The Spectral Dual Resolution of the Collatz and Goldbach Conjectures via E8 →G24 Anti-Collision and Base-24 Harmonic Resonance
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.
log-periodic oscillations, Perron-Frobenius theorem, Hopf torsion, Goldbach conjecture, Goldbach comet, base-24 symmetry, Anti-Collision Identity, prime distribution, number theory, arithmetic dynamics, Collatz conjecture, E8 lattice, spectral map, D8 dihedral group
log-periodic oscillations, Perron-Frobenius theorem, Hopf torsion, Goldbach conjecture, Goldbach comet, base-24 symmetry, Anti-Collision Identity, prime distribution, number theory, arithmetic dynamics, Collatz conjecture, E8 lattice, spectral map, D8 dihedral group
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!