{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:CUFAXY27AGIMHX7ZWM6POX4AKF","short_pith_number":"pith:CUFAXY27","schema_version":"1.0","canonical_sha256":"150a0be35f0190c3dff9b33cf75f80514f9e318dcc9bfbf95dc1755e7b1c0b7b","source":{"kind":"arxiv","id":"math/0401407","version":4},"attestation_state":"computed","paper":{"title":"The BIC of a singular foliation defined by an abelian group of isometries","license":"","headline":"","cross_cats":["math.AT"],"primary_cat":"math.DG","authors_text":"M. Saralegi-Aranguren, R. Wolak","submitted_at":"2004-01-28T23:57:54Z","abstract_excerpt":"We study the cohomology properties of the singular foliation $\\F$ determined by an action $\\Phi \\colon G \\times M\\to M$ where the abelian Lie group $G$ preserves a riemannian metric on the compact manifold $M$. More precisely, we prove that the basic intersection cohomology $\\lau{\\IH}{*}{\\per{p}}{\\mf}$ is finite dimensional and verifies the Poincar\\'e Duality. This duality includes two well-known situations:\n  -- Poincar\\'e Duality for basic cohomology (the action $\\Phi$ is almost free).\n  -- Poincar\\'e Duality for intersection cohomology (the group $G$ is compact and connected)."},"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/0401407","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2004-01-28T23:57:54Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"117e973503b8213ef7660cb063fe15a0de399e91e7b4f1b9d1c94d15e8abe746","abstract_canon_sha256":"d1a2c830cb1e1874691cfb065b1d54ab65401a717f5b0efb67e76ac477499380"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:26.615028Z","signature_b64":"kHGVrAfMYWd/o6MpUR5+VDcblsgM1kmRqDuEcmjV7wMKMUZO2/FcrPtXkXjo6OUJ0YLBl9GZ9EwdQpzIGI5WBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"150a0be35f0190c3dff9b33cf75f80514f9e318dcc9bfbf95dc1755e7b1c0b7b","last_reissued_at":"2026-05-18T01:05:26.614617Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:26.614617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The BIC of a singular foliation defined by an abelian group of isometries","license":"","headline":"","cross_cats":["math.AT"],"primary_cat":"math.DG","authors_text":"M. Saralegi-Aranguren, R. Wolak","submitted_at":"2004-01-28T23:57:54Z","abstract_excerpt":"We study the cohomology properties of the singular foliation $\\F$ determined by an action $\\Phi \\colon G \\times M\\to M$ where the abelian Lie group $G$ preserves a riemannian metric on the compact manifold $M$. More precisely, we prove that the basic intersection cohomology $\\lau{\\IH}{*}{\\per{p}}{\\mf}$ is finite dimensional and verifies the Poincar\\'e Duality. This duality includes two well-known situations:\n  -- Poincar\\'e Duality for basic cohomology (the action $\\Phi$ is almost free).\n  -- Poincar\\'e Duality for intersection cohomology (the group $G$ is compact and connected)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0401407","kind":"arxiv","version":4},"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/0401407","created_at":"2026-05-18T01:05:26.614680+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0401407v4","created_at":"2026-05-18T01:05:26.614680+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0401407","created_at":"2026-05-18T01:05:26.614680+00:00"},{"alias_kind":"pith_short_12","alias_value":"CUFAXY27AGIM","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_16","alias_value":"CUFAXY27AGIMHX7Z","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_8","alias_value":"CUFAXY27","created_at":"2026-05-18T12:25:52.687210+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/CUFAXY27AGIMHX7ZWM6POX4AKF","json":"https://pith.science/pith/CUFAXY27AGIMHX7ZWM6POX4AKF.json","graph_json":"https://pith.science/api/pith-number/CUFAXY27AGIMHX7ZWM6POX4AKF/graph.json","events_json":"https://pith.science/api/pith-number/CUFAXY27AGIMHX7ZWM6POX4AKF/events.json","paper":"https://pith.science/paper/CUFAXY27"},"agent_actions":{"view_html":"https://pith.science/pith/CUFAXY27AGIMHX7ZWM6POX4AKF","download_json":"https://pith.science/pith/CUFAXY27AGIMHX7ZWM6POX4AKF.json","view_paper":"https://pith.science/paper/CUFAXY27","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0401407&json=true","fetch_graph":"https://pith.science/api/pith-number/CUFAXY27AGIMHX7ZWM6POX4AKF/graph.json","fetch_events":"https://pith.science/api/pith-number/CUFAXY27AGIMHX7ZWM6POX4AKF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CUFAXY27AGIMHX7ZWM6POX4AKF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CUFAXY27AGIMHX7ZWM6POX4AKF/action/storage_attestation","attest_author":"https://pith.science/pith/CUFAXY27AGIMHX7ZWM6POX4AKF/action/author_attestation","sign_citation":"https://pith.science/pith/CUFAXY27AGIMHX7ZWM6POX4AKF/action/citation_signature","submit_replication":"https://pith.science/pith/CUFAXY27AGIMHX7ZWM6POX4AKF/action/replication_record"}},"created_at":"2026-05-18T01:05:26.614680+00:00","updated_at":"2026-05-18T01:05:26.614680+00:00"}