Unifying Planck and Boltzmann with Maxwell (1865): A Classically Quantised Electromagnetic Theory

We introduce an algebraically closed vortical field system and show that, under aLie-transport reinterpretation of Maxwell’s temporal evolution, it defines a Maxwell (1865) -compatible electromagnetic sector with dual-symmetric electric and magneticclosure. This closure admits a constructive Brouwerian route to a classically quantisedelectromagnetic theory via the discretisation of space and time. Within the sameMaxwellian framework, Planck’s energy--frequency relation and the Planck blackbodyspectral law are recovered constructively. This further permits the definition of atemperature scale in which one degree is the increase in energy content of one cubicmetre of vacuum by one joule, with zero degrees corresponding to\ (-272. 925\, \). An electromagnetically defined Boltzmann constant isthen obtained, numerically differing from the contemporary value by \ (0. 08\%\). Furthermore, an explicit electromagnetic mass gap is obtained in purely electromagneticterms, in analogy with the Yang--Mills mass-gap concept. The paper is intended as apurely mathematical grounding of a classically quantised electromagnetic theory; allfiner physical interpretations are deferred.