Volume 12, Issue 1, pages 684-714
The preceding G–series (G1–G3) established that equilibrium black–body radiation admits a finite, well–posed description based on discrete cavity geometry, finite boundary response, and standard equilibrium statistics, without invoking a continuum density of states. These results were obtained strictly within static, finite cavities and do not modify the dynamical structure or empirical predictions of quantum electrodynamics. In this capstone work, that reconstruction is elevated to an origin–framework statement. We formulate the Unified Lattice Framework (ULF) at the origin level by: (i) stating its primitive ontology, bounds, and observables explicitly; (ii) demonstrating that within the equilibrium radiation sector, the constant appearing in the Planck–Einstein relation may be interpreted as an operational calibration of bounded geometric exchange, without altering photon counting or field quantization; and (iii) proposing a concrete, falsifiable experimental discriminator based on geometry– dependent equilibrium linewidth scaling in high–$Q$ cavities. The ontological and epistemological commitments of ULF are clarified in Appendix~A, formal primitive closure across matter, radiation, and vacuum boundary exchange is established in Appendix~B, and the Casimir effect is shown in Appendix~C to arise as a curvature–bounded boundary–exchange phenomenon requiring no additional primitives. Taken together, these results complete the equilibrium radiation arc of the G–series and place ULF in a testable origin–level form in which physical constants and classical limits emerge from finite geometric structure while remaining fully compatible with standard quantum and classical predictions.
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