The Prisymphonic Coherence Extension of E = mc²: Incorporating φ-Scaling, Threshold Resonance, and Collapse Dynamics Across Physical Scales

The Prisymphonic Coherence Framework:
A Field-Theoretic Model of Harmonic Structure, φ-Recursion, and Emergent Stability**

Description:

This paper introduces the Prisymphonic Coherence Framework, a unified theoretical model proposing that coherent structure across physical scales emerges from harmonic field dynamics governed by φ-recursive symmetry. The framework develops a formal scalar coherence field C(x,t)C(x,t)C(x,t) and derives conditions under which stable energy configurations arise as preferred harmonic attractors.

A central result of the work is the demonstration that φ-recursion naturally produces the 3:2 gap ratio associated with the musical perfect fifth, suggesting that harmonic intervals are not metaphors but mathematically inevitable outcomes of recursive proportional systems. Numerical modeling shows 3:2 functioning as a low-energy attractor state, with implications for stability in quantum modes, cosmological patterning, and biological resonance.

The paper provides:

• a formal definition of the coherence field

• derivations linking gap ratios to φ-scaling

• a stability analysis demonstrating 3:2 dominance

• testable predictions that distinguish the model from existing physical theories

• falsifiable criteria for evaluating harmonic attractors in measurable systems

The framework is positioned not as a replacement for established physics, but as a complementary layer describing how structured order emerges from underlying ratios, tensions, and recursive symmetries. It extends the intuition that physical law may express harmonic principles and offers a mathematically grounded pathway for investigating resonance as a generative property of the universe.

This release (Version 0.1) presents the foundational principles, derivations, and the first set of predictions. Subsequent versions will expand the mathematical formalism, explore experimental pathways, and integrate coherence modeling across astrophysical, quantum, and biological domains.