Boltzmann, Stefan–Boltzmann, Wien, Radiation Constant, Planck Temperature from Coherence Geometry (UFEB): A Swarm Theory Derivation

Description
This paper consolidates thermal constants derived from coherence geometry in UFEB (Unified Field Equation, Budget form). Boltzmann’s constant (kB) is framed via per-update microstate counting on the coherence lattice. With SI-exact h, kB, and c, the Stefan–Boltzmann constant (sigma), the radiation constant (a = 4*sigma/c), and the Wien displacement constant (b) follow directly from the Planck spectrum written in update-budget form. Planck temperature TP then follows from UFEB’s Planck-scale closure, TP = EP/kB. All values match standard references; for sigma, a, and b they are exact consequences of the SI definitions. UFEB supplies a microphysical, atemporal interpretation (updates, not time flow) consistent with these results.

Highlights

• kB: per-update microstate interpretation (value exact by SI)

• sigma = (2pi^5kB^4)/(15h^3c^2) (exact given SI h, kB, c)

• a = 4*sigma/c (exact given sigma, c)

• Wien constant (wavelength form): b = (hc)/(kBx), with 5*(1 - exp(-x)) = x and x = 4.965114…

• Planck temperature: TP = EP/kB within UFEB Planck-scale closure

• Assumptions: isotropic equilibrium (large cavity); “no-time” formulation (T labels ensemble budgets per update)

Conventions
We use B_lambda (wavelength spectrum). The frequency-domain peak B_nu has a different numerical constant.

Reproducibility
Worked step-by-step evaluations and unit checks are included in the paper. A minimal script can reproduce all numbers from SI constants.

Additional materials and related work are available on GitHub: https://github.com/crumpler4/Swarm-Theory-Unified-Field-Equation-Series