Ecliptic Longitude of the Third Trans-Neptunian Perturber: A Full 360° Longitude Sweep with ATMAN v5.0 (Paper VIII)

(Abstract) We present a full 360° ecliptic longitude sweep for the third hypothetical trans-Neptunian perturber P3 (12 M⊕, a = 1000 au, i = 20°) identified in Paper VII, with Erebo and Solution B as fixed background bodies. Three Sednoid test particles (90377 Sedna, 2012 VP113, Leleakuhonua) are integrated over 1 Myr. The sweep reveals an extremely sharp signal at λ_P3 = 180° ± 4° (J2000: RA 12h00m, Dec +0°; Virgo), producing ΔqSedna = +7.46 au and S_joint = 0.692. All other longitudes yield Δq < 0 (perihelion depression). A striking geometrical result: P3 (λ = 180°) and Erebo (λ = 156°) are separated by only Δλ = 24°, placing both in the Leo/Virgo sky region and suggesting a possible common dynamical origin. The three-perturber system now has fully characterised sky positions: Solution B in Ophiuchus (260°), Erebo in Leo (156°), and P3 in Virgo (180°). SHA-256 (simulation output): e13d54b3dd4e433ebec89427c45737ee6257c90cf3555c311abf594f7ca7300f. This is Paper VIII of the ATMAN v5.0 series. Author: Ariel Fernando Martini, Buenos Aires, Argentina (2026).Contact: ariel_martini_3@hotmail.com