A Minimal Geometric Framework for Spectral Organization in Vacuum Fields

Abstract We present a minimal geometric framework for the description of a vacuum field, motivated by the observed regularity of radiation spectra across a wide range of physical regimes. The construction is formulated on a smooth four-dimensional manifold and is based on a single geometric field defined as a section over this manifold, without assuming predefined spacetime dynamics, particles, forces, or quantization principles. A purely geometric helical constraint is introduced at the level of field configurations. This constraint is not interpreted as an interaction or a dynamical law, but as a structural condition on admissible geometric states. From the constrained field, an effective scalar quantity, denoted , is defined as a functional of the field and its derivatives, serving as an organizing measure for spectral energy distribution. It is shown that the presence of the geometric constraint leads naturally to structured and regular spectral organization, while the gradual relaxation of the constraint corresponds to a free radiative regime. In appropriate limiting cases, the framework consistently recovers the standard Maxwell description of electromagnetic radiation and the Planck spectral distribution, without altering their established mathematical forms. The scope of the present work is intentionally limited. No attempt is made to address specific physical problems, introduce new interactions, or unify fundamental forces. Instead, the framework provides a minimal, consistent geometric baseline for exploring the structural origins of spectral organization in vacuum fields, fully compatible with experimental observations and established physical theories.