Entanglement Is Shared Coherence: Bell's Theorem, Mutual Coherence, and Why No Local Description Captures Resonance

The Spektre corpus has treated coherence as a property of individual systems. This paper extends it to interactions. When two systems meet, their joint coherence KA⊗B is not in general the product K_A · K_B. The difference E(A,B) = KA⊗B - K_A · K_B is the mutual coherence — the non-separable component belonging to neither system alone. At quantum scale, E > 0 is entanglement. Bell’s theorem proves mutual coherence cannot be reduced to local properties — a universal structural result, not a quantum peculiarity. The same structure appears at every scale: biological symbiosis, institutional alliance, orchestrated intelligence, and human resonance are all instances of E > 0. Destructive interference (E < 0) is the mechanism of conflict. The interaction equation governs how mutual coherence evolves through shared channels. An institutional Bell test is proposed: M&A outcomes should not be predictable from local institutional metrics alone. Part of the Spektre research corpus.