Prisymphonic Resonance Framework: A Mathematical Model of Coherence, Identity, and Harmonic Interaction

The Prisymphonic Resonance Framework proposes a harmonic model of coherence as an organizing principle across coupled physical, informational, and complex systems. Drawing from synchronization theory, statistical mechanics, information theory, and scalar field extensions, the framework introduces a decoherence scalar (Dᶜ) to model phase instability, entropy accumulation, and relational misalignment within interacting systems. The manuscript presents: A modified scalar–tensor action incorporating a decoherence field Derivation of extended field equations with recovery of General Relativity under limiting conditions A φ-scaled stability structure and attractor analysis Minimal coupled oscillator formulations to model phase convergence dynamics Testable predictions in cosmological background evolution and gravitational perturbations The framework treats coherence not as metaphor but as a measurable dynamical configuration characterized by bounded phase displacement, entropy modulation, and stability attractors. This version (vX.X) represents an architectural formulation intended to establish mathematical structure and falsifiable pathways for future refinement and interdisciplinary collaboration.