Spintronic Octonionic Tensor Processor (SOTP): Hardware Architecture, Non-Associative Causal Logic, and Subatomic State Engineering

While photonic computing platforms exploit bosonic states and four-dimensional quaternionic geometry (H) to manipulate metric fields and execute linear tensor operations, subatomic interactions and color gauge degrees of freedom demand higher-dimensional, fermionic architectures. Here, we present the theoretical foundation, physical mapping, and device architecture for the Spintronic Octonionic Tensor Processor (SOTP). Operating within an eight-dimensional normed division algebra (O), the SOTP extends the non-commutative Causal Quaternionic Field Theory (CQFT) into a non-associative regime governed by the Causal Tensor Product (⊠). In this framework, computational states depend not only on chronological execution order (τ) but also on topological clustering geometry, as formalized by a non-vanishing associator [A,B,C] ̸ = 0. We physically map the seven imaginary octonionic units (e1,...,e7) into non-collinear spintronic degrees of freedom: electron spin polarization vectors (σx,σy,σz), magnetic skyrmion topological winding numbers (Qtop ∈ Z), helicity angles, and orbital/valley pseudo-spins in two-dimensional topological heterostructures. The hardware executes non-associative logic via pure spin currents (Js) without net charge transport (Jc = 0), driven by spin-orbit torques (SOT) and Dzyaloshinskii-Moriya interactions (DMI) across Fano-plane integrated routing meshes. Finally, we model hypothetical applications in subatomic state engineering, quark-gluon field structuring, and macroscopic angular momentum-induced metric deformations, establishing the theoretical baseline for post-photonic computation.