{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:BBY62U3JPM7EZYPE3ZNZPL57PL","short_pith_number":"pith:BBY62U3J","canonical_record":{"source":{"id":"1209.3164","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-09-14T12:05:35Z","cross_cats_sorted":[],"title_canon_sha256":"4814a44ac69ce1686857e51d7674b5ab9c7bf45ae53f4f1fd4533a42e1cba111","abstract_canon_sha256":"148f7f8a7ff704192639aa9ac58bbf5ff44c381f69ea2697d7a7872105ec5c2f"},"schema_version":"1.0"},"canonical_sha256":"0871ed53697b3e4ce1e4de5b97afbf7ace35fe42d8de35c8a1db3770ec3461c9","source":{"kind":"arxiv","id":"1209.3164","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3164","created_at":"2026-05-18T03:45:32Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3164v1","created_at":"2026-05-18T03:45:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3164","created_at":"2026-05-18T03:45:32Z"},{"alias_kind":"pith_short_12","alias_value":"BBY62U3JPM7E","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"BBY62U3JPM7EZYPE","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"BBY62U3J","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:BBY62U3JPM7EZYPE3ZNZPL57PL","target":"record","payload":{"canonical_record":{"source":{"id":"1209.3164","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-09-14T12:05:35Z","cross_cats_sorted":[],"title_canon_sha256":"4814a44ac69ce1686857e51d7674b5ab9c7bf45ae53f4f1fd4533a42e1cba111","abstract_canon_sha256":"148f7f8a7ff704192639aa9ac58bbf5ff44c381f69ea2697d7a7872105ec5c2f"},"schema_version":"1.0"},"canonical_sha256":"0871ed53697b3e4ce1e4de5b97afbf7ace35fe42d8de35c8a1db3770ec3461c9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:32.645711Z","signature_b64":"Ie/QhSyFWuIKs9fag9XHY/UimbjxjDb9x5RUCUbjUIkH0A5zPfbNqL6kmKkzEpGk3RQfbR5N4mUd0w+0dJAsAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0871ed53697b3e4ce1e4de5b97afbf7ace35fe42d8de35c8a1db3770ec3461c9","last_reissued_at":"2026-05-18T03:45:32.645101Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:32.645101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.3164","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":"2026-05-18T03:45:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n+hkQQjxd2Y4oPYrlNgPo5CLG6cUPxw7K4VV93/Omae+jruR89Xv2ipSz1WsvDf9pQjoigc7nO8WLvxBpq8UAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:57:42.110991Z"},"content_sha256":"f456d2123ebc7eea9658023bdb475e16cc36d4abbf325de10844fc926f687880","schema_version":"1.0","event_id":"sha256:f456d2123ebc7eea9658023bdb475e16cc36d4abbf325de10844fc926f687880"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:BBY62U3JPM7EZYPE3ZNZPL57PL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Derivations and automorphism groups of the original deformative Schr\\\"odinger-Virasoro algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Qifen Jiang, Song Wang","submitted_at":"2012-09-14T12:05:35Z","abstract_excerpt":"In this paper, we determine the derivation algebra and the automorphism group of the original deformative ${\\rm Schr\\ddot{o}dinger}$-{\\rm Virasoro} algebras which is the semi-direct product Lie algebra of the Witt algebra and its tensor density module ${\\rm I^g}(a,b)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3164","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":"2026-05-18T03:45:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IcSYA4nbMzIKc0QQ+/TWDHAWcPwv4Tfk0qj83TSGEJGPYeydLUGs+9altsgmjROPH5gKNyC4s5rklOVv7K8DBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:57:42.111459Z"},"content_sha256":"28f66dad893b9b2daff6fc53a10680b2bd64b9f8cd824994f7c801772c61f51a","schema_version":"1.0","event_id":"sha256:28f66dad893b9b2daff6fc53a10680b2bd64b9f8cd824994f7c801772c61f51a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BBY62U3JPM7EZYPE3ZNZPL57PL/bundle.json","state_url":"https://pith.science/pith/BBY62U3JPM7EZYPE3ZNZPL57PL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BBY62U3JPM7EZYPE3ZNZPL57PL/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":"2026-06-04T03:57:42Z","links":{"resolver":"https://pith.science/pith/BBY62U3JPM7EZYPE3ZNZPL57PL","bundle":"https://pith.science/pith/BBY62U3JPM7EZYPE3ZNZPL57PL/bundle.json","state":"https://pith.science/pith/BBY62U3JPM7EZYPE3ZNZPL57PL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BBY62U3JPM7EZYPE3ZNZPL57PL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BBY62U3JPM7EZYPE3ZNZPL57PL","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":"148f7f8a7ff704192639aa9ac58bbf5ff44c381f69ea2697d7a7872105ec5c2f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-09-14T12:05:35Z","title_canon_sha256":"4814a44ac69ce1686857e51d7674b5ab9c7bf45ae53f4f1fd4533a42e1cba111"},"schema_version":"1.0","source":{"id":"1209.3164","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3164","created_at":"2026-05-18T03:45:32Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3164v1","created_at":"2026-05-18T03:45:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3164","created_at":"2026-05-18T03:45:32Z"},{"alias_kind":"pith_short_12","alias_value":"BBY62U3JPM7E","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"BBY62U3JPM7EZYPE","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"BBY62U3J","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:28f66dad893b9b2daff6fc53a10680b2bd64b9f8cd824994f7c801772c61f51a","target":"graph","created_at":"2026-05-18T03:45:32Z","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, we determine the derivation algebra and the automorphism group of the original deformative ${\\rm Schr\\ddot{o}dinger}$-{\\rm Virasoro} algebras which is the semi-direct product Lie algebra of the Witt algebra and its tensor density module ${\\rm I^g}(a,b)$.","authors_text":"Qifen Jiang, Song Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-09-14T12:05:35Z","title":"Derivations and automorphism groups of the original deformative Schr\\\"odinger-Virasoro algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3164","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:f456d2123ebc7eea9658023bdb475e16cc36d4abbf325de10844fc926f687880","target":"record","created_at":"2026-05-18T03:45:32Z","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":"148f7f8a7ff704192639aa9ac58bbf5ff44c381f69ea2697d7a7872105ec5c2f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-09-14T12:05:35Z","title_canon_sha256":"4814a44ac69ce1686857e51d7674b5ab9c7bf45ae53f4f1fd4533a42e1cba111"},"schema_version":"1.0","source":{"id":"1209.3164","kind":"arxiv","version":1}},"canonical_sha256":"0871ed53697b3e4ce1e4de5b97afbf7ace35fe42d8de35c8a1db3770ec3461c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0871ed53697b3e4ce1e4de5b97afbf7ace35fe42d8de35c8a1db3770ec3461c9","first_computed_at":"2026-05-18T03:45:32.645101Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:32.645101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ie/QhSyFWuIKs9fag9XHY/UimbjxjDb9x5RUCUbjUIkH0A5zPfbNqL6kmKkzEpGk3RQfbR5N4mUd0w+0dJAsAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:32.645711Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.3164","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f456d2123ebc7eea9658023bdb475e16cc36d4abbf325de10844fc926f687880","sha256:28f66dad893b9b2daff6fc53a10680b2bd64b9f8cd824994f7c801772c61f51a"],"state_sha256":"469414a8790e23a37b60a2ba001bb3346bdc67ef3136185449a14a5573f3c1f9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FHuLIDRKpzk6ouBjPPfS7fD1AJuYaR2ihEPErUB/93RBEXoHf+jZFun4vGBswl/fBBA/s92vWp/QVqwGJiDzAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T03:57:42.113851Z","bundle_sha256":"ce0093967b7710190bb0c00ea23552fdb9128b875000411ff100afd23972e1c3"}}