Volume 12, Issue 1, pages 630-642
The black–body radiation problem historically exposed a fundamental inconsistency between classical field theory and thermal equilibrium, culminating in the Rayleigh–Jeans ultraviolet catastrophe and the subsequent introduction of quantum energy quantization. In this work, we present a geometric formulation of equilibrium radiation based on discrete cavity modes governed by curvature–bounded geometry and finite boundary response. Rather than postulating a continuum density of states, equilibrium radiation is described in terms of geometry–determined cavity modes whose exchange and observability are regulated by finite boundary quality. This formulation yields a finite, well–posed description of equilibrium radiation without invoking an \emph{a priori} continuum assumption, ultraviolet cutoff, renormalization procedure, or thermodynamic scaling law. This paper constitutes the first installment of the G–series within the Unified Lattice Framework and is devoted exclusively to establishing the geometric foundations and finiteness of equilibrium radiation in static cavities. Macroscopic spectral structure, integrated thermodynamic scaling, and absolute normalization are deferred to subsequent papers, which build directly on the formulation developed here.
Please comment with your real name using good manners.