The Infinite Tangent manifests as a shimmering golden trajectory that eternally approaches—but never quite intersects—a perfect circle suspended in dimensional space. As it shifts between realms, it takes on the characteristics of each: organic spiral growth in the Primal Schism, crystalline geometric precision in the Clockwork Schism, and a void-defined line of absence in the Hollow Schism. When a Linewalker's throw achieves momentary tangent contact with the Perfect Line, the entity generates a harmonic resonance that ripples across all three dimensions, marking the achievement while simultaneously revealing how much farther the infinite approach extends.

It functions as reality's response to the question 'Can perfection be achieved?' by proving that perfection can be touched, approached, and momentarily aligned with, but never fully possessed—and that this relationship is more meaningful than possession ever could be. The Infinite Tangent teaches Linewalkers that each perfect throw is merely a point of contact along an endless curve, transforming the pursuit of the Perfect Line from a goal to be reached into an eternal relationship to be honored.