Geometric Derivation of the Uncertainty Principle and Reconstruction of Deterministic Quantum Mechanics via Non-Associative Octonionic Algebra

A deterministic framework for quantum mechanics is constructed utilizing the split octonionic algebra Osplit. Heisenberg’s uncertainty principle is derived as an algebraic identity from the trivalent associator on the manifold, restricting microscopic state functions to minimal left ideals. The current formulation ensures that quantum uncertainty remains a purely deterministic topological effect, governed by the intrinsic discrete volume constraints of the underlying division algebra. The present framework maps quantum observables directly into a completely deterministic geometric flow, defining the mass quantum as a stable topological soliton on the non-associative worldsheet.