P25 — Emergence of Fi and Psi as Effective Variables in a Two-Substrate System

This paper is part of a coherent research program developing an informationally emergent physical framework. P25 introduces the emergence of the effective variables Φ (Fi) and Ψ (Psi) within a two-substrate informational system. The paper shows how these variables arise as complementary effective descriptions associated with distinct but coupled informational layers, capturing coherent and dynamical aspects of the underlying structure. The analysis clarifies the roles of Fi and Psi as emergent variables governing stability, dynamics, and coupling between informational substrates. This formulation provides the conceptual and mathematical foundation for the effective field descriptions, interactions, and large-scale behaviors 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