{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EY37DN6AAW6FA55GE46KMFLIVN","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":"c9be500ca62b1128efc74f82cfe6b8254c0f6996dc86a4a9cb33ac3ddaac943b","cross_cats_sorted":["math.AT","math.FA","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-08-04T21:09:03Z","title_canon_sha256":"95e77abf7be0bb78d6aaee3a0b2cdfde0a81be63f56d7526343735516312f898"},"schema_version":"1.0","source":{"id":"1608.01699","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01699","created_at":"2026-05-18T00:25:34Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01699v2","created_at":"2026-05-18T00:25:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01699","created_at":"2026-05-18T00:25:34Z"},{"alias_kind":"pith_short_12","alias_value":"EY37DN6AAW6F","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"EY37DN6AAW6FA55G","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"EY37DN6A","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:d04d226c556ffbd7ad1c5c8e3dde348532291649dca9e8b1939346eee8da913e","target":"graph","created_at":"2026-05-18T00:25:34Z","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":"We develop elliptic regularity theory for Dirac operators in a very general framework: we consider Dirac operators linear over $C^*$-algebras, on noncompact manifolds, and in families which are not necessarily locally trivial fibre bundles.","authors_text":"Johannes Ebert","cross_cats":["math.AT","math.FA","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-08-04T21:09:03Z","title":"Elliptic regularity for Dirac operators on families of noncompact manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01699","kind":"arxiv","version":2},"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":"sha256:86eeb180e00bc821ed128837b257464abd3ef023c131f4ebfd4eb7e88563b5e9","target":"record","created_at":"2026-05-18T00:25:34Z","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":"c9be500ca62b1128efc74f82cfe6b8254c0f6996dc86a4a9cb33ac3ddaac943b","cross_cats_sorted":["math.AT","math.FA","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-08-04T21:09:03Z","title_canon_sha256":"95e77abf7be0bb78d6aaee3a0b2cdfde0a81be63f56d7526343735516312f898"},"schema_version":"1.0","source":{"id":"1608.01699","kind":"arxiv","version":2}},"canonical_sha256":"2637f1b7c005bc5077a6273ca61568ab57b3220e7d4154bb059ff6bbf2cfac4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2637f1b7c005bc5077a6273ca61568ab57b3220e7d4154bb059ff6bbf2cfac4d","first_computed_at":"2026-05-18T00:25:34.887776Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:34.887776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aAvDe544yzxr03at4hxZcEYy4/pAA9QvJ952aIDRLUJ3imjAYMMJaf+BDCyCTgrsCTiPMI95Ib2xjtxIPosiBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:34.888484Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.01699","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86eeb180e00bc821ed128837b257464abd3ef023c131f4ebfd4eb7e88563b5e9","sha256:d04d226c556ffbd7ad1c5c8e3dde348532291649dca9e8b1939346eee8da913e"],"state_sha256":"9ede556b6c6567dd18f575be70cb8bc833d04169deb7e1331bd5b9cb3b0f3ac2"}