{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:F2YQCXWFPSB7HXQQECKX336H6H","short_pith_number":"pith:F2YQCXWF","schema_version":"1.0","canonical_sha256":"2eb1015ec57c83f3de1020957defc7f1c495995b65316c023b1032906094335b","source":{"kind":"arxiv","id":"1310.1577","version":5},"attestation_state":"computed","paper":{"title":"On homological rigidity and flexibility of exact Lagrangian endocobordisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Georgios Dimitroglou Rizell, Roman Golovko","submitted_at":"2013-10-06T11:56:34Z","abstract_excerpt":"We show that an exact Lagrangian cobordism $L\\subset \\mathbb R \\times P \\times \\mathbb R$ from a Legendrian submanifold $\\Lambda\\subset P\\times \\mathbb R$ to itself satisfies $H_i(L;\\mathbb F)=H_i(\\Lambda;\\mathbb F)$ for any field $\\mathbb F$ in the case when $\\Lambda$ admits a spin exact Lagrangian filling and the concatenation of any spin exact Lagrangian filling of $\\Lambda$ and $L$ is also spin. The main tool used is Seidel's isomorphism in wrapped Floer homology. In contrast to that, for loose Legendrian submanifolds of $\\mathbb{C}^n \\times \\mathbb R$, we construct examples of such cobord"},"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":"1310.1577","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-10-06T11:56:34Z","cross_cats_sorted":[],"title_canon_sha256":"20c232af36e6ad8c658939581541fd493df3cee74f8360e815f336069c1ec754","abstract_canon_sha256":"ec41a5f88ca13136b8891f95dd4ccc261f0ad2fdfbefda420df571a98fa2cabc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:08.864522Z","signature_b64":"8a16sJiCpL/vODIcdJDoKUzlf9jOL3avjFAfCTYuNPFr0Tw6oDwTqjGrmGiaCRLgDaolzNnT72Bh9D4Z99tbCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2eb1015ec57c83f3de1020957defc7f1c495995b65316c023b1032906094335b","last_reissued_at":"2026-05-18T01:25:08.863902Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:08.863902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On homological rigidity and flexibility of exact Lagrangian endocobordisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Georgios Dimitroglou Rizell, Roman Golovko","submitted_at":"2013-10-06T11:56:34Z","abstract_excerpt":"We show that an exact Lagrangian cobordism $L\\subset \\mathbb R \\times P \\times \\mathbb R$ from a Legendrian submanifold $\\Lambda\\subset P\\times \\mathbb R$ to itself satisfies $H_i(L;\\mathbb F)=H_i(\\Lambda;\\mathbb F)$ for any field $\\mathbb F$ in the case when $\\Lambda$ admits a spin exact Lagrangian filling and the concatenation of any spin exact Lagrangian filling of $\\Lambda$ and $L$ is also spin. The main tool used is Seidel's isomorphism in wrapped Floer homology. In contrast to that, for loose Legendrian submanifolds of $\\mathbb{C}^n \\times \\mathbb R$, we construct examples of such cobord"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1577","kind":"arxiv","version":5},"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":"1310.1577","created_at":"2026-05-18T01:25:08.863987+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.1577v5","created_at":"2026-05-18T01:25:08.863987+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1577","created_at":"2026-05-18T01:25:08.863987+00:00"},{"alias_kind":"pith_short_12","alias_value":"F2YQCXWFPSB7","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"F2YQCXWFPSB7HXQQ","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"F2YQCXWF","created_at":"2026-05-18T12:27:43.054852+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/F2YQCXWFPSB7HXQQECKX336H6H","json":"https://pith.science/pith/F2YQCXWFPSB7HXQQECKX336H6H.json","graph_json":"https://pith.science/api/pith-number/F2YQCXWFPSB7HXQQECKX336H6H/graph.json","events_json":"https://pith.science/api/pith-number/F2YQCXWFPSB7HXQQECKX336H6H/events.json","paper":"https://pith.science/paper/F2YQCXWF"},"agent_actions":{"view_html":"https://pith.science/pith/F2YQCXWFPSB7HXQQECKX336H6H","download_json":"https://pith.science/pith/F2YQCXWFPSB7HXQQECKX336H6H.json","view_paper":"https://pith.science/paper/F2YQCXWF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.1577&json=true","fetch_graph":"https://pith.science/api/pith-number/F2YQCXWFPSB7HXQQECKX336H6H/graph.json","fetch_events":"https://pith.science/api/pith-number/F2YQCXWFPSB7HXQQECKX336H6H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F2YQCXWFPSB7HXQQECKX336H6H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F2YQCXWFPSB7HXQQECKX336H6H/action/storage_attestation","attest_author":"https://pith.science/pith/F2YQCXWFPSB7HXQQECKX336H6H/action/author_attestation","sign_citation":"https://pith.science/pith/F2YQCXWFPSB7HXQQECKX336H6H/action/citation_signature","submit_replication":"https://pith.science/pith/F2YQCXWFPSB7HXQQECKX336H6H/action/replication_record"}},"created_at":"2026-05-18T01:25:08.863987+00:00","updated_at":"2026-05-18T01:25:08.863987+00:00"}