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The observation that the orbits of long-period Kuiper Belt objects areanomalously clustered in physical space has recently prompted the Planet Ninehypothesis - the proposed existence of a distant and eccentric planetary memberof our solar system. Within the framework of this model, a Neptune-likeperturber sculpts the orbital distribution of distant Kuiper Belt objectsthrough a complex interplay of resonant and secular effects, such that inaddition to perihelion-circulating objects, the surviving orbits get organizedinto apsidally aligned and anti-aligned configurations with respect to PlanetNine's orbit. In this work, we investigate the role of Kuiper Belt initialconditions on the evolution of the outer solar system using numericalsimulations. Intriguingly, we find that the final perihelion distancedistribution depends strongly on the primordial state of the system, anddemonstrate that a bimodal structure corresponding to the existence of bothaligned and anti-aligned clusters is only reproduced if the initial periheliondistribution is assumed to extend well beyond $\sim 36$ AU. The bimodality inthe final perihelion distance distribution is due to the existence ofpermanently stable objects, with the lower perihelion peak corresponding to theanti-aligned orbits and the higher perihelion peak corresponding to the alignedorbits. We identify the mechanisms which enable the persistent stability ofthese objects and locate the regions of phase space in which they reside. Theobtained results contextualize the Planet Nine hypothesis within the broadernarrative of solar system formation, and offer further insight into theobservational search for Planet Nine.

The Generation of the Distant Kuiper Belt by Planet Nine from an Initially Broad Perihelion Distribution