Grand Unification of the ATMAN v5.0 Perturber Series: A Simultaneous Three-Body Integration of Solution B, Erebo, and P3 (Paper IX)

(Abstract) We present the first simultaneous three-body N-body integration of all hypothetical trans-Neptunian perturbers identified in the ATMAN v5.0 series: Solution B (6 M⊕, 75 au, λ=260°; Paper V), Erebo (7 M⊕, 600 au, λ=156°; Paper II), and P3 (12 M⊕, 1000 au, λ=180°; Paper VIII). Six scenarios are evaluated over 1 Myr with a mixed test-particle population of classical Kuiper Belt objects and three Sednoids. The key result is constructive interference on Sedna's perihelion: P3 alone lifts ΔqSedna = +2.37 au, but in the full three-body run this rises to ΔqSedna = +6.02 au (+154% amplification), with S_joint = 0.656 — the highest in the series. The Sednoid checkpoint count in the joint run (31) is twice that of single-perturber scenarios (≤19), confirming enhanced dynamical coherence. Solution B and Erebo act as secular resonance mediators that amplify P3's Kozai-Lidov torque on Sedna's orbit. The three-perturber architecture is dynamically synergistic. SHA-256 (simulation output): 64d561ab4cf8c439b27feb53d87e8544dee887529ad996c1e666bf65bbc9f9a4. This is Paper IX of the ATMAN v5.0 series.