A Monte Carlo Forecast for the Detection of Planet Nine

Revision 3 (June 2026). This version corrects a load-bearing error in the LSST detection-timing model. Revision 2 modelled the Rubin/LSST northern footprint as a hard cutoff at Dec +15°; in fact the Wide-Fast-Deep baseline spans Dec −72° to +12°, and the northern boundary is an editable survey-strategy parameter rather than a hardware limit (the telescope reaches Dec +33.5°, and Northern Ecliptic Spur extensions can fill toward Dec +30°). Replacing the hard wall with a graded northern-coverage model raises cumulative detection probability by 2036 from ~61% to ~72% (the latter contingent on plausible northern-cadence coverage; the honest figure is a range, ~61–72%, whose width reflects an undecided Rubin scheduling choice), and strengthens the null-detection posterior from ~47% to ~40%. The albedo prior was also widened to U(0.2, 0.75) to match Fortney et al. (2016), and LSST depth tiers were aligned to documented Rubin limits. The correction was identified by a companion detectability-gap analysis (forthcoming). Revision 2 remains available in the version history.