Universal Processing Law (UPL) — Track 2: Kerr Metric Derivation, Geometric Gradient QNM Prediction, and Development Notes

This upload contains the Track 2 mathematical working documents for the Universal Processing Law (UPL) framework, building upon the foundational UPL preprint (DOI: 10.5281/zenodo.19154977). This record includes four documents: UPL Session Development Notes: Documents the theoretical development trajectory, the DRR dual-saturation mechanism, the Schwarzschild/Kerr complementarity hypothesis, and a pattern analysis of 176 LIGO/Virgo/KAGRA merger events. UPL Track 2 — DRR Tensor Derivation: Formal derivation of the Kerr metric structural functions Σ and Δ from the UPL dual-saturation boundary conditions, with proofs. The ergosphere emerges as the DRR activation boundary. UPL Track 2 — Teukolsky Framework and Geometric Gradient QNM Prediction: Establishes that Φ = Lg·Lv is a geometric functional of the metric, not a Brans-Dicke scalar. Derives a parameter-free structural QNM frequency shift prediction for near-extremal Kerr black holes detectable by the Einstein Telescope. UPL PRL Draft (v2): Complete 4-page Physical Review Letters format manuscript presenting the full Level 2.8 framework for journal submission. All theoretical concepts, derivations, and original ideas are the sole intellectual work of Ahmed Lahmidi. Contact: ahmed.lahmidi.contact@gmail.com