The Sanctum exists simultaneously in all three fractured dimensions, appearing as a spiraling predatory den in the Primal Realm, a geometric cathedral in the Clockwork Realm, and a tangible absence-made-architecture in the Hollow Realm. Within each manifestation, successful Perfect Line trajectories are preserved as crystallized flight paths—organic amber curves, mathematical light-trails, and solidified shadow-arcs respectively. When a new Perfect Line is achieved anywhere in the tri-realm system, the Sanctum generates a harmonic pulse that resonates with the Invariant Pulse itself, and only Linewalkers who have touched the Perfect Line at least once can perceive and access its archives.

It functions as the objective arbiter of what constitutes a true Perfect Line versus mere excellent throws. Its acceptance or rejection of a trajectory determines whether a Linewalker has achieved genuine transcendence, and only throws that manifest simultaneously in all three realm manifestations are deemed authentic Perfect Lines worthy of preservation.