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Here we introduce a one-parameter family of out-of-time-ordered correlators $F_\\gamma(t)$ ($0\\leq\\gamma\\leq 1$), which has as good properties as $F(t)$ as a regularization of the out-of-time-ordered part of the squared commutator $\\langle [A(t), B(0)]^2\\rangle$ that diagnoses quantum many-body chaos, and coincides with $F(t)$ at $\\gamma=1/2$. We rigorously prove that "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1706.09160","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-06-28T08:05:27Z","cross_cats_sorted":["hep-th","quant-ph"],"title_canon_sha256":"73ef4b1cb83e950a62ef36c8d68e2aee0fde56e590dded063b06de3aa72cd887","abstract_canon_sha256":"970d6f6e8b61128233640faee5335e4baeb7a61b58c371aca71b2a607ad7af83"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:48.560716Z","signature_b64":"fQS2nntDdLLAG+Eh0CHWtGmXk+LMyfamo5fR8Wa7DbFzuAKvf0+dr7GWI0fp/gtFYb4aGTg1NxE05M2jKcRxAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97d4af32293e28b3dad50383178fd357bc2dd8a3968af07388e36bf7f1ea1b53","last_reissued_at":"2026-05-18T00:08:48.560177Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:48.560177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bound on the exponential growth rate of out-of-time-ordered correlators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","quant-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Masahito Ueda, Naoto Tsuji, Tomohiro Shitara","submitted_at":"2017-06-28T08:05:27Z","abstract_excerpt":"It has been conjectured by Maldacena, Shenker, and Stanford [J. High Energy Phys.~08 (2016) 106] that the exponential growth rate of the out-of-time-ordered correlator (OTOC) $F(t)$ has a universal upper bound $2\\pi k_B T/\\hbar$. Here we introduce a one-parameter family of out-of-time-ordered correlators $F_\\gamma(t)$ ($0\\leq\\gamma\\leq 1$), which has as good properties as $F(t)$ as a regularization of the out-of-time-ordered part of the squared commutator $\\langle [A(t), B(0)]^2\\rangle$ that diagnoses quantum many-body chaos, and coincides with $F(t)$ at $\\gamma=1/2$. 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