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This bound is sharp and it becomes an equality for an eigenvalue of a simple irreversible cycle $A_1 \\to A_2 \\to... \\to A_n \\to A_1$ with equal rate constants of all transitions. Therefore, the simple cycle with the equal rate constants has the slowest decay of the oscillations among all first order kinetic systems wi"},"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":"1301.2379","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"physics.chem-ph","submitted_at":"2013-01-11T02:00:18Z","cross_cats_sorted":[],"title_canon_sha256":"2e39d5cff0b288c24eb8d6ab78804216aa93a2b5010eca234715b2aa4f939b9e","abstract_canon_sha256":"f693f4c28adcece1fee31506a70325dea72ce8f8c46cac8b66b547961622251f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:38.082432Z","signature_b64":"LPFvYRdagGtMsSEswecrhUOp5OoFNbJ1bI5/yRM2wTVsQAoDeGepGdCKeNVg271iPE/yvErJe8VpmFI4Kpr7BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56eb6117ee80231ddb6c64cb919c5698c8a04b25f382a66eac6761e92a09a8b4","last_reissued_at":"2026-05-18T03:36:38.081969Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:38.081969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extremal property of a simple cycle","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"physics.chem-ph","authors_text":"A. 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