Entropy–Coupled Harmonic Field Dynamics: A 3–6–9 Framework for Structured Energy Transformation

Entropy–Coupled Harmonic Field Dynamics (ECHFD): A 3–6–9 Framework for Structured Energy Transformation Author: Kevin L. Brown, Independent ResearcherDate: September 2026DOI: 10.5281/zenodo.17216734 Abstract Entropy–Coupled Harmonic Field Dynamics (ECHFD) extends the Triune Harmonic Dynamics (THD) framework to explore how entropy-gradient couplings, embedded in 3–6–9 harmonic scaling, drive coherence-driven amplification. Unlike speculative free-energy claims, ECHFD provides a dimensionally consistent, testable field-theoretic model where entropy gradients act as couplings that restructure stability under symmetry constraints. Laboratory data suggest anomalous amplification correlated with harmonic resonance, though falsifiability protocols are defined to rigorously constrain outcomes.. Key Contributions Triune grounding: Extends THD 10.5281/zenodo.1568691910.5281/zenodo.1568691910.5281/zenodo.15686919, the Equilibrium Index 10.5281/zenodo.1699095510.5281/zenodo.1699095510.5281/zenodo.16990955, and the Calista Loop cycle 10.5281/zenodo.1681321910.5281/zenodo.1681321910.5281/zenodo.16813219. Dimensional consistency: Entropy coupling normalized by $\Phi_0$ resolves earlier mismatches. Experimental evidence: Prototype resonance stacks show 112–216% apparent gain under controlled boundary conditions. Falsifiability: Framework is rejected if harmonic peaks (3f, 6f, 9f) are absent or amplification falls below ±5% under replication. Testability Experimental layers: Entropy field gradients: derived via probability distribution estimates over oscillator states. Resonant stacks: toroidal geometries tuned to harmonic ratios. Cross-domain checks: include oscillator coherence, energy throughput, and entropy-field proxies. Protocols: Baseline oscillator null trials. Harmonic resonance tests at 3–6–9 multiples. Replication across ≥3 labs with preregistered controls. Scientific Significance ECHFD reframes “free energy” within structured entropy dynamics and harmonic field theory. If validated, it could: Extend THD symmetry into measurable laboratory physics. Provide predictive tools for entropy-driven amplification. Open new directions in coherence science and complex system energetics. Even null results provide value by constraining THD-based harmonic field claims under rigorous falsifiability protocols. Foundational References THD: Scalar Field Framework for Quantum–Gravity Unification — 10.5281/zenodo.15686919 THD Equilibrium Index: Axiomatic Stability Metrics — 10.5281/zenodo.16990955 Singularity Cycle and the Calista Loop — 10.5281/zenodo.16813219 Energy–Information Equivalence — 10.5281/zenodo.16813373