Universal Processing Law (UPL) Track 6: Resolution of the Ultraviolet Catastrophe from Discrete Click Statistics via the Universal Processing Law

We derive the functional form of the Planck blackbody spectrum from the discrete computational axioms of the Universal Processing Law (UPL) without assuming energy quantization (E = h). In UPL, each pixel of the Planck-scale hardware graph executes at most C_ irreducible state-updates (Clicks) per hardware cycle. Rendering a radiation mode of frequency costs Clicks per second per pixel, because each oscillation cycle requires one state-update. In thermal equilibrium, the hardware distributes its finite Click budget among competing modes. Because Clicks are indivisible, mode occupation numbers are restricted to non-negative integers. Maximizing the number of microstates (Click allocation configurations) subject to the finite per-pixel budget yields the Bose-Einstein distribution: n () = 1 () - 1 producing the Planck spectrum shape: ³ () - 1 with no free parameters beyond the Lagrange multiplier (conjugate to the Click budget, identified with h/ (kT) ). The ultraviolet catastrophe is resolved because high-frequency modes are combinatorially suppressed: they cost too many indivisible Clicks per quantum for the finite pixel budget to sustain. This derivation complements companion results deriving the cosmological constant (97. 3% accuracy), the Bekenstein-Hawking entropy (S = A4lP²), and the objective wavefunction collapse time (= 8 EG) from the same UPL master equation. All theoretical concepts, derivations, and original ideas are the sole intellectual work of Ahmed Lahmidi. Contact: ahmed. lahmidi. contact@gmail. com