{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:DXI7VGBD4IHN7R5ZLV52422L2W","short_pith_number":"pith:DXI7VGBD","canonical_record":{"source":{"id":"1311.2118","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-11-09T01:06:20Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"e2ab6a0fc015c67a1eb31c14dd00acea8f29a2c6bb9d5fdc454b665afd2efeee","abstract_canon_sha256":"959537f73577047c0991cb349842e14a1309a35b87f5a9a2507f91698d8af51a"},"schema_version":"1.0"},"canonical_sha256":"1dd1fa9823e20edfc7b95d7bae6b4bd59e8f8b2e5b6db5c60080f1ec9b422e47","source":{"kind":"arxiv","id":"1311.2118","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.2118","created_at":"2026-05-18T03:07:33Z"},{"alias_kind":"arxiv_version","alias_value":"1311.2118v1","created_at":"2026-05-18T03:07:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2118","created_at":"2026-05-18T03:07:33Z"},{"alias_kind":"pith_short_12","alias_value":"DXI7VGBD4IHN","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DXI7VGBD4IHN7R5Z","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DXI7VGBD","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:DXI7VGBD4IHN7R5ZLV52422L2W","target":"record","payload":{"canonical_record":{"source":{"id":"1311.2118","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-11-09T01:06:20Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"e2ab6a0fc015c67a1eb31c14dd00acea8f29a2c6bb9d5fdc454b665afd2efeee","abstract_canon_sha256":"959537f73577047c0991cb349842e14a1309a35b87f5a9a2507f91698d8af51a"},"schema_version":"1.0"},"canonical_sha256":"1dd1fa9823e20edfc7b95d7bae6b4bd59e8f8b2e5b6db5c60080f1ec9b422e47","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:33.497301Z","signature_b64":"Gi+t2m1M5H+/NMcRsacYQRUvo4LAQ5Wq+dza5dDo1HTlZOZbQNqRC5okgBHVdUq/bqwYObzUhoEiXxDEQKA/Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1dd1fa9823e20edfc7b95d7bae6b4bd59e8f8b2e5b6db5c60080f1ec9b422e47","last_reissued_at":"2026-05-18T03:07:33.496830Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:33.496830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.2118","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":"2026-05-18T03:07:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MNsPDFXUE1lbrorknr2kQVYhqNrFjDJ5mqT0uETwABzrilOvTbarJlXN3yZu5emMgkM+r4oeifj3TZrH7x7bDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:31:15.878921Z"},"content_sha256":"4261aa20027dbd5017281ccd10e6504bf94f51f8b5de5eaaa0dffcd2134666a2","schema_version":"1.0","event_id":"sha256:4261aa20027dbd5017281ccd10e6504bf94f51f8b5de5eaaa0dffcd2134666a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:DXI7VGBD4IHN7R5ZLV52422L2W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Whittaker Modules for the Schr\\\"{o}dinger Algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Xiufu Zhang, Yongsheng Cheng","submitted_at":"2013-11-09T01:06:20Z","abstract_excerpt":"In this paper, the property and the classification the simple Whittaker modules for the schr\\\"{o}dinger algebra are studied. A quasi-central element plays an important role in the study of Whittaker modules of level zero. For the Whittaker modules of nonzero level, our arguments use the Casimir element of semisimple Lie algebra $sl_2$ and the description of simple modules over conformal Galilei algebras by R. L\\\"{u}, V. Mazorchuk and K. Zhao."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2118","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":""},"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":"2026-05-18T03:07:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"68Ne5drRZAC8X2+gOEEcApOg65ZENDbX+GUc/JAlOO8p/ThbxhiXu1zpay5euDbNvup9GWBblfRwjC3l2IkIBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:31:15.879259Z"},"content_sha256":"f74e6157376fe2ddd67e03d370d93896653961f034a879305d3c7edf6ac49e33","schema_version":"1.0","event_id":"sha256:f74e6157376fe2ddd67e03d370d93896653961f034a879305d3c7edf6ac49e33"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DXI7VGBD4IHN7R5ZLV52422L2W/bundle.json","state_url":"https://pith.science/pith/DXI7VGBD4IHN7R5ZLV52422L2W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DXI7VGBD4IHN7R5ZLV52422L2W/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":"2026-06-11T09:31:15Z","links":{"resolver":"https://pith.science/pith/DXI7VGBD4IHN7R5ZLV52422L2W","bundle":"https://pith.science/pith/DXI7VGBD4IHN7R5ZLV52422L2W/bundle.json","state":"https://pith.science/pith/DXI7VGBD4IHN7R5ZLV52422L2W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DXI7VGBD4IHN7R5ZLV52422L2W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DXI7VGBD4IHN7R5ZLV52422L2W","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":"959537f73577047c0991cb349842e14a1309a35b87f5a9a2507f91698d8af51a","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-11-09T01:06:20Z","title_canon_sha256":"e2ab6a0fc015c67a1eb31c14dd00acea8f29a2c6bb9d5fdc454b665afd2efeee"},"schema_version":"1.0","source":{"id":"1311.2118","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.2118","created_at":"2026-05-18T03:07:33Z"},{"alias_kind":"arxiv_version","alias_value":"1311.2118v1","created_at":"2026-05-18T03:07:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2118","created_at":"2026-05-18T03:07:33Z"},{"alias_kind":"pith_short_12","alias_value":"DXI7VGBD4IHN","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DXI7VGBD4IHN7R5Z","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DXI7VGBD","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:f74e6157376fe2ddd67e03d370d93896653961f034a879305d3c7edf6ac49e33","target":"graph","created_at":"2026-05-18T03:07:33Z","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":"In this paper, the property and the classification the simple Whittaker modules for the schr\\\"{o}dinger algebra are studied. A quasi-central element plays an important role in the study of Whittaker modules of level zero. For the Whittaker modules of nonzero level, our arguments use the Casimir element of semisimple Lie algebra $sl_2$ and the description of simple modules over conformal Galilei algebras by R. L\\\"{u}, V. Mazorchuk and K. Zhao.","authors_text":"Xiufu Zhang, Yongsheng Cheng","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-11-09T01:06:20Z","title":"Whittaker Modules for the Schr\\\"{o}dinger Algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2118","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":"sha256:4261aa20027dbd5017281ccd10e6504bf94f51f8b5de5eaaa0dffcd2134666a2","target":"record","created_at":"2026-05-18T03:07:33Z","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":"959537f73577047c0991cb349842e14a1309a35b87f5a9a2507f91698d8af51a","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-11-09T01:06:20Z","title_canon_sha256":"e2ab6a0fc015c67a1eb31c14dd00acea8f29a2c6bb9d5fdc454b665afd2efeee"},"schema_version":"1.0","source":{"id":"1311.2118","kind":"arxiv","version":1}},"canonical_sha256":"1dd1fa9823e20edfc7b95d7bae6b4bd59e8f8b2e5b6db5c60080f1ec9b422e47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1dd1fa9823e20edfc7b95d7bae6b4bd59e8f8b2e5b6db5c60080f1ec9b422e47","first_computed_at":"2026-05-18T03:07:33.496830Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:33.496830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gi+t2m1M5H+/NMcRsacYQRUvo4LAQ5Wq+dza5dDo1HTlZOZbQNqRC5okgBHVdUq/bqwYObzUhoEiXxDEQKA/Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:33.497301Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.2118","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4261aa20027dbd5017281ccd10e6504bf94f51f8b5de5eaaa0dffcd2134666a2","sha256:f74e6157376fe2ddd67e03d370d93896653961f034a879305d3c7edf6ac49e33"],"state_sha256":"f1f2cba93341bbae524dbf4c1460873ecedb8329956461fefe5fc8f84910761b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AnXT3YifdkDoCvXdk2Ae9vlIdz7mIG4CDSqhdYRUXTfpWkl2Wf2rdoteeCWRSa9PQS+aa95so34bZEJMGuXTCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T09:31:15.881158Z","bundle_sha256":"0bdd9cbd0de43e888fef4c928a60ebc1a8ce5127e7b3b7d051b086c77bc5adcb"}}