Gaussian Unit Symmetry as an Algebraic Origin for Discrete Charge on the E_7 Lattice

Electric charge is quantized: all observed charges are integer multiples of e/3. The Standard Modelaccommodates this fact but does not explain it. The two existing explanations — Dirac's magneticmonopole argument (1931) and grand unification — both require physics beyond the StandardModel that has not been observed. We present a third mechanism: the Gaussian unit groupZ[i]* = {1, i, -1, -i} acts as a Z_4 symmetry on the 56-dimensional charge lattice of E_7(7), theU-duality group of maximal supergravity in four dimensions. This Z_4 action forces the quarticinvariant I_4 — which determines black hole entropy — to be the lowest nontrivial polynomialinvariant, and restricts all charges to a discrete lattice. The mechanism requires no magneticmonopoles and no grand unification: it derives charge quantization from the arithmetic of Gaussianintegers acting on an exceptional Lie algebra's charge representation. We verify the Z_4 actionexplicitly on the full 56-dimensional representation and show that three independently defined Z_4symmetries (topological, algebraic, and Hamiltonian) act identically.