Information Relational Manifestation Theory (II): Quantum Correlations and Gauge Structure from a Discrete Relational Substrate

This work introduces a foundational framework referred to as Information Relational Manifestation Theory (IRMT). Within this framework, quantum correlations, gauge dynamics, and the appearance of matter arise from the requirement that information remain consistent across a discrete causal structure. The universe is modeled as a causal set composed of events, each carrying internal relational records that encode informational relationships with other events. A key principle of the theory is that informational consistency must hold across shared causal domains. These domains are defined as the Unity Wedge. When the relational records inside such a domain are constrained to remain globally consistent, the admissible internal orientations of events follow a maximum-entropy distribution on the circle S^1. The resulting equilibrium distribution is the von Mises distribution. Analyzing the spectral properties of the causal adjacency matrix reveals a direct microstructural relation between the concentration parameter κand the number of discrete records N, yielding the scaling relation κ∼N. From this relation the framework predicts a small but universal correlation deficit, given by ϵ=1/(2N), which corresponds to approximately 10^(-150)at laboratory scales. The relational constraints governing the substrate can be represented geometrically as orientation-preserving embeddings into the Positive Grassmannian Gr^+ (2,n). Within this geometric description the Parke–Taylor scattering structure appears naturally as a residue of the relational embedding. The dynamical sector of the theory is constructed using a Diamond Holonomy Action. Taking the continuum limit of this action yields Yang–Mills gauge dynamics. In this setting, conserved gauge currents arise from topological irregularities in the valence of the causal graph. Matter therefore appears not as a fundamental ingredient, but as a structural defect in the connectivity of the relational substrate. From this perspective, both physical laws and material particles emerge from the requirement that a finite discrete network maintain relational coherence.