ATMAN v5.0 Paper XIV: Resolution of the Invariable Plane–Sedna Degeneracy via a 2D Joint Inclination Sweep, Cartography of the Kozai–Lidov Resonance Window of P3, and 100 Myr Stability Confirmation of the Optimal Three-Perturber Architecture

Paper XIV of the ATMAN v5.0 series. The invariable plane–Sedna degeneracy of Paper XIII is resolved through three successive analyses. First, a 2D joint sweep over iSolB∈[0°,5°] and iP3∈[0°,10°] (121 trials) confirms no solution exists in the low-inclination regime. Second, an extended 1D sweep over iP3∈[10°,25°] identifies two solutions satisfying both constraints simultaneously: iP3=16° (ΔqSedna=+6.47au) and iP3=20° (ΔqSedna=+7.50au). Third, a fine sweep (Δi=0.1°) over iP3∈[15°,17.1°] cartographs the Kozai–Lidov resonance window, revealing a fringe structure of width ΔiKL=1.4° with maximum lifting ΔqSedna=+8.30au at iP3=17.1°. A 100 Myr stability integration with optimal inclinations (iSolB=1.5°, iErebo=30°, iP3=16°) confirms zero orbital drift for Erebo (a=715.21±0.00au) and P3 (a=1039.93±0.00au) and sustained Kuiper Cliff depletion Ddep=0.654. Definitive model: iSolB=1.5°, iErebo=30°, iP3=16°–17.1°. SHA-256 fine sweep: 6a9557ed7fea27d209a6b07f1f989f9a95c53cf17c33fe00d695292242a77caa. SHA-256 stability: 83b9d903af42de7d5df020ed5b3ea0a298371cefe8ac09ab8ee5874e2a15327b. Paper XIV of the ATMAN v5.0 series.