P21 — Emergent Geometry and Metric Dynamics from Spectral Coherence

This paper is part of a coherent research program developing an informationally emergent physical framework. P21 derives the emergence of effective geometric and metric dynamics from spectral coherence properties of the underlying informational structure. By analyzing how coherent spectral features organize across scales, the paper shows how metric notions and dynamical geometric behavior arise without presupposing a fundamental spacetime background. The work establishes the connection between informational coherence, spectral geometry, and emergent gravitational degrees of freedom, providing the geometric foundation for the relativistic and gravitational dynamics developed in subsequent papers. 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