The Fibonacci Transfer Theorem: Why x² − x − 1 = 0 Appears Across Independent Physical Domains

A unified framework proving that the characteristic polynomial x² − x − 1 = 0 of the Fibonacci transfer matrix A = [[1,1],[1,0]] appears as the unique minimal solution across six independently discovered physical domains: Fibonacci Hamiltonian spectra, KAM stability, Hardy nonlocality, KCBS contextuality, phyllotaxis, and AVL tree balance. The classification theorem proves uniqueness among binary second-order recurrences. The transfer matrix discriminant Δ = Tr² − 4·det classifies dynamics into three algebraically coupled regimes; the fourth quadrant (det < 0, Δ < 0) is empty by algebraic identity. A companion derivation shows complex quantum amplitudes, the Born rule, and the Schrödinger equation emerge from det(A) = −1. The golden critical point of decoherence occurs at Γ_c = 1/φ³.