Information Relational Manifestation Theory: A Relational Causal Set Framework for the Standard Model

ABSTRACT Information Relational Manifestation Theory (IRMT) proposes a discrete relational framework for fundamental physics in which spacetime, matter, and interaction emerge from the global organization of an informational substrate. Building on the relational ontology and coherence structure developed in earlier work, this paper develops the kinematic and spectral framework of fermionic matter using a Dirac operator defined directly on a causal set. Relational states are modeled as informational records constrained by causal structure and the Unity Wedge coherence condition. The statistical equilibrium of relational orientations is described by a von Mises distribution, introducing a coherence parameter that governs the alignment of informational states across the network and leads to a universal correlation deficit in systems with many degrees of freedom. Fermionic kinematics are formulated through a discrete Dirac operator constructed on the Hasse diagram of a causal set, incorporating Benincasa–Dowker-inspired weighting and relational tetrad transport. In the continuum limit, this operator recovers the standard Lorentzian Dirac operator, providing a background-independent realization of fermionic propagation. Within this framework, particle states correspond to low-lying eigenmodes of the relational Dirac operator, while the bulk spectrum represents the informational background of the causal substrate. The existence of multiple fermion generations is interpreted as a problem of spectral structure subject to observational constraints imposed by the spatial boundary algebra. In particular, the dimensionality of the emergent spatial hypersurface limits the number of independent observational channels available to stabilize distinct modes. Rather than assuming a fixed spectral universality class, the spectral behavior of the relational Dirac operator is treated as an emergent property of the interplay between causal connectivity and internal transport structure. This leads to a reformulation of the generation problem: the multiplicity of fermion families must arise through a dynamical process of spectral organization consistent with both relational coherence and observational constraints. The resulting framework separates the kinematic construction of matter from the unresolved problem of spectral structure formation. While a complete mechanism for fermion generations is not yet established, the theory defines a constrained setting in which such a mechanism must operate, providing a clear foundation for further investigation. NOTE: An earlier version of this paper was previously circulated presenting a proposed spectral mechanism for the emergence of structured modes within the IRMT framework, based on assumptions of a fixed spectral universality class. Subsequent analysis and a systematic experimental investigation of candidate mechanisms have shown that these assumptions are not generally supported within the relational construction. In particular, the spectral behavior of the relational Dirac operator depends sensitively on its phase structure, which is not fixed a priori. The present version reflects this refinement. The earlier mechanism is retained in a revised form as a conditional candidate (see Appendix C), while the main text reformulates the problem in terms of spectral phase and observational constraints. This revision strengthens the internal consistency of the framework and clarifies the open problems that remain. A detailed account of the experimental investigations underlying this revision is provided in companion works.