Juncai Zhou

The Hybrid Group ⊕_γ over ℝ and 𝔽_p: Face Operations, Transport Rigidity, Gradient-free Learning, and a Fully-Resident Software Protection Loader

This work develops a self-contained algebraic framework based on the hybrid group operator a ⊕_γ b = a + b + γ ab, defined simultaneously on real vector spaces and prime fields. We establish the face-operation calculus (M, A, D, E faces), prove the dual-derivative power theorem which gives an exact additive-to-multipli...