{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:OMBZJTJSPGJQXKIW3FTR4ZZSIP","short_pith_number":"pith:OMBZJTJS","schema_version":"1.0","canonical_sha256":"730394cd3279930ba916d9671e673243ced4ae7c5557c74268b29f6df515ce55","source":{"kind":"arxiv","id":"1803.03342","version":1},"attestation_state":"computed","paper":{"title":"Chern characters in equivariant basic cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Wenran Liu","submitted_at":"2018-03-09T00:53:36Z","abstract_excerpt":"From 1980s, it is an open problem of proposing cohomologic formula for the basic index of a transversally elliptic basic differential operator on a vector bundle over a foliated manifold. In 1990s, El Kacimi-Alaoui has proprosed to use the Molino theory for study this index. Molino has proved that to every transversally oriented Riemannien foliation, we can associate a manifold, called basique manifold, which is \\'equiped with an action of orthogonal group, El Kacimi-Alaoui has shown how to associate a transversally elliptic basic differential operator an operator on a vector bundle, called us"},"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":"1803.03342","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-09T00:53:36Z","cross_cats_sorted":[],"title_canon_sha256":"ead637ebdfd787231d9c10ce14d469c201c2537fcb0ca790836c305f8c093b02","abstract_canon_sha256":"8acbb20bd7bbc3f154cfb0ed03b4a48041376915115d41409a38d9c7dcbd9fd2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:39.883739Z","signature_b64":"E23+4I2wNTJrJBhxp/J109DK5A9okTpH9Py69ixvuSZ/ZWpY7sW6fQH7c2tQZvQyI9LZnUS1Hgvvk4DJU1XyAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"730394cd3279930ba916d9671e673243ced4ae7c5557c74268b29f6df515ce55","last_reissued_at":"2026-05-18T00:21:39.883121Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:39.883121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Chern characters in equivariant basic cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Wenran Liu","submitted_at":"2018-03-09T00:53:36Z","abstract_excerpt":"From 1980s, it is an open problem of proposing cohomologic formula for the basic index of a transversally elliptic basic differential operator on a vector bundle over a foliated manifold. In 1990s, El Kacimi-Alaoui has proprosed to use the Molino theory for study this index. Molino has proved that to every transversally oriented Riemannien foliation, we can associate a manifold, called basique manifold, which is \\'equiped with an action of orthogonal group, El Kacimi-Alaoui has shown how to associate a transversally elliptic basic differential operator an operator on a vector bundle, called us"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03342","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":"1803.03342","created_at":"2026-05-18T00:21:39.883233+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.03342v1","created_at":"2026-05-18T00:21:39.883233+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03342","created_at":"2026-05-18T00:21:39.883233+00:00"},{"alias_kind":"pith_short_12","alias_value":"OMBZJTJSPGJQ","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"OMBZJTJSPGJQXKIW","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"OMBZJTJS","created_at":"2026-05-18T12:32:43.782077+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/OMBZJTJSPGJQXKIW3FTR4ZZSIP","json":"https://pith.science/pith/OMBZJTJSPGJQXKIW3FTR4ZZSIP.json","graph_json":"https://pith.science/api/pith-number/OMBZJTJSPGJQXKIW3FTR4ZZSIP/graph.json","events_json":"https://pith.science/api/pith-number/OMBZJTJSPGJQXKIW3FTR4ZZSIP/events.json","paper":"https://pith.science/paper/OMBZJTJS"},"agent_actions":{"view_html":"https://pith.science/pith/OMBZJTJSPGJQXKIW3FTR4ZZSIP","download_json":"https://pith.science/pith/OMBZJTJSPGJQXKIW3FTR4ZZSIP.json","view_paper":"https://pith.science/paper/OMBZJTJS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.03342&json=true","fetch_graph":"https://pith.science/api/pith-number/OMBZJTJSPGJQXKIW3FTR4ZZSIP/graph.json","fetch_events":"https://pith.science/api/pith-number/OMBZJTJSPGJQXKIW3FTR4ZZSIP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OMBZJTJSPGJQXKIW3FTR4ZZSIP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OMBZJTJSPGJQXKIW3FTR4ZZSIP/action/storage_attestation","attest_author":"https://pith.science/pith/OMBZJTJSPGJQXKIW3FTR4ZZSIP/action/author_attestation","sign_citation":"https://pith.science/pith/OMBZJTJSPGJQXKIW3FTR4ZZSIP/action/citation_signature","submit_replication":"https://pith.science/pith/OMBZJTJSPGJQXKIW3FTR4ZZSIP/action/replication_record"}},"created_at":"2026-05-18T00:21:39.883233+00:00","updated_at":"2026-05-18T00:21:39.883233+00:00"}