{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:TURJV63MU4HOFQQEKNOWMRQ7SS","short_pith_number":"pith:TURJV63M","schema_version":"1.0","canonical_sha256":"9d229afb6ca70ee2c204535d66461f9494d89dc1360f66477c331357bb017e59","source":{"kind":"arxiv","id":"1801.00539","version":2},"attestation_state":"computed","paper":{"title":"A local systolic-diastolic inequality in contact and symplectic geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.DS"],"primary_cat":"math.SG","authors_text":"Gabriele Benedetti, Jungsoo Kang","submitted_at":"2018-01-02T03:07:40Z","abstract_excerpt":"Let $\\Sigma$ be a connected closed three-manifold, and let $t_\\Sigma$ be the order of the torsion subgroup of $H_1(\\Sigma;\\mathbb Z)$. For a contact form $\\alpha$ on $\\Sigma$, we denote by $\\mathrm{Volume}(\\alpha)$ the contact volume of $\\alpha$, and by $T_{\\min}(\\alpha)$ and $T_{\\max}(\\alpha)$ the minimal period and the maximal period of prime periodic orbits of the Reeb flow of $\\alpha$ respectively. We say that $\\alpha$ is Zoll if its Reeb flow generates a free $S^1$-action on $\\Sigma$. We prove that every Zoll contact form $\\alpha_*$ on $\\Sigma$ admits a $C^3$-neighbourhood $\\mathcal U$ in"},"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":"1801.00539","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-01-02T03:07:40Z","cross_cats_sorted":["math.DG","math.DS"],"title_canon_sha256":"90da80d7a3f55c080349ae16829ac5e527de515dd9ccb4f5960fb8212865ba95","abstract_canon_sha256":"9926e2e72eed09dc9fa7342faa702cd18fa662353201e16ab69747f5284f0760"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:41.641579Z","signature_b64":"5gmL7hOcvu9UIObP5NeZlV3AY9VOGd6D2rSQDaT2BgSGczJZvq7rSXXKQSheuuHQQD//WPByWtvqtbC3pr/zDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d229afb6ca70ee2c204535d66461f9494d89dc1360f66477c331357bb017e59","last_reissued_at":"2026-05-17T23:54:41.641009Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:41.641009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A local systolic-diastolic inequality in contact and symplectic geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.DS"],"primary_cat":"math.SG","authors_text":"Gabriele Benedetti, Jungsoo Kang","submitted_at":"2018-01-02T03:07:40Z","abstract_excerpt":"Let $\\Sigma$ be a connected closed three-manifold, and let $t_\\Sigma$ be the order of the torsion subgroup of $H_1(\\Sigma;\\mathbb Z)$. For a contact form $\\alpha$ on $\\Sigma$, we denote by $\\mathrm{Volume}(\\alpha)$ the contact volume of $\\alpha$, and by $T_{\\min}(\\alpha)$ and $T_{\\max}(\\alpha)$ the minimal period and the maximal period of prime periodic orbits of the Reeb flow of $\\alpha$ respectively. We say that $\\alpha$ is Zoll if its Reeb flow generates a free $S^1$-action on $\\Sigma$. We prove that every Zoll contact form $\\alpha_*$ on $\\Sigma$ admits a $C^3$-neighbourhood $\\mathcal U$ in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00539","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1801.00539","created_at":"2026-05-17T23:54:41.641123+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.00539v2","created_at":"2026-05-17T23:54:41.641123+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00539","created_at":"2026-05-17T23:54:41.641123+00:00"},{"alias_kind":"pith_short_12","alias_value":"TURJV63MU4HO","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"TURJV63MU4HOFQQE","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"TURJV63M","created_at":"2026-05-18T12:32:56.356000+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TURJV63MU4HOFQQEKNOWMRQ7SS","json":"https://pith.science/pith/TURJV63MU4HOFQQEKNOWMRQ7SS.json","graph_json":"https://pith.science/api/pith-number/TURJV63MU4HOFQQEKNOWMRQ7SS/graph.json","events_json":"https://pith.science/api/pith-number/TURJV63MU4HOFQQEKNOWMRQ7SS/events.json","paper":"https://pith.science/paper/TURJV63M"},"agent_actions":{"view_html":"https://pith.science/pith/TURJV63MU4HOFQQEKNOWMRQ7SS","download_json":"https://pith.science/pith/TURJV63MU4HOFQQEKNOWMRQ7SS.json","view_paper":"https://pith.science/paper/TURJV63M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.00539&json=true","fetch_graph":"https://pith.science/api/pith-number/TURJV63MU4HOFQQEKNOWMRQ7SS/graph.json","fetch_events":"https://pith.science/api/pith-number/TURJV63MU4HOFQQEKNOWMRQ7SS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TURJV63MU4HOFQQEKNOWMRQ7SS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TURJV63MU4HOFQQEKNOWMRQ7SS/action/storage_attestation","attest_author":"https://pith.science/pith/TURJV63MU4HOFQQEKNOWMRQ7SS/action/author_attestation","sign_citation":"https://pith.science/pith/TURJV63MU4HOFQQEKNOWMRQ7SS/action/citation_signature","submit_replication":"https://pith.science/pith/TURJV63MU4HOFQQEKNOWMRQ7SS/action/replication_record"}},"created_at":"2026-05-17T23:54:41.641123+00:00","updated_at":"2026-05-17T23:54:41.641123+00:00"}