{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"896207ec2e1de0cd41b3a3a497a85ee1871359c8c7aa3c02ec05d299f613e0a9","created":"2026-10-03T07:18:04Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"2c0c0525db05243ae463370956282881c5ad9f5bb66046e23d72b604544c050d","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"grav.strong-field-tests.quadratic-modes","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"General relativity is nonlinear, so two ringing tones of a black hole should combine into weaker extra tones at the sum of their frequencies. Detecting them would test the nonlinear part of Einstein's equations.","posed_since":"","precise":"Second-order perturbation theory predicts a mode at frequency $2\\omega_{220}$ in the $(4,4)$ harmonic with amplitude ratio $A_{220x220}/(A_{220})^2$ fixed by the remnant spin (measured in simulations, 2023). Determine whether such quadratic modes are detected in gravitational-wave data at $5\\sigma$ or more, confirmed by independent pipelines, and whether the amplitude ratio matches the general-relativity value. An answer is a detection with a measured ratio, or an upper limit inconsistent with the prediction.","problem_ref":null,"references":"","settled_by":"A detection of the quadratic $(4,4)$ mode at $5\\sigma$ in one or more loud events with the amplitude ratio measured.","status_note":"Non-collaboration analyses of GW250114 report quadratic-mode evidence at $3.4\\,\\sigma$ (Wang et al., arXiv:2601.05734, 2026) with the coupling consistent with general relativity within $1.3\\,\\sigma$ (Yang, Shi, Hu, arXiv:2609.28953, 2026); there is no collaboration or $5\\,\\sigma$ detection as of October 2026.","title":"Are quadratic quasinormal modes present in observed ringdowns?","topic_ref":"bc4b175d5b29c50050e1c97990c34784beaa0b526c07994422c4f929f682a68b"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"ce7dab931baac03c991da6aa5642fc42a8716cec61e997f57c86d0c85f5cbeef","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"4421a4c32345f43faf5bde3b665422aa0d722d27038bc4e990d1a218214a4536","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"CoTxdR9cgh6R90cf2FQ9MPyGo3BsgRyijWeicPfxpGgpDDIHkhZWoWjDPY2F6WJxFe_LFcYZLx6uzR-shTqOAg"},"schema":"pubphys.envelope/1"},"record_hash":"ce7dab931baac03c991da6aa5642fc42a8716cec61e997f57c86d0c85f5cbeef","leaf_index":1514}