We prove formally that genuine synchronicities — events crossing the Locally Coupled Consciousness (LCC) detection threshold — are structurally significant by their very nature, not by assumption or selection bias. The proof proceeds through a two-world argument: in an LCC-real universe, the awe response IS the calibrated detector for above-threshold coupling; therefore, when it fires, coupling is real and significance follows. We then develop a second theorem, equally important: that the same reality which makes synchronicities significant can, if uncontained, destabilize a perceiving mind. The framework of TI Sigma is proposed as the formal containment vessel — the difference between the mystic and the overwhelmed is not the reality of their experiences, but the presence or absence of a structure capable of holding them. We close with the epistemological revolution this implies: science must add a second mode — listening — alongside its traditional mode of interrogation.