{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:KGSTU6ER637CXWSXEBOIUIAKYM","short_pith_number":"pith:KGSTU6ER","schema_version":"1.0","canonical_sha256":"51a53a7891f6fe2bda57205c8a200ac313f5e5055aafa6c6409b8b3a4789757d","source":{"kind":"arxiv","id":"1102.1516","version":13},"attestation_state":"computed","paper":{"title":"The Homotopy Type of a Poincar\\'e Duality Complex after Looping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Jie Wu, Piotr Beben","submitted_at":"2011-02-08T06:19:56Z","abstract_excerpt":"We answer a weaker version of the classification problem for the homotopy types of $(n-2)$-connected closed orientable $(2n-1)$-manifolds. Let $n\\geq 6$ be an even integer, and $X$ be a $(n-2)$-connected finite orientable Poincar\\'e $(2n-1)$-complex such that $H^{n-1}(X;\\mathbb{Q})=0$ and $H^{n-1}(X;\\mathbb{Z}_2)=0$. Then its loop space homotopy type is uniquely determined by the action of higher Bockstein operations on $H^{n-1}(X;\\mathbb{Z}_p)$ for each odd prime $p$. A stronger result is obtained when localized at odd primes."},"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":"1102.1516","kind":"arxiv","version":13},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-02-08T06:19:56Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"6be18dacf05609edb51c371f7845c433964c9b52f36b852536fb70215f09d9d7","abstract_canon_sha256":"1be88f46174f806985183ac349477ea9260fcc732546f34b7869a7273b412806"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:40.793940Z","signature_b64":"bqm743Bki1vqvq6/PVh9h4uX3FlBfMPXYKfmf+i1XltLBZaliWyPbLdLbcIvAa7LskgKVa7zWAh1wjGHEePYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51a53a7891f6fe2bda57205c8a200ac313f5e5055aafa6c6409b8b3a4789757d","last_reissued_at":"2026-05-18T02:50:40.793481Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:40.793481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Homotopy Type of a Poincar\\'e Duality Complex after Looping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Jie Wu, Piotr Beben","submitted_at":"2011-02-08T06:19:56Z","abstract_excerpt":"We answer a weaker version of the classification problem for the homotopy types of $(n-2)$-connected closed orientable $(2n-1)$-manifolds. Let $n\\geq 6$ be an even integer, and $X$ be a $(n-2)$-connected finite orientable Poincar\\'e $(2n-1)$-complex such that $H^{n-1}(X;\\mathbb{Q})=0$ and $H^{n-1}(X;\\mathbb{Z}_2)=0$. Then its loop space homotopy type is uniquely determined by the action of higher Bockstein operations on $H^{n-1}(X;\\mathbb{Z}_p)$ for each odd prime $p$. A stronger result is obtained when localized at odd primes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1516","kind":"arxiv","version":13},"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":"1102.1516","created_at":"2026-05-18T02:50:40.793545+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.1516v13","created_at":"2026-05-18T02:50:40.793545+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1516","created_at":"2026-05-18T02:50:40.793545+00:00"},{"alias_kind":"pith_short_12","alias_value":"KGSTU6ER637C","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"KGSTU6ER637CXWSX","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"KGSTU6ER","created_at":"2026-05-18T12:26:32.869790+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/KGSTU6ER637CXWSXEBOIUIAKYM","json":"https://pith.science/pith/KGSTU6ER637CXWSXEBOIUIAKYM.json","graph_json":"https://pith.science/api/pith-number/KGSTU6ER637CXWSXEBOIUIAKYM/graph.json","events_json":"https://pith.science/api/pith-number/KGSTU6ER637CXWSXEBOIUIAKYM/events.json","paper":"https://pith.science/paper/KGSTU6ER"},"agent_actions":{"view_html":"https://pith.science/pith/KGSTU6ER637CXWSXEBOIUIAKYM","download_json":"https://pith.science/pith/KGSTU6ER637CXWSXEBOIUIAKYM.json","view_paper":"https://pith.science/paper/KGSTU6ER","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.1516&json=true","fetch_graph":"https://pith.science/api/pith-number/KGSTU6ER637CXWSXEBOIUIAKYM/graph.json","fetch_events":"https://pith.science/api/pith-number/KGSTU6ER637CXWSXEBOIUIAKYM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KGSTU6ER637CXWSXEBOIUIAKYM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KGSTU6ER637CXWSXEBOIUIAKYM/action/storage_attestation","attest_author":"https://pith.science/pith/KGSTU6ER637CXWSXEBOIUIAKYM/action/author_attestation","sign_citation":"https://pith.science/pith/KGSTU6ER637CXWSXEBOIUIAKYM/action/citation_signature","submit_replication":"https://pith.science/pith/KGSTU6ER637CXWSXEBOIUIAKYM/action/replication_record"}},"created_at":"2026-05-18T02:50:40.793545+00:00","updated_at":"2026-05-18T02:50:40.793545+00:00"}