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The systolic ratio of $\\alpha$ is defined as $\\rho_{\\mathrm{sys}}(\\alpha):=\\tfrac{1}{\\mathrm{Vol}(\\alpha)}T_{\\min}(\\alpha)^2$, where $T_{\\min}(\\alpha)$ and $\\mathrm{Vol}(\\alpha)$ denote the minimal period of periodic Reeb orbits and the contact volume. The form $\\alpha$ is said to be Zoll if its Reeb flow generates a free $S^1$-action on $\\Sigma$. We prove that the set of Zoll contact forms on $\\Sigma$ locally maximises the systolic ratio in the $C^3$-topology. More precisely, we show that every Zoll form $\\alpha_*$ "},"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":"1902.01249","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2019-02-04T15:24:16Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"fb852662b0602cc4de53d88e4cfcd2d7d183e50d52cf747bb5395c160e48efac","abstract_canon_sha256":"b5a82380eb744dda0a7ab06cfc7d7984d0d5488977f8e14108a4a689fdd914ac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:38.672922Z","signature_b64":"vFzCF/61o6mR0H3Sg2yVQN43vmiWUoC9xYqGqvcmnUVQtvM1MW4QRT4T6U0r8GINI7X2bikrrBvHDop7UnbxCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbe9b9b086a8472814f73b2ba5cb2236956744ce43e718ef2553df61f7ad87ae","last_reissued_at":"2026-05-17T23:54:38.672338Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:38.672338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A local contact systolic inequality in dimension three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Gabriele Benedetti, Jungsoo Kang","submitted_at":"2019-02-04T15:24:16Z","abstract_excerpt":"Let $\\alpha$ be a contact form on a connected closed three-manifold $\\Sigma$. The systolic ratio of $\\alpha$ is defined as $\\rho_{\\mathrm{sys}}(\\alpha):=\\tfrac{1}{\\mathrm{Vol}(\\alpha)}T_{\\min}(\\alpha)^2$, where $T_{\\min}(\\alpha)$ and $\\mathrm{Vol}(\\alpha)$ denote the minimal period of periodic Reeb orbits and the contact volume. The form $\\alpha$ is said to be Zoll if its Reeb flow generates a free $S^1$-action on $\\Sigma$. We prove that the set of Zoll contact forms on $\\Sigma$ locally maximises the systolic ratio in the $C^3$-topology. 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