In the framework of Quantum Cellular Automata (QCA) and finite information ontology, we construct an effective description of single-particle long-wavelength excitations and prove a core result based on Hilbert space geometry and unitarity: for any discrete quantum walk/QCA defined by local unitary evolution and translation invariance that emerges a one-dimensional Dirac-type Hamiltonian in the continuous limit, the external group velocity (v_{ext}) and internal state evolution velocity (v_{int}