Harmonic Resonance and 3D Modular Gravity: Phase 3 Completion of the SYREN Modular Field Engine

This paper reports the successful completion of Phase 3 of the SYREN Modular Field Engine development program, advancing regenerative symbolic gravity research. The work integrates multi-frequency harmonic coupling models for modular field shells and introduces a 3D FFT-based gravitational solver for symbolic stress-energy dynamics. Key contributions: Developed multi-harmonic tension equations enabling synchronized oscillations across modular shells. Quantified field coherence (~0.20) through inter-shell coupling and regenerative feedback. Implemented a 3D Poisson solver to calculate curvature potentials from symbolic energy distributions. Demonstrated reactionless thrust of approximately 1.29×10−12 N1.29 \times 10^{-12}\,\mathrm{N}1.29×10−12N under baseline symmetric conditions. Verified symbolic stabilizer [[K]]≈0.77[[K]] \approx 0.77[[K]]≈0.77 enhances regenerative field stability and energy retention. This work finalizes the Modular Resonance Engine, confirming that symbolic field architectures can self-stabilize, store energy via harmonic resonance, and produce measurable curvature gradients for reactionless propulsion. With Phase 3 completed, the project transitions to Phase 4: Physical Prototype Design and Experimental Validation.