  Trans-Neptunian Objects (TNOs) in the scattered disk with 50 < a < 100 au are
thought to cluster near Neptune's n:1 resonances (e.g: 3:1, 4:1, and so on).
While these objects spend lengthy periods of time at large heliocentric
distances, if their perihelia remain less than around 40 au, their dynamical
evolution is still largely coupled to Neptune's. Conversely, around a dozen
extreme TNOs with a > 250 au and detached perihelia seem to exist in a regime
where they are too distant to be affected by the giant planets, and too close
for their dynamics to be governed by external forces. Recent work suggests that
the apparent alignment of these orbits in physical space is a signature of
gravitational shepherding by a distant massive planet. In this paper, we
investigate the evolution of TNOs in each of Neptune's n:1 resonances between
the 3:1 and 14:1. We conclude that both resonant and non-resonant objects
beyond the 12:1 near ~157 au are removed rather efficiently via perturbations
from the hypothetical Planet Nine. Additionally, we uncover a population of
simulated TNOs with a < 100 au, 40 < q < 45 au and low inclinations that
experience episodes of resonant interactions with both Neptune and Planet Nine.
Finally, we simulate the evolution of observed objects with a > 100 au and
identify several TNOs that are potentially locked in n:1 resonances with
Neptune; including the most distant known resonant candidates 2014 JW80 and
2014 OS394 that appear to be in the 10:1 and 11:1 resonances, respectively. Our
results suggest that the detection of similar remote objects might provide a
useful constraint on hypotheses invoking the existence of additional distant
planets.
