The Universal Processing Law (UPL): From One Node to All of Physics (Working Reference)

STATUS: HYPOTHESIS!!.
This document records a logical chain that is internally consistent and physically motivated.
The equations marked PROVEN already appear in published UPL papers.
The equations marked DERIVED are new results developed in working sessions.
The sections marked OPEN PROBLEM contain unsolved steps that, if resolved, would complete specific predictions.
Nothing in this document is to be cited as established until those steps are solved.

This is the V15 working reference containing the complete derivation chain from the master equation $N_{\mathrm{local}} = \mathcal{C} \cdot L_g \cdot L_v$ through: gravity from the discrete Laplacian ($\nabla^2_d(N^2) = 0$), the Pythagorean budget ($\Delta k^2 = \Delta N^2 + \Delta n^2$), optics as refractive routing ($n = 1/N_{\mathrm{local}}$), cosmic expansion from node insertion ($p = 1/k$), and CMB spectral index predictions. Includes $200^3$ GPU simulation verification, 175-galaxy SPARC rotation curve test (69:19 decisive UPL wins over isothermal dark matter), DDO dwarf galaxy IMBH prediction, and partial derivation of the DRR efficiency parameter $\eta$.

All theoretical concepts, derivations, and original ideas are the sole intellectual work of Ahmed Lahmidi.
Contact: ahmed.lahmidi.contact@gmail.com

Complete UPL Publication Record:
Main Preprint (46 pages): https://doi.org/10.5281/zenodo.19241539
Track 2 — Kerr DRR Recovery and PRL Draft: https://doi.org/10.5281/zenodo.19241587
Track 3 — Cosmological Constant (97.3%): https://doi.org/10.5281/zenodo.19241696
Track 4 — Bekenstein-Hawking Entropy: https://doi.org/10.5281/zenodo.19241737
Track 5 — Objective Collapse Time: https://doi.org/10.5281/zenodo.19241785
Track 6 — UV Catastrophe and Planck Spectrum: https://doi.org/10.5281/zenodo.19241810