We introduce infrared finite, analytic, crossing symmetric, Regge behaved, and Lorentz invariant amplitudes \( {\mathcal{M}}_{\mathcal{E}} \) , labeled by the experimental energy resolution \( \mathcal{E} \) for detecting soft photons and gravitons. For \( \mathcal{E} \) exponentially smaller than any hard scale, they also satisfy unitarity and their associated cross sections reproduce the inclusive, infrared-finite cross sections of ordinary amplitudes. These properties make \( {\mathcal{M}}_{\mathcal{E}} \) suitable for deriving infrared-safe positivity bounds on effective field theories in the presence of long-range forces even in D = 4. As an illustration, we present explicit bounds in the low-energy theory of pions coupled to electromagnetism and gravity.
