{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DU73OD4VYQHWWDUT722L566RXZ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2a0c6ff96edfd2e715c3be56b745c9937c15e148da005ada825e5be52510a747","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-07-08T22:01:47Z","title_canon_sha256":"3529c453cd58c9f5af57d02d55ed1569d209d58b06cf3e08f5ec8265cca3291f"},"schema_version":"1.0","source":{"id":"1107.1741","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1741","created_at":"2026-05-18T03:39:05Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1741v3","created_at":"2026-05-18T03:39:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1741","created_at":"2026-05-18T03:39:05Z"},{"alias_kind":"pith_short_12","alias_value":"DU73OD4VYQHW","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DU73OD4VYQHWWDUT","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DU73OD4V","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:bc70b0bdf26653edf803ee43de5ee30f012a649732b097d4573562073c3dc67d","target":"graph","created_at":"2026-05-18T03:39:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let X be a closed connected contact manifold. On X there is a naturally arising class of hypoelliptic (but not elliptic) operators which are Fredholm. In this paper we solve the index problem for this class of operators. The solution is achieved by combining Van Erp's earlier partial result with the Baum-Douglas isomorphism of analytic and geometric K-homology.","authors_text":"Erik van Erp, Paul F. Baum","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-07-08T22:01:47Z","title":"K-homology and index theory on contact manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1741","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:70bbc540cfb0a1b5998566e2c5ff96a6c8d45b2c715ee956d07c462343f0c118","target":"record","created_at":"2026-05-18T03:39:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2a0c6ff96edfd2e715c3be56b745c9937c15e148da005ada825e5be52510a747","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-07-08T22:01:47Z","title_canon_sha256":"3529c453cd58c9f5af57d02d55ed1569d209d58b06cf3e08f5ec8265cca3291f"},"schema_version":"1.0","source":{"id":"1107.1741","kind":"arxiv","version":3}},"canonical_sha256":"1d3fb70f95c40f6b0e93feb4befbd1be5fb32517f1010e9ac0fdbc2cdacb6537","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d3fb70f95c40f6b0e93feb4befbd1be5fb32517f1010e9ac0fdbc2cdacb6537","first_computed_at":"2026-05-18T03:39:05.417970Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:05.417970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z+2dKeae7Q+6ODRRnNn1Ze4yGU3fl/3hUfj9GIuI6Q/Mg/X7uRYgj9+v9uYVWBvGfu3Gr4/esjZMglHhCOd/DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:05.418651Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.1741","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70bbc540cfb0a1b5998566e2c5ff96a6c8d45b2c715ee956d07c462343f0c118","sha256:bc70b0bdf26653edf803ee43de5ee30f012a649732b097d4573562073c3dc67d"],"state_sha256":"1d160788b9a909af29b94eeab870b8461157b00b250187909cb77d55cb71442c"}