01 - Axiomatic Foundation of a Coherence-Driven Discrete Informational Framework

This series presents a structured and logically sequential formulation of a discrete informational framework governed by global coherence constraints. Although it originates from the same research program developed in the earlier exploratory preprint series (P-series), the works presented here constitute an autonomous and self-contained series, organized in a progressively axiomatic form and focused on the explicit derivation of the framework’s effective structures. The goal of the construction is to investigate whether structures commonly associated with quantum mechanics, thermodynamics, and geometry may emerge from a discrete relational substrate without being introduced as fundamental postulates. Each article addresses a specific level of the theoretical derivation and forms part of a progressive logical structure based on results established in the preceding works of the series. This article develops the axiomatic foundation of the framework and introduces the discrete informational system underlying the construction. The paper defines the admissible configuration space, the local update structure, the global coherence constraint, and the dynamical selection principles leading to the emergence of a coherent sector. The analysis establishes the existence, invariance, and structural uniqueness of the coherent sector, together with the effective restrictions that prepare the minimal two-component structure developed in Paper 02 and the emergent quantum framework constructed in Paper 03. No quantum-mechanical, geometric, or probabilistic structure is assumed at the foundational level. The purpose of the work is to establish the minimal structural and dynamical layer from which the later effective constructions emerge.