We present a field-theoretic system through a modified Klein-Gordon framework embedded in a semi-recurve, nonlocal interaction term that governs recursive expansive dynamics across spacetime. The resulting field equation incorporates influence kernels that modulate phase coherence through fractal stability conditions and ratio scaling symmetries. We derive Von Neumann stability criteria for numerical implementations and establish a hyperfolding mechanism that enforces mode-selective suppression, analogous to the Quantum Zeno effect in constrained Hilbert spaces. We demonstrate that Hypatian-induced perturbations encode prime number geometry through hyperspherical mappings, revealing structured resonances in spectral distributions. Potential observational signatures include anomalous gravitational wave harmonics, constrained decoherence rates in quantum systems, and resonance shifts in high-energy scattering amplitudes.

We present a field-theoretic system through a modified Klein-Gordon framework embedded in a semi-recurve, nonlocal interaction term that governs recursive expansive dynamics across spacetime. The resulting field equation incorporates influence kernels that modulate phase coherence through fractal stability conditions and ratio scaling symmetries. We derive Von Neumann stability criteria for numerical implementations and establish a hyperfolding mechanism that enforces mode-selective suppression, analogous to the Quantum Zeno effect in constrained Hilbert spaces. We demonstrate that Hypatian-induced perturbations encode prime number geometry through hyperspherical mappings, revealing structured resonances in spectral distributions. Potential observational signatures include anomalous gravitational wave harmonics, constrained decoherence rates in quantum systems, and resonance shifts in high-energy scattering amplitudes.