Golden-Angle Φ-Resonances for Interstellar Object 3I/ATLAS: Defining Optimal Observation Windows around Perihelion and Jupiter Encounter

I present a complete set of Φ-GPS windows for the interstellar object 3I/ATLAS, derived around its perihelion (2025-10-29 11:34:35 TT) and closest approach to Jupiter (2026-03-16 01:32:30 TT).My method is based on the golden ratio Φ (carried to 100 decimals) and the golden angle$$\Gamma = 360/\Phi^2 \approx 137.5078^{\circ}$$, combined with Φ-damping weights $$w_k = \exp(-\Phi k)$$ for Fibonacci offsets $$k \in \{3,5,8,13\}$$. For each window we provide: Planetary ecliptic longitude, RA and Dec Minimal circular ΔRA and |ΔDec| relative to the 3I perihelion axis Great-circle separations Φ-residuals to nearest multiples of the golden angle Φ-damping weights Key findings: Mars acts as a Φ-beacon in perihelion windows (−8 d, −5 d, −13 d). Venus aligns within 0.25° of a golden-angle multiple at −3 d before Jupiter CA, with high Φ-weight. These resonances define optimal periods for detecting non-gravitational accelerations, jet activity, and PAH spectral modulation. The dataset (phi_gps_windows_3IATLAS.csv) and the LaTeX source (main.tex) are included for reproducibility.This work connects planetary geometry with Φ-based damping from our Theory of Everything framework, and provides testable predictions for upcoming observation campaigns.