{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:7SWHDK2YPKJ67OK43JJTFQEXXC","short_pith_number":"pith:7SWHDK2Y","canonical_record":{"source":{"id":"1007.4823","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-07-27T20:58:44Z","cross_cats_sorted":[],"title_canon_sha256":"bd5441de238a722eca03eb84c812532e1c6673f8568db5587e8618d5049d9ac1","abstract_canon_sha256":"0130b7c4a125120002c211abbab9c309be20ca12c20b56d9c600664891777c2f"},"schema_version":"1.0"},"canonical_sha256":"fcac71ab587a93efb95cda5332c097b894afc1c7ecbebe24fedb0024f3d263eb","source":{"kind":"arxiv","id":"1007.4823","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.4823","created_at":"2026-07-04T17:32:24Z"},{"alias_kind":"arxiv_version","alias_value":"1007.4823v1","created_at":"2026-07-04T17:32:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.4823","created_at":"2026-07-04T17:32:24Z"},{"alias_kind":"pith_short_12","alias_value":"7SWHDK2YPKJ6","created_at":"2026-07-04T17:32:24Z"},{"alias_kind":"pith_short_16","alias_value":"7SWHDK2YPKJ67OK4","created_at":"2026-07-04T17:32:24Z"},{"alias_kind":"pith_short_8","alias_value":"7SWHDK2Y","created_at":"2026-07-04T17:32:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:7SWHDK2YPKJ67OK43JJTFQEXXC","target":"record","payload":{"canonical_record":{"source":{"id":"1007.4823","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-07-27T20:58:44Z","cross_cats_sorted":[],"title_canon_sha256":"bd5441de238a722eca03eb84c812532e1c6673f8568db5587e8618d5049d9ac1","abstract_canon_sha256":"0130b7c4a125120002c211abbab9c309be20ca12c20b56d9c600664891777c2f"},"schema_version":"1.0"},"canonical_sha256":"fcac71ab587a93efb95cda5332c097b894afc1c7ecbebe24fedb0024f3d263eb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:32:24.836825Z","signature_b64":"p/GwcPTESCzlKj5UV0wlEsNi4Uw0XHbwqVxp01GvyugE0MzTM3Cy7FpK+J6VxSCxJSftXbr/lEyptloQGtuPDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fcac71ab587a93efb95cda5332c097b894afc1c7ecbebe24fedb0024f3d263eb","last_reissued_at":"2026-07-04T17:32:24.836432Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:32:24.836432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.4823","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T17:32:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VEGRiNDPYbqyPMA8MI4EijHguD8nH7nsMyb1ZhPl+47qI36kkSRXXbEmDCAdsX5bEOV3iBeplxPFpqRGEcdZAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T02:38:42.624609Z"},"content_sha256":"a81cf960fa370abb256835007c7c6a90451b397d7ecfea8379ddc576e4360333","schema_version":"1.0","event_id":"sha256:a81cf960fa370abb256835007c7c6a90451b397d7ecfea8379ddc576e4360333"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:7SWHDK2YPKJ67OK43JJTFQEXXC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quasimodular forms, Jacobi-like forms, and pseudodifferential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Minho Lee, YoungJu Choie","submitted_at":"2010-07-27T20:58:44Z","abstract_excerpt":"We study various properties of quasimodular forms by using their connections with Jacobi-like forms and pseudodifferential operators. Such connections are made by identifying quasimodular forms for a discrete subgroup $\\G$ of $SL(2, \\bR)$ with certain polynomials over the ring of holomorphic functions of the Poincar\\'e upper half plane that are $\\G$-invariant. We consider a surjective map from Jacobi-like forms to quasimodular forms and prove that it has a right inverse, which may be regarded as a lifting from quasimodular forms to Jacobi-like forms. We use such liftings to study Lie brackets "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.4823","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1007.4823/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T17:32:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d+26Z8o0EYfrrC3fMh/zIOsI/YAJaqYqprlrXQRbm/upD+DODOkV0839vin1S0vNN5InJa6PH4v2yraZolevBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T02:38:42.625137Z"},"content_sha256":"e384e217affcd89984b5a04b09937a18a7e83853a58e5dab6f257d67135a4379","schema_version":"1.0","event_id":"sha256:e384e217affcd89984b5a04b09937a18a7e83853a58e5dab6f257d67135a4379"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7SWHDK2YPKJ67OK43JJTFQEXXC/bundle.json","state_url":"https://pith.science/pith/7SWHDK2YPKJ67OK43JJTFQEXXC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7SWHDK2YPKJ67OK43JJTFQEXXC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-14T02:38:42Z","links":{"resolver":"https://pith.science/pith/7SWHDK2YPKJ67OK43JJTFQEXXC","bundle":"https://pith.science/pith/7SWHDK2YPKJ67OK43JJTFQEXXC/bundle.json","state":"https://pith.science/pith/7SWHDK2YPKJ67OK43JJTFQEXXC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7SWHDK2YPKJ67OK43JJTFQEXXC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:7SWHDK2YPKJ67OK43JJTFQEXXC","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":"0130b7c4a125120002c211abbab9c309be20ca12c20b56d9c600664891777c2f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-07-27T20:58:44Z","title_canon_sha256":"bd5441de238a722eca03eb84c812532e1c6673f8568db5587e8618d5049d9ac1"},"schema_version":"1.0","source":{"id":"1007.4823","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.4823","created_at":"2026-07-04T17:32:24Z"},{"alias_kind":"arxiv_version","alias_value":"1007.4823v1","created_at":"2026-07-04T17:32:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.4823","created_at":"2026-07-04T17:32:24Z"},{"alias_kind":"pith_short_12","alias_value":"7SWHDK2YPKJ6","created_at":"2026-07-04T17:32:24Z"},{"alias_kind":"pith_short_16","alias_value":"7SWHDK2YPKJ67OK4","created_at":"2026-07-04T17:32:24Z"},{"alias_kind":"pith_short_8","alias_value":"7SWHDK2Y","created_at":"2026-07-04T17:32:24Z"}],"graph_snapshots":[{"event_id":"sha256:e384e217affcd89984b5a04b09937a18a7e83853a58e5dab6f257d67135a4379","target":"graph","created_at":"2026-07-04T17:32:24Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1007.4823/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study various properties of quasimodular forms by using their connections with Jacobi-like forms and pseudodifferential operators. Such connections are made by identifying quasimodular forms for a discrete subgroup $\\G$ of $SL(2, \\bR)$ with certain polynomials over the ring of holomorphic functions of the Poincar\\'e upper half plane that are $\\G$-invariant. We consider a surjective map from Jacobi-like forms to quasimodular forms and prove that it has a right inverse, which may be regarded as a lifting from quasimodular forms to Jacobi-like forms. We use such liftings to study Lie brackets ","authors_text":"Minho Lee, YoungJu Choie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-07-27T20:58:44Z","title":"Quasimodular forms, Jacobi-like forms, and pseudodifferential operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.4823","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:a81cf960fa370abb256835007c7c6a90451b397d7ecfea8379ddc576e4360333","target":"record","created_at":"2026-07-04T17:32:24Z","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":"0130b7c4a125120002c211abbab9c309be20ca12c20b56d9c600664891777c2f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-07-27T20:58:44Z","title_canon_sha256":"bd5441de238a722eca03eb84c812532e1c6673f8568db5587e8618d5049d9ac1"},"schema_version":"1.0","source":{"id":"1007.4823","kind":"arxiv","version":1}},"canonical_sha256":"fcac71ab587a93efb95cda5332c097b894afc1c7ecbebe24fedb0024f3d263eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fcac71ab587a93efb95cda5332c097b894afc1c7ecbebe24fedb0024f3d263eb","first_computed_at":"2026-07-04T17:32:24.836432Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:32:24.836432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p/GwcPTESCzlKj5UV0wlEsNi4Uw0XHbwqVxp01GvyugE0MzTM3Cy7FpK+J6VxSCxJSftXbr/lEyptloQGtuPDA==","signature_status":"signed_v1","signed_at":"2026-07-04T17:32:24.836825Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.4823","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a81cf960fa370abb256835007c7c6a90451b397d7ecfea8379ddc576e4360333","sha256:e384e217affcd89984b5a04b09937a18a7e83853a58e5dab6f257d67135a4379"],"state_sha256":"cde8b1e6f1a1aa499e31867b6c4a6fa1725cda7f12199e0322f4d9757b5b6d11"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9TbXwXuRjH47VVM2ujNT7ksz8LO8KttqDNM4up/PxDgLjJiln/sOCJrG82u7NbywtN2nW4wKLogLh/wpa57mAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T02:38:42.630898Z","bundle_sha256":"3160d071b4b25bb50a66eb3764dbb44813b6d75d44725afdd31ad6d22b5a8e78"}}