P13 — Maxwell Equations as an Effective Closure of the U(1) Sector

This paper is part of a coherent research program developing an informationally emergent physical framework. P13 shows how the classical Maxwell equations arise as an effective closure of the emergent U(1) gauge sector derived in the previous paper. Starting from the informationally generated gauge structure, the work demonstrates that the standard electromagnetic field equations appear as macroscopic consistency conditions governing the coherent sector. The analysis clarifies the relationship between discrete informational coherence, emergent gauge invariance, and classical field dynamics, providing a concrete link between the underlying informational substrate and familiar continuum electromagnetic theory. While this paper 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