BBGT–Allotey Formalism: Ambient Temperature Topological Quantum Computing & Quantum Processing Advantage

Quantum computing architectures remain fundamentally constrained by thermal decoherence, soft-error scaling bottlenecks, and computational complexity limits when simulatingstrongly correlated quantum systems. In this paper, we present an updated theoretical framework that unifies Darkon Research Laboratory’s Big Boot Gauge Theory (BBGT)with the Allotey Formalism of resonance scattering to establish both Ambient Temperature Topological Quantum Computing and a novel class of Quantum ProcessingAdvantage. By mapping localized core-electron excitations to non-Abelian gauge sourceson non-associative octonionic manifolds (OZIP), we demonstrate how topological boundaryconstraints natively protect qubit coherence against thermal noise at ambient temperatures(T ≈ 300 K). We then derive exact mathematical proofs for three distinct forms of quantum processing advantage enabled by this architecture: exponential fault-tolerance withoutactive error correction overhead, O(1) constant-time simulation of non-linear field thresholdsingularities, and non-associative gate compilation efficiency for complex multi-body transformations.