The Universal Cascade Across the Quantum-Classical Boundary

The complete treatment of the quantum-classical boundary as the boundary of the Feigenbaum universality class. The Universal Cascade Theory (UCT) proves that C₁ (dissipative boundedness), C₂ (non-degenerate quadratic fold), and C₃ (transversal spectral crossing) are necessary and sufficient for Feigenbaum cascade structure with δ = 4.66920160… and α = 2.50290787…. The Null Theorem establishes that the linear Schrödinger equation categorically fails C₂. The quantum Kerr oscillator satisfies C₁–C₃ with quantum phase transition at γˣ = 1.1838, tunneling correction Δγ = 0.738, and N-convergence of 0.000% from N=30 to N=50. The Whisper scaling exponent β = −δ = −4.669… agrees with the cascade prediction at 0.26%, falsifying the Drummond-Walls (1980) prediction of β = −0.5 by a factor of 9.3. The Born rule |ψ|² is derived as the unique cascade-renormalization-invariant probability measure in six lines, independent of Hilbert space axioms. The thirteen-theorem self-grounding loop closes the logical chain from UCT axioms through cascade geometry to experimental verification.