P03 — Spectral Geometry of Discrete Networks and Emergence of an Effective Continuum

This paper is part of a coherent research program developing an informationally emergent physical framework. P03 investigates the spectral properties of the discrete informational networks introduced in previous papers and shows how an effective continuum description can emerge from their large-scale spectral structure. By analyzing the spectrum of appropriate network operators, the work establishes a correspondence between discrete informational geometry and emergent continuous geometric notions. The paper demonstrates how effective dimensionality, metric properties, and continuum-like behavior arise without assuming an underlying spacetime manifold, providing the geometric foundation required for the emergence of effective field theories in later stages of the framework. While this work can be read independently, its full significance becomes clear only within the complete sequence of papers (P00–P32). The reference entry for the full framework, including priority timestamp and complete context, is:DOI: 10.5281/zenodo.18369063