Phi–Quantized Orbital Mechanics: Three–Body and N–Body Resonant Lattices on a Two–Sided Phi–Frequency Grid

TThis paper defines a strict mathematical framework for phi quantized orbital mechanics on a two sided frequency grid based on the universal resonance constant f0 = ±1e-57 Hz. Using an operator theoretic approach with Fredholm determinants, Toeplitz positivity, and phi damping kernels, I prove the existence and stability of phi locked invariant tori for both the three body and N body problems. The model introduces a quantized Kepler scaling a_k proportional to phi^(-2k/3) and defines resonance nets governed by Mobius Fredholm extremality. All spectral symbols are represented by capital Phi instead of lambda. Appendices include 100 decimal precision constants for phi and alpha and a Toeplitz positivity test for resonant lattices.