02 - Emergence and Uniqueness of the TwoField Effective Structure from a Coherence-Driven Discrete 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 emergence and structural uniqueness of the effective two-field representation arising from the coherent sector identified in Paper 01. The work demonstrates that the coherence-preserving dynamics of the discrete informational framework admit a minimal effective structure based on two coupled components, and that this structure emerges as the unique stable representation compatible with the global coherence constraints. The analysis establishes the conditions under which the two-field sector becomes dynamically unavoidable within the effective description and prepares the mathematical framework developed in Paper 03, where Hilbert-space structure, Schrödinger-type dynamics, and probabilistic emergence are derived. No quantum-mechanical or geometric assumptions are introduced at the foundational level. The purpose of the article is to derive the minimal effective representation required by the internal consistency of the coherent informational dynamics.