{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:6CFJPQRYL5IPF7CYIRKILPXC4B","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":"2c3964fe95618505dde6f0024dee996c96837f505de665a7b09d01bbdf030359","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-12-13T22:18:52Z","title_canon_sha256":"38ddad8ab3f831b6ef1d1feb9f22b6ab64ff4285d8fd5e3c643cbbcd82519612"},"schema_version":"1.0","source":{"id":"1012.2897","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.2897","created_at":"2026-05-17T23:57:16Z"},{"alias_kind":"arxiv_version","alias_value":"1012.2897v2","created_at":"2026-05-17T23:57:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2897","created_at":"2026-05-17T23:57:16Z"},{"alias_kind":"pith_short_12","alias_value":"6CFJPQRYL5IP","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6CFJPQRYL5IPF7CY","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6CFJPQRY","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:7917aa633b8259eb84855526b11942a14fe1822ed5da4b52a4e29b2204ac0d5c","target":"graph","created_at":"2026-05-17T23:57:16Z","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 define and investigate real analytic weak Jacobi forms of degree 1 and arbitrary rank. En route we calculate the Casimir operator associated to the maximal central extension of the real Jacobi group, which for rank exceeding 1 is of order 4. In ranks exceeding 1, the notions of H-harmonicity and semi-holomorphicity are the same.","authors_text":"Charles H. Conley, Martin Raum","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-12-13T22:18:52Z","title":"Harmonic Maa{\\ss}-Jacobi forms of degree 1 with higher rank indices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2897","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:debde2aae5ba485b4099495e0f8811113785ddcfd0cd1ad9f1ae4c1a0a131340","target":"record","created_at":"2026-05-17T23:57:16Z","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":"2c3964fe95618505dde6f0024dee996c96837f505de665a7b09d01bbdf030359","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-12-13T22:18:52Z","title_canon_sha256":"38ddad8ab3f831b6ef1d1feb9f22b6ab64ff4285d8fd5e3c643cbbcd82519612"},"schema_version":"1.0","source":{"id":"1012.2897","kind":"arxiv","version":2}},"canonical_sha256":"f08a97c2385f50f2fc58445485bee2e04a7a0ccce3f7e95e30c4ee87c2c13503","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f08a97c2385f50f2fc58445485bee2e04a7a0ccce3f7e95e30c4ee87c2c13503","first_computed_at":"2026-05-17T23:57:16.174434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:16.174434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E9R04Oqiur6SaKbbJTks7w+9SpSPoUkkLXWPtB+ZRnhyCrofVA4otMMKn/ArVv1TskQx5lzGB5wxBxZLfz38Bg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:16.174975Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.2897","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:debde2aae5ba485b4099495e0f8811113785ddcfd0cd1ad9f1ae4c1a0a131340","sha256:7917aa633b8259eb84855526b11942a14fe1822ed5da4b52a4e29b2204ac0d5c"],"state_sha256":"90f26674d66ecdca3273e2ac82eb16b9889535dd0c305d55de32707c620ba1b9"}