The Universal Resonance Principle (URP): A Scale-Invariant Coupling of Order, Chaos, and Energy Flow Across Astrophysical Systems

We present the Universal Resonance Principle (URP), a minimal and scale-invariant framework describing energy flow as a dynamic balance between structural order ($O$) and chaos ($C$). Across four independent astrophysical domains — galactic rotation curves (SPARC), dwarf spheroidals (Gaia DR3), gravitational lensing (HSC/KiDS/DES), and gravitational-wave ringdowns (LIGO/Virgo GWTC-3) — we apply a single operator R = k_R\,O^p (1 - C)^q, with globally fixed exponents $p = q = 1$. Without re-optimization or new free parameters, the URP reproduces observed energy distributions and systematically improves residual accuracy and information criteria ($\Delta$AIC < 0) compared to standard models (ΛCDM, NFW, MOND, GR). The results suggest that classical quantities such as energy, gravitation, and spacetime curvature are not replaced but appear as boundary cases of a resonance-gradient field in which energy responds to the internal ratio of structure and disorder. This interpretation unifies macroscopic and microscopic dynamics under a shared formalism of resonant equilibrium. The URP offers a falsifiable extension of classical physics: it predicts specific coupling patterns ($p, q ≈ 1$), cross-domain parameter transferability, and residual whiteness as markers of structural balance. All data, code, and posterior samples are openly archived on Zenodo (DOI: 10.5281/zenodo.17428961). We conclude that resonance gradients may represent a fundamental organizing law of physical systems. Resonance Gradient Energy Flow Equilibrium Order and Chaos Emergent Gravitation Scale Invariance