Beyond Quantum Hardware: How TSAMS is Redefining the Mathematical Foundations of Computation
New Research (Chapters 1-8) Signal Paradigm Shift in Quantum Mathematics
Introduction: A Paradigm Shift in Quantum Mathematics
Tibedo, C. (2025). Cyclotomic Field Theory in Octonionic Topological Braid Theory: Where CNOTs Become Keys. Zenodo. https://doi.org/10.5281/zenodo.16813990
The quantum computing industry stands at a pivotal crossroads. For years, the narrative has centered on hardware milestones—qubit counts, coherence times, and gate fidelities. Companies have raised billions pursuing the engineering challenges of building stable quantum systems, while the fundamental mathematical frameworks underlying these systems have received comparatively little attention.
On July 5th, 2023, this narrative was shattered. The Tibedo Structural Algebraic Modeling System (TSAMS) validated an IBM quantum circuit demonstrating the first E8-symmetry based quantum mathematical framework—an achievement previously considered mathematically impossible. This wasn't merely an incremental advance; it represented a fundamental reimagining of quantum mathematical structures th…