From Theoretical Prediction to Experimental Reality: The Tibedo Quantum Framework and IonQ-Oxford Room-Temperature Quantum Gates

This document provides a rigorous mathematical analysis demonstrating that the IonQ-Oxford experimental achievement of >99.99% fidelity two-qubit gates at room temperature (arXiv.2510.17286, October 21, 2025) is a direct physical manifestation of the theoretical predictions established across Chapters 14-21 of the Tibedo Quantum Framework. We show explicitly how each mathematical structure - from braiding polynomial class layers to Yang-Baxter solutions to cyclotomic field theory - maps precisely onto the experimental methodology and results published by Hughes, Malinowski, Harty et al.