Thermal Coherence Transitions in Water — The φ-Lock Model (v1.0) Part of: The Oxygen Octave Series

This paper introduces the φ-Lock Model, extending the Dynamic Coherence Solver (Ojeda 2025) toward the study of thermal phase transitions in water. The model proposes that below a critical threshold, geometric phase symmetry stabilizes, marking the onset of crystallization as a coherence attractor — a state where ΔC(λ) → 0 and φ(t) → 1.

Using the logistic form

dφ/dt = κ·ζ³·(C/λ)·(1 − φ))

the system self-organizes toward coherence under decreasing thermal noise. The resulting φ-Lock condition provides a dynamic explanation for the transition between molecular disorder and harmonic order in condensed media.

This version formalizes the first temperature-dependent extension of The Oxygen Octave framework and serves as a bridge between molecular resonance, crystallization, and coherence theory.

Author: Jaime Ojeda

Collaborative AI Tools: ChatGPT-5, Grok (xAI)

Date: November 2025

License: CC BY 4.0

DOI linked to: The Oxygen Octave v1.0