Geometric Resolution of the Ultraviolet Catastrophe within a Unified Helical Field Framework

Abstract The ultraviolet catastrophe is traditionally seen as a failure of classical physics, resolved only by postulating energy quantization. Here, we show that the divergence originates not from classical fields themselves, but from hidden geometric assumptions in standard mode counting. In the Unified Geometric Helical Field Framework, radiation arises as a limit of a geometrically constrained helical field, where spectral structure emerges from topological and confinement conditions rather than imposed quantization. Classical assumptions of an unbounded spectral continuum conflict with confined helical geometry. The field instead possesses a finite effective spectral capacity, determined by the breakdown of helical constraints at high frequencies. By deriving the spectral density from geometric confinement, a finite, Planck-like radiation spectrum emerges naturally, without introducing Planck’s constant as a primitive. The standard Planck distribution appears uniquely as a weak-constraint limit, consistent with thermodynamic and experimental results. Beyond ideal cavities, the framework predicts systematic spectral deviations in non-ideal blackbodies, dense media, and high-curvature environments, providing observable signatures in laboratory and astrophysical contexts. The cosmic microwave background is interpreted as a high-entropy, non-helical radiation state, explaining its spectral stability while allowing for small geometry-induced distortions. This work establishes the ultraviolet cutoff as a necessary geometric outcome rather than a quantum postulate, transforming the resolution of the ultraviolet catastrophe from a phenomenological fix to a self-contained geometric explanation. These results motivate a unified treatment of geometric statistics, spectral dynamics, and cosmological radiation in Paper VIII.