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In the special case of the linearized Reeb flow on the boundary of a convex domain $X$ in $\\mathbb{R}^{2n}$, we prove that the Ruelle invariant $\\text{Ru}(X)$, the period of the systole $c(X)$ and the volume $\\text{vol}{X}$ satisfy \\[\\text{Ru}(X) \\cdot c(X) \\le C(n) \\cdot \\text{vol}{X}\\] Here $C(n) > 0$ is an explicit constant dependent on $n$. As an application, we construct dynamically convex contact forms on $S^{2n-1}$ that are not convex, disproving the equi"},"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":"2205.00935","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2022-05-02T14:33:57Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"0edd9462c7e957398c50b28b1ca1926ba479db8e845cc30282a00c73cf5ee2c3","abstract_canon_sha256":"cd392af8e532b179ce0dc095e6f78fff4a9d1353d9c1b7939cad42619c13fe35"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:19:26.258901Z","signature_b64":"rSXUu6h6AlTnCMRddDzSVjRY3BXNEkiJNoOgc/QG8vDJ8kQrVrDg5SswtS+MNM/QWrDUavyYHiYe2/Sk0T40CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f6978d9df7aca3f2aa96106f4eb1d0cf80cd5c848f0fe31a667763da1e30658","last_reissued_at":"2026-07-05T04:19:26.258545Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:19:26.258545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Ruelle Invariant And Convexity In Higher Dimensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.SG","authors_text":"Julian Chaidez, Oliver Edtmair","submitted_at":"2022-05-02T14:33:57Z","abstract_excerpt":"We construct the Ruelle invariant of a volume preserving flow and a symplectic cocycle in any dimension and prove several properties. 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