Volume 12, Issue 1, pages 664-683
Equilibrium black–body radiation is examined as a geometric phenomenon governed by discrete cavity eigenmodes and finite boundary response. Rather than assuming a continuum density of states or idealized cavity conditions, equilibrium radiation is constructed directly from geometry–determined standing–wave modes populated by Bose–Einstein statistics and coupled through finite–quality boundaries. We show that a smooth Planck–like spectral envelope emerges as an observable macroscopic limit of discrete equilibrium mode populations once finite spectral resolution is taken into account. Individual cavity modes possess finite linewidths set by boundary quality factors, and the measured spectrum arises as an envelope formed by overlapping broadened modes. No ultraviolet cutoff, \emph{a priori} smoothing procedure, or continuum limit is invoked. The agreement with the classical Planck distribution is structural rather than exact: low–frequency scaling and overall normalization reflect the one–dimensional, finite–geometry setting, while the characteristic exponential tail and temperature–dependent peak emerge from equilibrium statistics acting on bounded geometry. Planck’s law is thus interpreted as an effective macroscopic description valid in the regime where discrete geometric structure becomes dense relative to observational resolution. In this way, the spectral features of black–body radiation arise from finite cavity geometry and bounded exchange, providing the geometric and statistical foundation upon which subsequent analyses of thermodynamic scaling within the Unified Lattice Framework are built.
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