A Real-Constrained Analytic Continuation of 5D SVS-EFT: from Real Cl(2,3) to Complex Cl(5,C)

This paper physically strengthens a proposed five-dimensional Scalar-Vector-Spinor effective field theory (5D SVS-EFT) by analytic continuation. The starting point is the real 5D SVS-EFT paper in which a single real Clifford multivector in Cl(2,3) is projected to four-dimensional scalar, vector, gauge, spinor, and gravitational sectors through compact-order and metaplectic maps 1. The present paper asks whether a controlled complex continuation to Cl(5,C) can play a role analogous to the Dirac linearization of relativistic wave mechanics: not as an arbitrary doubling of fields, but as a guiding analytic structure that sharpens real physical constraints. We therefore replace the phrase 'complex freedom' by a more restrictive principle: real constraints, complex guidance. The complexified algebra supplies a natural language for minimal ideals, color-like subspaces, monogenic equations, reflection conditions, and global analytic continuation. Physical observables, however, remain anchored on a real four-dimensional slice, where causality, positivity, compact-order boundary conditions, and Standard Model phenomenology must be recovered. A Global Analyticity Constraint (GAC) is proposed as a non-local selection rule: among all local complex extensions that agree with a real low-energy surface, only the extension satisfying reality, reflection, boundary-spectrum, and monodromy constraints is admissible. In this way, complexification can reduce rather than increase the viable parameter space. The paper deliberately simplifies formal derivations and emphasizes the physical content: how the real Cl(2,3) framework, compact Matsubara-like order coordinate, metaplectic projection, and Cl(5,C) continuation may be organized into a falsifiable effective theory. The expected signatures include correlated carrier-frequency shifts in complex scattering systems, coherent gravitational-wave residuals, constrained birefringence, and the absence of generic SU(5)-like proton decay channels.