{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:VYF2IWZ5HOOROO7ZCCDTBSTLPZ","short_pith_number":"pith:VYF2IWZ5","schema_version":"1.0","canonical_sha256":"ae0ba45b3d3b9d173bf9108730ca6b7e6134ecd4275b48a54a0a4c75c18ef749","source":{"kind":"arxiv","id":"math/0504008","version":2},"attestation_state":"computed","paper":{"title":"Bounding volume by systoles of 3-manifolds","license":"","headline":"","cross_cats":["math.AT","math.GT","math.MG"],"primary_cat":"math.DG","authors_text":"Mikhail G. Katz, Yuli B. Rudyak","submitted_at":"2005-04-01T06:32:08Z","abstract_excerpt":"We prove a new systolic volume lower bound for non-orientable n-manifolds, involving the stable 1-systole and the codimension 1 systole with coefficients in Z_2. As an application, we prove that Lusternik-Schnirelmann category and systolic category agree for non-orientable closed manifolds of dimension 3, extending our earlier result in the orientable case. Finally, we prove the homotopy invariance of systolic category."},"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":"math/0504008","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2005-04-01T06:32:08Z","cross_cats_sorted":["math.AT","math.GT","math.MG"],"title_canon_sha256":"86ea0c08e7ef6420ece4bcec8de643e5b6b0bc2e120e97c9cc140a00b8033aed","abstract_canon_sha256":"8e8da770615d27520408ffc4636f024b6d2c4e9741a64cf403edc21601ee5d5d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:51.119621Z","signature_b64":"Ho2EePHTwqdf9QtjlkWnTsfr38uuVHK2AtoeGuFSvLCK9xp+SM6TC6PoG56OVjw3UAZRxCPthUS5VoSrF6sbAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae0ba45b3d3b9d173bf9108730ca6b7e6134ecd4275b48a54a0a4c75c18ef749","last_reissued_at":"2026-05-18T02:57:51.119061Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:51.119061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounding volume by systoles of 3-manifolds","license":"","headline":"","cross_cats":["math.AT","math.GT","math.MG"],"primary_cat":"math.DG","authors_text":"Mikhail G. Katz, Yuli B. Rudyak","submitted_at":"2005-04-01T06:32:08Z","abstract_excerpt":"We prove a new systolic volume lower bound for non-orientable n-manifolds, involving the stable 1-systole and the codimension 1 systole with coefficients in Z_2. As an application, we prove that Lusternik-Schnirelmann category and systolic category agree for non-orientable closed manifolds of dimension 3, extending our earlier result in the orientable case. Finally, we prove the homotopy invariance of systolic category."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0504008","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":"math/0504008","created_at":"2026-05-18T02:57:51.119137+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0504008v2","created_at":"2026-05-18T02:57:51.119137+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0504008","created_at":"2026-05-18T02:57:51.119137+00:00"},{"alias_kind":"pith_short_12","alias_value":"VYF2IWZ5HOOR","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_16","alias_value":"VYF2IWZ5HOOROO7Z","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_8","alias_value":"VYF2IWZ5","created_at":"2026-05-18T12:25:53.939244+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/VYF2IWZ5HOOROO7ZCCDTBSTLPZ","json":"https://pith.science/pith/VYF2IWZ5HOOROO7ZCCDTBSTLPZ.json","graph_json":"https://pith.science/api/pith-number/VYF2IWZ5HOOROO7ZCCDTBSTLPZ/graph.json","events_json":"https://pith.science/api/pith-number/VYF2IWZ5HOOROO7ZCCDTBSTLPZ/events.json","paper":"https://pith.science/paper/VYF2IWZ5"},"agent_actions":{"view_html":"https://pith.science/pith/VYF2IWZ5HOOROO7ZCCDTBSTLPZ","download_json":"https://pith.science/pith/VYF2IWZ5HOOROO7ZCCDTBSTLPZ.json","view_paper":"https://pith.science/paper/VYF2IWZ5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0504008&json=true","fetch_graph":"https://pith.science/api/pith-number/VYF2IWZ5HOOROO7ZCCDTBSTLPZ/graph.json","fetch_events":"https://pith.science/api/pith-number/VYF2IWZ5HOOROO7ZCCDTBSTLPZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VYF2IWZ5HOOROO7ZCCDTBSTLPZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VYF2IWZ5HOOROO7ZCCDTBSTLPZ/action/storage_attestation","attest_author":"https://pith.science/pith/VYF2IWZ5HOOROO7ZCCDTBSTLPZ/action/author_attestation","sign_citation":"https://pith.science/pith/VYF2IWZ5HOOROO7ZCCDTBSTLPZ/action/citation_signature","submit_replication":"https://pith.science/pith/VYF2IWZ5HOOROO7ZCCDTBSTLPZ/action/replication_record"}},"created_at":"2026-05-18T02:57:51.119137+00:00","updated_at":"2026-05-18T02:57:51.119137+00:00"}