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 multiple independently discovered physical domains: Fibonacci Hamiltonian spectra, KAM stability, Hardy nonlocality, KCBS contextuality, Schwarzschild quasinormal modes, phyllotaxis, and AVL tree balance. The classification theorem proves uniqueness among binary second-order recurrences. A companion derivation shows the Born rule, complex quantum amplitudes, and the Schrödinger equation emerge from det(A) = −1. The decoherence phase transition occurs at Γ_c = 1/φ³.