{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HC66WXYZMOBVW7BTCPUVNRSK7R","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":"b2cbf40db6c621d75d124cdb48c9657ceaa199b464efe3580594102fb9638d9c","cross_cats_sorted":["math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-01-05T12:57:12Z","title_canon_sha256":"64980fd510b405c7fbac595083cab206b933fc9c9274bb80824232042bca2928"},"schema_version":"1.0","source":{"id":"1501.00842","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.00842","created_at":"2026-05-18T00:10:04Z"},{"alias_kind":"arxiv_version","alias_value":"1501.00842v1","created_at":"2026-05-18T00:10:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00842","created_at":"2026-05-18T00:10:04Z"},{"alias_kind":"pith_short_12","alias_value":"HC66WXYZMOBV","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"HC66WXYZMOBVW7BT","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"HC66WXYZ","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:045cf3fe5b157592ee8bf92c36585df7079b3221291bf986f2d0efcb769236f3","target":"graph","created_at":"2026-05-18T00:10:04Z","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 $M$ be a compact abstract $CR$ manifold of arbitrary $CR$ codimension. Under certain conditions on the Levi form we prove the infinite dimensionality of some global cohomology groups of $M$.","authors_text":"C. Denson Hill, Judith Brinkschulte","cross_cats":["math.AP","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-01-05T12:57:12Z","title":"Obstructions to finite dimensional cohomology of abstract Cauchy-Riemann complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00842","kind":"arxiv","version":1},"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":"sha256:619aa970ea24af79187630e2d6d3941f149acb0011f9a77f9ca078777e591a82","target":"record","created_at":"2026-05-18T00:10:04Z","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":"b2cbf40db6c621d75d124cdb48c9657ceaa199b464efe3580594102fb9638d9c","cross_cats_sorted":["math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-01-05T12:57:12Z","title_canon_sha256":"64980fd510b405c7fbac595083cab206b933fc9c9274bb80824232042bca2928"},"schema_version":"1.0","source":{"id":"1501.00842","kind":"arxiv","version":1}},"canonical_sha256":"38bdeb5f1963835b7c3313e956c64afc59f22bf09b845bd49b048eef10136cd6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38bdeb5f1963835b7c3313e956c64afc59f22bf09b845bd49b048eef10136cd6","first_computed_at":"2026-05-18T00:10:04.609492Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:04.609492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zyyxzHS6nJSpHXq33iTnM7jXdxkLTQzgU1Q72MwvgAAD4mWLreICczzsZUUevSNfRo2fJitFq5bHuEiDnFY+Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:04.610271Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.00842","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:619aa970ea24af79187630e2d6d3941f149acb0011f9a77f9ca078777e591a82","sha256:045cf3fe5b157592ee8bf92c36585df7079b3221291bf986f2d0efcb769236f3"],"state_sha256":"1bffde95e1b7ff173550eab35c7cc0a3720ba79a5e71bada35489f2ff09893dc"}