{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NYEEAFWW4AB2USHHIZQJDVM2XC","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":"7af54a63d4950f840f83f96a08370526ee1048dda79f3fda4f2201d8066b5730","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-29T04:02:55Z","title_canon_sha256":"f452c095c029a199c577f720687a34354c0457bc8f11e24dd4ab9871276f3002"},"schema_version":"1.0","source":{"id":"1608.07908","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.07908","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"arxiv_version","alias_value":"1608.07908v1","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07908","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"pith_short_12","alias_value":"NYEEAFWW4AB2","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NYEEAFWW4AB2USHH","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NYEEAFWW","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:e6413e438f62ec09bd6a1224ed356f5d228ef5bae3540cf5ca2ade819e5c99bf","target":"graph","created_at":"2026-05-18T01:07:49Z","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 article, a large class of simple modules over the Schr\\\"odinger-Virasoro algebra $\\mathcal{G}$ are constructed, which include highest weight modules and Whittaker modules. These modules are determined by the simple modules over the finite-dimensional quotient algebras of some subalgebras. Moreover, we show that all simple modules of $\\mathcal{G}$ with locally finite actions of elements in a certain positive part belong to this class of simple modules. Similarly, a large class of simple modules over the $W$-algebra $W(2,2)$ are constructed.","authors_text":"Haibo Chen, Yanyong Hong, Yucai Su","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-29T04:02:55Z","title":"A family of new simple modules over the Schr\\\"odinger-Virasoro algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07908","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":"sha256:6b5df0585748cbbb4d436743b54724bd984e137f7b9bb2ba5b889c8447ab5ef0","target":"record","created_at":"2026-05-18T01:07:49Z","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":"7af54a63d4950f840f83f96a08370526ee1048dda79f3fda4f2201d8066b5730","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-29T04:02:55Z","title_canon_sha256":"f452c095c029a199c577f720687a34354c0457bc8f11e24dd4ab9871276f3002"},"schema_version":"1.0","source":{"id":"1608.07908","kind":"arxiv","version":1}},"canonical_sha256":"6e084016d6e003aa48e7466091d59ab88c4d32d9ed1b91e164009a2e7eba26d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e084016d6e003aa48e7466091d59ab88c4d32d9ed1b91e164009a2e7eba26d4","first_computed_at":"2026-05-18T01:07:49.623362Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:49.623362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qZ/Zit47EUVB8cwq8ryBYUArL0h4E+qDTjfwtd4ZofL7C59zxeDOw4YtaLQnyRYyBGqDouDxOiVLkPwLM+dTDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:49.623861Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.07908","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b5df0585748cbbb4d436743b54724bd984e137f7b9bb2ba5b889c8447ab5ef0","sha256:e6413e438f62ec09bd6a1224ed356f5d228ef5bae3540cf5ca2ade819e5c99bf"],"state_sha256":"d15b4e5d31da7ad20a850af036f0f72dfd916636055ccb904cdc31632d2f965a"}