{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:WW3IUDEGUI3VLY4UI6KRQL2FDV","short_pith_number":"pith:WW3IUDEG","schema_version":"1.0","canonical_sha256":"b5b68a0c86a23755e3944795182f451d5d9db546324cb86b9b25325eb0ae9c34","source":{"kind":"arxiv","id":"1610.01368","version":1},"attestation_state":"computed","paper":{"title":"Non-vanishing cohomology classes in uniform lattices of $\\text{SO}(n,\\mathbb{H})$ and automorphic representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Arghya Mondal, Parameswaran Sankaran","submitted_at":"2016-10-05T11:35:17Z","abstract_excerpt":"Let $X$ denote the non-compact globally Hermitian symmetric space of type $DIII$, namely, $\\text{SO}(n,\\mathbb{H})/\\text{U}(n)$. Let $\\Lambda$ be a uniform torsionless lattice in $\\text{SO}(n,\\mathbb{H})$. In this note we construct certain complex analytic submanifolds in the locally symmetric space $X_\\Gamma:=\\Gamma\\backslash \\text{SO}(n,\\mathbb{H})/\\text{U}(n)$ for certain finite index sub lattices $\\Gamma\\subset \\Lambda$ and show that their dual cohomology classes in $H^*(X_\\Gamma;\\mathbb{C})$ are not in the image of the Matsushima homomorphism $H^*(X_u; \\mathbb{C})\\to H^*(X_\\Gamma;\\mathbb{"},"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":"1610.01368","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-10-05T11:35:17Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"7fccc8a6611f6073e8d697e71da9904ce410fb579ce8da202d41433a0749f02d","abstract_canon_sha256":"50ccee2ec25bb74f974efb8d587ea5cda6ca6902779749ba8ec641793404c23b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:11.025515Z","signature_b64":"p+NrM0rRm16yUjyRSORWJP1Zs7Bg7qzIsKH6wkDG7L8tnE7yCB6v9755kpS6m5ii8xhFFF97EKQb2NXKBvfMBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5b68a0c86a23755e3944795182f451d5d9db546324cb86b9b25325eb0ae9c34","last_reissued_at":"2026-05-18T01:03:11.024898Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:11.024898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-vanishing cohomology classes in uniform lattices of $\\text{SO}(n,\\mathbb{H})$ and automorphic representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Arghya Mondal, Parameswaran Sankaran","submitted_at":"2016-10-05T11:35:17Z","abstract_excerpt":"Let $X$ denote the non-compact globally Hermitian symmetric space of type $DIII$, namely, $\\text{SO}(n,\\mathbb{H})/\\text{U}(n)$. Let $\\Lambda$ be a uniform torsionless lattice in $\\text{SO}(n,\\mathbb{H})$. In this note we construct certain complex analytic submanifolds in the locally symmetric space $X_\\Gamma:=\\Gamma\\backslash \\text{SO}(n,\\mathbb{H})/\\text{U}(n)$ for certain finite index sub lattices $\\Gamma\\subset \\Lambda$ and show that their dual cohomology classes in $H^*(X_\\Gamma;\\mathbb{C})$ are not in the image of the Matsushima homomorphism $H^*(X_u; \\mathbb{C})\\to H^*(X_\\Gamma;\\mathbb{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01368","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":"1610.01368","created_at":"2026-05-18T01:03:11.024971+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.01368v1","created_at":"2026-05-18T01:03:11.024971+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01368","created_at":"2026-05-18T01:03:11.024971+00:00"},{"alias_kind":"pith_short_12","alias_value":"WW3IUDEGUI3V","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"WW3IUDEGUI3VLY4U","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"WW3IUDEG","created_at":"2026-05-18T12:30:51.357362+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/WW3IUDEGUI3VLY4UI6KRQL2FDV","json":"https://pith.science/pith/WW3IUDEGUI3VLY4UI6KRQL2FDV.json","graph_json":"https://pith.science/api/pith-number/WW3IUDEGUI3VLY4UI6KRQL2FDV/graph.json","events_json":"https://pith.science/api/pith-number/WW3IUDEGUI3VLY4UI6KRQL2FDV/events.json","paper":"https://pith.science/paper/WW3IUDEG"},"agent_actions":{"view_html":"https://pith.science/pith/WW3IUDEGUI3VLY4UI6KRQL2FDV","download_json":"https://pith.science/pith/WW3IUDEGUI3VLY4UI6KRQL2FDV.json","view_paper":"https://pith.science/paper/WW3IUDEG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.01368&json=true","fetch_graph":"https://pith.science/api/pith-number/WW3IUDEGUI3VLY4UI6KRQL2FDV/graph.json","fetch_events":"https://pith.science/api/pith-number/WW3IUDEGUI3VLY4UI6KRQL2FDV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WW3IUDEGUI3VLY4UI6KRQL2FDV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WW3IUDEGUI3VLY4UI6KRQL2FDV/action/storage_attestation","attest_author":"https://pith.science/pith/WW3IUDEGUI3VLY4UI6KRQL2FDV/action/author_attestation","sign_citation":"https://pith.science/pith/WW3IUDEGUI3VLY4UI6KRQL2FDV/action/citation_signature","submit_replication":"https://pith.science/pith/WW3IUDEGUI3VLY4UI6KRQL2FDV/action/replication_record"}},"created_at":"2026-05-18T01:03:11.024971+00:00","updated_at":"2026-05-18T01:03:11.024971+00:00"}