{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"47730b5040ee19e1f09da700a370aa18ba1ac401f369d0930fc0b1088f0fe2d4","created":"2026-10-03T07:18:09Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"d0d3747eaf340169a3a925e34574afdeec0bf47c1249102f75486bf59479ed1e","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"qft.gravity-positivity.four-d-ir-log","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"In four dimensions, the known bounds that account for gravity depend, through a logarithm, on an arbitrary largest distance, because gravity's pull falls off too slowly. A version free of this dependence is not known.","posed_since":"","precise":"Dispersive bounds on 4D gravitational EFT coefficients (for example $R^3$ and $R^4$ corrections to Einstein gravity) obtained from smeared impact-parameter sum rules hold only up to a factor $\\log(b_{\\mathrm{IR}} M)$, where $b_{\\mathrm{IR}}$ is an infrared impact-parameter cutoff and $M$ the EFT cutoff (Caron-Huot, Li, Parra-Martinez, Simmons-Duffin, JHEP 05 (2023) 122). Find an infrared-safe observable whose sum rules give bounds independent of $b_{\\mathrm{IR}}$, or prove that the logarithm cannot be removed.","problem_ref":null,"references":"","settled_by":"A 4D sum rule built from infrared-finite quantities that yields cutoff-independent bounds, or a no-go theorem.","status_note":"Bounds valid up to the infrared logarithm were derived in 2022; cutoff-independent versions are not established.","title":"Bounds on four-dimensional gravitational couplings free of infrared logarithms","topic_ref":"c287e09ddd295934e0940296a3c2ccaa657a88b499d8136c31f6e679a27a272a"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"72fb660f95d4165c8e4ea70809f6c9423eff3f1902bdd64c6812f7b319e4b59e","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"fb2fd2e94e8646495f24a44035e223b14064a3181269a9eac4f7afedea81b543","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"xWh9ulayw7OKO4o_GNpZhtGMeYqdfzPFDr-1-2O9E08cdakj5qc_xwnPGfzJfSBiB1B7tT1HWfA74YthLwgKBA"},"schema":"pubphys.envelope/1"},"record_hash":"72fb660f95d4165c8e4ea70809f6c9423eff3f1902bdd64c6812f7b319e4b59e","leaf_index":1915}