{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:WG23M4A3INRNYRQQ5463PGQDP5","short_pith_number":"pith:WG23M4A3","schema_version":"1.0","canonical_sha256":"b1b5b6701b4362dc4610ef3db79a037f58d61a7162dc025acaaf3e1acdc61140","source":{"kind":"arxiv","id":"1201.0361","version":1},"attestation_state":"computed","paper":{"title":"Hyperellipticity and Systoles of Klein Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.GT","math.MG"],"primary_cat":"math.DG","authors_text":"Mikhail G. Katz, Stephane Sabourau","submitted_at":"2012-01-01T16:16:38Z","abstract_excerpt":"Given a hyperelliptic Klein surface, we construct companion Klein bottles, extending our technique of companion tori already exploited by the authors in the genus 2 case. Bavard's short loops on such companion surfaces are studied in relation to the original surface so to improve a systolic inequality of Gromov's. A basic idea is to use length bounds for loops on a companion Klein bottle, and then analyze how curves transplant to the original nonorientable surface. We exploit the real structure on the orientable double cover by applying the coarea inequality to the distance function from the r"},"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":"1201.0361","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-01-01T16:16:38Z","cross_cats_sorted":["math.CV","math.GT","math.MG"],"title_canon_sha256":"71a98ccdf89849ac4e9435edb29624d617a201a6eb0a9845325daa9764653ee5","abstract_canon_sha256":"b79a75c3698037ed530f0ad9d262501d907f9518076bc74c18926ca03a966088"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:25.423096Z","signature_b64":"iGBa5Jg9kCFbQla+Ob+ARCVogX4KEFDJd4nHKEo4GWooPt9k1JiSXWykgLwV71x812dNV1Gh4PkVxm55x/6vAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1b5b6701b4362dc4610ef3db79a037f58d61a7162dc025acaaf3e1acdc61140","last_reissued_at":"2026-05-18T04:05:25.422553Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:25.422553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hyperellipticity and Systoles of Klein Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.GT","math.MG"],"primary_cat":"math.DG","authors_text":"Mikhail G. Katz, Stephane Sabourau","submitted_at":"2012-01-01T16:16:38Z","abstract_excerpt":"Given a hyperelliptic Klein surface, we construct companion Klein bottles, extending our technique of companion tori already exploited by the authors in the genus 2 case. Bavard's short loops on such companion surfaces are studied in relation to the original surface so to improve a systolic inequality of Gromov's. A basic idea is to use length bounds for loops on a companion Klein bottle, and then analyze how curves transplant to the original nonorientable surface. We exploit the real structure on the orientable double cover by applying the coarea inequality to the distance function from the r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0361","kind":"arxiv","version":1},"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":"1201.0361","created_at":"2026-05-18T04:05:25.422647+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.0361v1","created_at":"2026-05-18T04:05:25.422647+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0361","created_at":"2026-05-18T04:05:25.422647+00:00"},{"alias_kind":"pith_short_12","alias_value":"WG23M4A3INRN","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_16","alias_value":"WG23M4A3INRNYRQQ","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_8","alias_value":"WG23M4A3","created_at":"2026-05-18T12:27:25.539911+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/WG23M4A3INRNYRQQ5463PGQDP5","json":"https://pith.science/pith/WG23M4A3INRNYRQQ5463PGQDP5.json","graph_json":"https://pith.science/api/pith-number/WG23M4A3INRNYRQQ5463PGQDP5/graph.json","events_json":"https://pith.science/api/pith-number/WG23M4A3INRNYRQQ5463PGQDP5/events.json","paper":"https://pith.science/paper/WG23M4A3"},"agent_actions":{"view_html":"https://pith.science/pith/WG23M4A3INRNYRQQ5463PGQDP5","download_json":"https://pith.science/pith/WG23M4A3INRNYRQQ5463PGQDP5.json","view_paper":"https://pith.science/paper/WG23M4A3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.0361&json=true","fetch_graph":"https://pith.science/api/pith-number/WG23M4A3INRNYRQQ5463PGQDP5/graph.json","fetch_events":"https://pith.science/api/pith-number/WG23M4A3INRNYRQQ5463PGQDP5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WG23M4A3INRNYRQQ5463PGQDP5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WG23M4A3INRNYRQQ5463PGQDP5/action/storage_attestation","attest_author":"https://pith.science/pith/WG23M4A3INRNYRQQ5463PGQDP5/action/author_attestation","sign_citation":"https://pith.science/pith/WG23M4A3INRNYRQQ5463PGQDP5/action/citation_signature","submit_replication":"https://pith.science/pith/WG23M4A3INRNYRQQ5463PGQDP5/action/replication_record"}},"created_at":"2026-05-18T04:05:25.422647+00:00","updated_at":"2026-05-18T04:05:25.422647+00:00"}