6.2 Spectral Interlock Closure Theorem

This article proves the Spectral Interlock Closure Theorem—the rigid locking of the three-field spectra. Any change in the spectrum of a single sector propagates to the other two sectors, leading to global inconsistency. Spectral interlock is the manifestation of Benign Mutual Conjugate Locking (Theorem 1.6.3.01) at the three-field level. This article provides a complete algebraic proof of spectral interlock, eigenvalue analysis of closure conditions, the three-layer mechanism of rigid locking, as well as perturbation analysis and testable predictions of interlock.