While not large enough to explain the observed clustering, this small dynamical sculpting of the perihelion longitudes could become relevant for future, larger TNO datasets. Our analysis also demonstrates that Neptune's resonances impart a modest (few percent) non-uniformity in the longitude of perihelion distribution of the currently observable distant TNOs. Only three objects are in orbital regions not appreciably affected by resonances: Sedna, 2012 VP1 KG163. Five objects can be ruled currently non-resonant, despite their large orbital uncertainties, because our mapping approach determines the resonance boundaries in angular phase space in addition to semimajor axis. Nearly half (11) of these TNOs have orbits consistent with stable libration in Neptune's resonances in particular, the orbits of TNOs 148240 overlap with Neptune's 20:1 and 36:1 resonances, respectively. We find that, counter to common expectations, almost none of these TNOs are far removed from Neptune's resonances.
With this approach, we explore the dynamical landscape of the 23 most distant TNOs under the perturbations of the known giant planets. We use a recently-developed Poincare mapping approach for orbital phase space studies of the circular planar restricted three body problem, which we have extended to the case of the three-dimensional restricted problem with $N$ planetary perturbers. Realizing this potential requires understanding how the known planets influence their orbital dynamics. The most distant known trans-Neptunian objects (perihelion distance above 38 au and semimajor axis above 150 au) are of interest for their potential to reveal past, external, or present but unseen perturbers.