Information Relational Manifestation Theory (X): From Spectral Universality Failure to Spectral Self-Organization

Information Relational Manifestation Theory (IRMT) proposes that matter and spacetime emerge from a discrete relational substrate governed by causal structure and coherence constraints. In earlier work, the spectral properties of a relational Dirac operator were assumed to belong to the chiral Gaussian Unitary Ensemble (chGUE), providing the basis for a Baik–Ben Arous–Péché (BBP) mechanism intended to account for the emergence of fermion generations. In this paper, that assumption is tested directly through numerical construction of relational Dirac operators on Poisson-sprinkled causal sets. Across all tested configurations, the operator exhibits Poisson-like spectral statistics consistent with Anderson localization on sparse graphs, rather than the level repulsion characteristic of chGUE. This result is robust under variations in system size, causal density, and transport construction, and constitutes a clear falsification of the original universality assumption. We show that this behavior arises from the intrinsic sparsity of causal connectivity, placing the operator in a localized spectral phase. Introducing non-commuting internal transport induces a transition to a delocalized regime with GOE-like statistics, governed by a critical threshold in transport dimensionality. This establishes that spectral phase in relational operators is controlled by internal transport richness rather than geometric structure alone. A systematic investigation of candidate mechanisms for low-spectrum organization—including node-based encoding, ancestry-conditioned transport, constraint satisfaction systems, frustration models, and low-rank perturbations—finds no robust generation of structured spectral separation beyond matched control ensembles. These results define a broad negative boundary: structure does not arise from local, static, or purely constraint-based mechanisms. We then introduce a spectral feedback mechanism in which the lowest eigenmodes influence the evolution of relational transport. Numerical validation demonstrates the first consistent aggregate advantage of true relational geometry over randomized controls, characterized by improved low-mode separation, persistence, and stability. While full generational structure is not yet achieved, these results identify global spectral–dynamical coupling as a necessary condition for structure formation. The IRMT spectral sector is thereby reformulated from an assumed universality framework to an experimentally constrained program. The emergence of fermion generations is recast as a problem of spectral self-organization, governed by feedback between global eigenstructure and relational dynamics.