Scale as a Fifth Coordinate

We explore a minimal geometric extension of spacetime in which therenormalization scale is treated as a physical coordinate. Within thisframework, physics is described by a five-dimensional metric in whichscale-dependent effects arise from geometric structure rather thanad hoc running parameters. The formalism preserves standard four-dimensional physics on fixed-scale slices while providing a geometricinterpretation of renormalization group flow. We outline the basicconstruction and discuss implications for effective four-dimensionaldescriptions.