IV.P145 — UV finiteness

Every morphism in tau^3 is UV-finite: loop integrals are sums over intermediate addresses at tower level n with at most prod_{p <= p_n} p terms, each well-defined in H_partial[n]. No limit n -> infinity is taken; the profinite limit is projective, not a supremum. No ultraviolet divergence arises at any perturbative order.