as part of the present alongside the past. No background time is presupposed; temporal order arises from irreducible events themselves. In this work, we bring together a formal structure, definitions, axioms, computational models, and open proof obligations into a unified mathematical exposition and research program whose objective is to enable independent mathematical evaluation and further development. The fundamental structural unit of FNT is the irreducible event (Eₜ), from which structural memory (D), compatibility, continuity, and higher-order structures emerge. Structural development is described using directed acyclic graphs (DAGs), stochastic processes, and the mathematical conditions governing admissible continuations. The following formal operationalization chain is presented: Eₜ → (D, μ) → Q → C → M → π and demonstrates how non-deterministic monotonicity governs long-term structural development without the system collapsing into determinism. The monograph distinguishes proven results, conjectures, and open research problems from one another. It provides both an analytical and a computational foundation for investigating an event-based conception of reality. FNT describes reality as continuous event formation, in which the future is not merely an extension of the past, but a structural continuity constructed through new events. Reality is therefore not described as a system of persistent objects. https://sites.google.com/view/field-network-theory