{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"4b11e95b100404f987a5b9a69c5724df8d33343fd1da1a284e2df8935eda315f","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b","df45c1fff56a5577cac4689c0fc8e4aec93697163d7d850de81b3992b7b593c7"],"salt":"68e590f1d607cefe4a5eb601a98861fb3c6d0c6f903125febc85846b688d9337","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"qft.gravity-positivity.allowed-negativity","kind":"well-posed","literature_status":"contested","n":"2","parents":[],"plain":"Without gravity, a certain coefficient in the scattering of two particles must be positive. With gravity it may be slightly negative, and the size of the allowed negative value is not known.","posed_since":"","precise":"For a weakly coupled 4D effective field theory of a massless scalar coupled to Einstein gravity, with $2\\to 2$ amplitude $M(s,t) = 8\\pi G s^2/(-t) + c_2 s^2/\\Lambda^4 + ...$, determine the lowest value of $c_2$ consistent with unitarity, analyticity, crossing and a UV completion whose amplitude Reggeizes (grows as $s^{2 + \\alpha' t}$) above a scale $M_*$. Under this Regge assumption proposals give $c_2 \\ge -\\operatorname{O}(\\Lambda^4/(M_{\\mathrm{pl}}^2 M_*^2))$; smeared impact-parameter sum rules in $D = 4$ instead give $c_2 \\ge -\\operatorname{O}(G \\Lambda^4/M^2)\\log(M b_{\\mathrm{IR}})$, where $M$ is the EFT cutoff and $b_{\\mathrm{IR}}$ an infrared impact-parameter cutoff. An answer is the optimal bound in $D = 4$ with its assumptions stated, saying which form is optimal, or an explicit consistent UV completion that violates it.","problem_ref":"df45c1fff56a5577cac4689c0fc8e4aec93697163d7d850de81b3992b7b593c7","references":"","settled_by":"A derivation from stated axioms of the optimal lower bound on $c_{2}$, checked against explicit string-theory amplitudes.","status_note":"Bounds allowing Planck-suppressed negativity have been derived since 2020, but their size depends on the assumed Regge behavior of the UV completion or on an infrared cutoff.","title":"How negative can forward-limit coefficients be once gravity is included?","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"21af56577f363265dbce1688acb8cbb490255b8929f231d109ef9534ee8e9a21","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"d0fef892c8d9e78dcff432b64013abcb1711d785c58c540407890103d1d5fe92","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"Nf1ZFNIIK963_lmDRvLkofKL6L0RTkp3GoydFiZjx_ah_uqw6M2_BK-x2D7kT0Ykkpu9NC3NqPruH8-ccAd-Dw"},"schema":"pubphys.envelope/1"},"record_hash":"21af56577f363265dbce1688acb8cbb490255b8929f231d109ef9534ee8e9a21","leaf_index":3648}