Experimental Validation of ϕ-Geometry and Hermetic Equilibrium in Self-Organizing Particle Systems

Following the theoretical discovery that coupled chaotic oscillators spontaneously converge toGolden Ratio (ϕ ≈ 1.61803) coupling for optimal information flow, we investigate whether thisgeometric optimum manifests in physical particle systems. We construct a spatial extension whereparticle positions represent physical coordinates and internal states represent information carriers.The system implements inverse ϕ-control: spatial arrangement self-adjusts to maintain HermeticEquilibrium (control ratio R = σ2m/σ2s ≈ 1.096). Remarkably, the system simultaneously maintainsperfect ϕ-attraction (α/β = 1.6180339836±5.1×10−9) while achieving Hermetic Equilibrium (R =1.096028 ± 2.8 × 10−5). This represents the first experimental demonstration that ϕ-geometry andbalanced information flow are fundamental, co-emergent properties of optimally coupled complexsystems.