It manifests as a self-sustaining waveform that pulses with mathematically perfect intervals, visible as spiraling golden frequencies in the Clockwork Schism, felt as predatory heartbeat rhythms in the Primal Schism, and perceived as the measured breath between silences in the Hollow Schism. Each pulse emits a harmonic that only those synchronized with the Perfect Line can perceive. The theorem's frequency remains constant across all three dimensions, but each realm interprets the same beat through its own framework—geometry hears equations, nature feels hunts, void measures absence.

It exists as the ultimate proof that mastery requires four-dimensional awareness—that the Perfect Line isn't just a path through space but a rhythm through time, and only those who can feel when to release as clearly as they see where to aim have truly transcended dimensional limitation.