III.T16 — Bipolar Euler Product

The split-complex zeta ζ_τ(s) admits a bipolar Euler product: ζ_τ(s) = ∏_p (1 − Label(p)·p^{−s})^{−1} where Label(p) ∈ {e₊, e₋, mixed} via the spectral trichotomy. CRT decomposition at each primorial level recovers the partial products.