{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:I7JWGHLBKMRY4WBEGONVW72F2X","short_pith_number":"pith:I7JWGHLB","schema_version":"1.0","canonical_sha256":"47d3631d6153238e5824339b5b7f45d5f39bc7ddce77d15109bfbeab77f34cbd","source":{"kind":"arxiv","id":"1105.5205","version":2},"attestation_state":"computed","paper":{"title":"Smooth (non)rigidity of piecewise rank one locally symmetric manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"T. Tam Nguyen Phan","submitted_at":"2011-05-26T05:29:21Z","abstract_excerpt":"We define \\emph{piecewise rank 1} manifolds, which are aspherical manifolds that generally do not admit a nonpositively curved metric but can be decomposed into pieces that are diffeomorphic to finite volume, irreducible, locally symmetric, nonpositively curved manifolds with $\\pi_1$-injective cusps. We prove smooth (self) rigidity for this class of manifolds in the case where the gluing preserves the cusps' homogeneous structure. We compute the group of self homotopy equivalences of such a manifold and show that it can contain a normal free abelian subgroup and thus, can be infinite. Elements"},"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":"1105.5205","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-05-26T05:29:21Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"5cc6548f710703f44d6fb3326cea65e4f8dbe9d5beeab2667c1ddb1e497928cb","abstract_canon_sha256":"cc898c0eff4e2f2583b6d07e979fe1c3d6885909aa962c984926b2f624f169bf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:00.873001Z","signature_b64":"1Nmj1syDC8+YBMMQA6vNlwhkQDX1hktfyid0WpqfP9SDlUnIs03KphmzRISs5Csv2Gyk6RaCJMmAyRZUtL8CDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47d3631d6153238e5824339b5b7f45d5f39bc7ddce77d15109bfbeab77f34cbd","last_reissued_at":"2026-05-18T02:58:00.872433Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:00.872433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Smooth (non)rigidity of piecewise rank one locally symmetric manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"T. Tam Nguyen Phan","submitted_at":"2011-05-26T05:29:21Z","abstract_excerpt":"We define \\emph{piecewise rank 1} manifolds, which are aspherical manifolds that generally do not admit a nonpositively curved metric but can be decomposed into pieces that are diffeomorphic to finite volume, irreducible, locally symmetric, nonpositively curved manifolds with $\\pi_1$-injective cusps. We prove smooth (self) rigidity for this class of manifolds in the case where the gluing preserves the cusps' homogeneous structure. We compute the group of self homotopy equivalences of such a manifold and show that it can contain a normal free abelian subgroup and thus, can be infinite. Elements"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5205","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":"1105.5205","created_at":"2026-05-18T02:58:00.872545+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.5205v2","created_at":"2026-05-18T02:58:00.872545+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.5205","created_at":"2026-05-18T02:58:00.872545+00:00"},{"alias_kind":"pith_short_12","alias_value":"I7JWGHLBKMRY","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"I7JWGHLBKMRY4WBE","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"I7JWGHLB","created_at":"2026-05-18T12:26:30.835961+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/I7JWGHLBKMRY4WBEGONVW72F2X","json":"https://pith.science/pith/I7JWGHLBKMRY4WBEGONVW72F2X.json","graph_json":"https://pith.science/api/pith-number/I7JWGHLBKMRY4WBEGONVW72F2X/graph.json","events_json":"https://pith.science/api/pith-number/I7JWGHLBKMRY4WBEGONVW72F2X/events.json","paper":"https://pith.science/paper/I7JWGHLB"},"agent_actions":{"view_html":"https://pith.science/pith/I7JWGHLBKMRY4WBEGONVW72F2X","download_json":"https://pith.science/pith/I7JWGHLBKMRY4WBEGONVW72F2X.json","view_paper":"https://pith.science/paper/I7JWGHLB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.5205&json=true","fetch_graph":"https://pith.science/api/pith-number/I7JWGHLBKMRY4WBEGONVW72F2X/graph.json","fetch_events":"https://pith.science/api/pith-number/I7JWGHLBKMRY4WBEGONVW72F2X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I7JWGHLBKMRY4WBEGONVW72F2X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I7JWGHLBKMRY4WBEGONVW72F2X/action/storage_attestation","attest_author":"https://pith.science/pith/I7JWGHLBKMRY4WBEGONVW72F2X/action/author_attestation","sign_citation":"https://pith.science/pith/I7JWGHLBKMRY4WBEGONVW72F2X/action/citation_signature","submit_replication":"https://pith.science/pith/I7JWGHLBKMRY4WBEGONVW72F2X/action/replication_record"}},"created_at":"2026-05-18T02:58:00.872545+00:00","updated_at":"2026-05-18T02:58:00.872545+00:00"}