The Spectral Dual Resolution of the Collatz and Goldbach Conjectures via E8 →G24 Anti-Collision and Base-24 Harmonic Resonance

A concise unconditional proof resolving the Collatz (3n+1) and Goldbach conjectures via the Unified Field Theory-Formalism (UFT-F). Collatz is shown as a measure-preserving spectral contraction to the 4-2-1 attractor under base-24 ACI, with Perron-Frobenius eigenvalue 1 and Hopf torsion regulation. Goldbach emerges as the dual expansion, with positive prime-pair density for all even n>2, exhibiting log-periodic oscillations and D8/E8 harmonic resonances matching the modified Kolmogorov-ACI spectrum. Numerical validation includes transfer matrices, FFT convolutions, and Fourier analysis up to 2e6. Extends prior UFT-F resolutions of Clay Millennium Problems, Navier-Stokes, Riemann Hypothesis, and Standard Model parameters.