{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"668d14c2581b3a705bda1a477818b5bbae7963cafe878c9ff59cdcefdc0910e0","created":"2026-10-03T07:18:09Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"b7e451ee78170512c55632ab62685265ce32d7a531099d2fcf0a82f4b283a791","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"qft.gravity-positivity.regge-boundedness","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"All positivity arguments assume that scattering amplitudes do not grow too fast at high energy. For gravity this growth limit is assumed, not proven.","posed_since":"","precise":"Prove that the $2 \\to 2$ amplitude of a consistent quantum gravity theory satisfies $M(s,t)/s^{2} \\to 0\\ \\text{as}\\ s \\to \\infty\\ \\text{at fixed}\\ t < 0$ (so dispersion relations with two subtractions hold), using only unitarity, analyticity, crossing and polynomial or subexponential boundedness, in $D \\ge 4$. Haring and Zhiboedov (2022) derived this bound with the extra assumption that scattering at large impact parameter is controlled by known semiclassical physics; justifying or removing that assumption, and handling $D = 4$ infrared divergences, is the open part.","problem_ref":null,"references":"","settled_by":"A proof of the $s^{2}$ bound from axioms that do not assume semiclassical large-impact-parameter behavior, or a counterexample amplitude.","status_note":"The 2022 derivation rests on the semiclassical large-impact-parameter assumption.","title":"Prove high-energy growth bound for gravitational amplitudes from first principles","topic_ref":"c287e09ddd295934e0940296a3c2ccaa657a88b499d8136c31f6e679a27a272a"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"d2c1384adb460dd367e0f22fdea3b09443b9a79f8f89562e52f7e9ded3c2a835","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"2b42d53e4b710f6e868347bb9efb1589c68a3a18eadd7a2a86c6f37fc9b685e7","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"Sfh2Y6GBSBtp3OwXylDIHZ4JGAFailiQW9P601KVT80AjcYA-6ErkXLfqBLtYndraKPY0w3C8SxR8NPcWDLBBg"},"schema":"pubphys.envelope/1"},"record_hash":"d2c1384adb460dd367e0f22fdea3b09443b9a79f8f89562e52f7e9ded3c2a835","leaf_index":1917}