{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1993:COWVJI5SL2QMGW626PAXNR2MW7","short_pith_number":"pith:COWVJI5S","canonical_record":{"source":{"id":"hep-th/9311134","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1993-11-22T19:15:01Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"f6160a0a7ad499f127502cd90a30eb0f626768c5457f99af632a6c76fd279101","abstract_canon_sha256":"c966a0e0580b43da6645e350bc5341d1f32013de585605c10e945f71ee2b9f93"},"schema_version":"1.0"},"canonical_sha256":"13ad54a3b25ea0c35bdaf3c176c74cb7e5f1e065d87c0c18ed5cd2068fa04e6f","source":{"kind":"arxiv","id":"hep-th/9311134","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9311134","created_at":"2026-05-18T01:06:04Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9311134v1","created_at":"2026-05-18T01:06:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9311134","created_at":"2026-05-18T01:06:04Z"},{"alias_kind":"pith_short_12","alias_value":"COWVJI5SL2QM","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"COWVJI5SL2QMGW62","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"COWVJI5S","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1993:COWVJI5SL2QMGW626PAXNR2MW7","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9311134","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1993-11-22T19:15:01Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"f6160a0a7ad499f127502cd90a30eb0f626768c5457f99af632a6c76fd279101","abstract_canon_sha256":"c966a0e0580b43da6645e350bc5341d1f32013de585605c10e945f71ee2b9f93"},"schema_version":"1.0"},"canonical_sha256":"13ad54a3b25ea0c35bdaf3c176c74cb7e5f1e065d87c0c18ed5cd2068fa04e6f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:04.726125Z","signature_b64":"3u1ZChavIa93CBHoLEAo7KeU/dZbEP62yndY0Ui7iKxX4YJnSDiOr92QShIMEzBQE7ZrHCHjidAG6ziWR0glDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13ad54a3b25ea0c35bdaf3c176c74cb7e5f1e065d87c0c18ed5cd2068fa04e6f","last_reissued_at":"2026-05-18T01:06:04.725417Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:04.725417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9311134","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":"2026-05-18T01:06:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1un3DqaJiN1+LOTPVThum4uDmcaZJe6L1EBQ5+PnldU2GOnTQBRw/KP6gCkfL+/2Mz+Mam7fg4Rvm9kbmGMbDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T05:51:46.327909Z"},"content_sha256":"98b6f25a7927d15fcbe8dd5bcce3af6412c4d759e8b15c2d4bd163232c9f762a","schema_version":"1.0","event_id":"sha256:98b6f25a7927d15fcbe8dd5bcce3af6412c4d759e8b15c2d4bd163232c9f762a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1993:COWVJI5SL2QMGW626PAXNR2MW7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the algebraic structures connected with the linear Poisson brackets of hydrodynamics type","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"hep-th","authors_text":"A. A. Balinsky, A. I. Balinsky","submitted_at":"1993-11-22T19:15:01Z","abstract_excerpt":"The generalized form of the Kac formula for Verma modules associated with linear brackets of hydrodynamics type is proposed. Second cohomology groups of the generalized Virasoro algebras are calculated. Connection of the central extensions with the problem of quntization of hydrodynamics brackets is demonstrated."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9311134","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":"2026-05-18T01:06:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OAP5TzyDuMRMFlQBt0XQ5NfNB08q9SbH9H2uQzs2AcuYy0BB4mGQ1/2meXWbQ3wziMPmB1vQ9paA00uf5pGRCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T05:51:46.328641Z"},"content_sha256":"30a245b7990c63689ae6d0c5f72a864672cd59ad8c355d2dea42eaf63c500629","schema_version":"1.0","event_id":"sha256:30a245b7990c63689ae6d0c5f72a864672cd59ad8c355d2dea42eaf63c500629"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/COWVJI5SL2QMGW626PAXNR2MW7/bundle.json","state_url":"https://pith.science/pith/COWVJI5SL2QMGW626PAXNR2MW7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/COWVJI5SL2QMGW626PAXNR2MW7/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":"2026-06-10T05:51:46Z","links":{"resolver":"https://pith.science/pith/COWVJI5SL2QMGW626PAXNR2MW7","bundle":"https://pith.science/pith/COWVJI5SL2QMGW626PAXNR2MW7/bundle.json","state":"https://pith.science/pith/COWVJI5SL2QMGW626PAXNR2MW7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/COWVJI5SL2QMGW626PAXNR2MW7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1993:COWVJI5SL2QMGW626PAXNR2MW7","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":"c966a0e0580b43da6645e350bc5341d1f32013de585605c10e945f71ee2b9f93","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"hep-th","submitted_at":"1993-11-22T19:15:01Z","title_canon_sha256":"f6160a0a7ad499f127502cd90a30eb0f626768c5457f99af632a6c76fd279101"},"schema_version":"1.0","source":{"id":"hep-th/9311134","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9311134","created_at":"2026-05-18T01:06:04Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9311134v1","created_at":"2026-05-18T01:06:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9311134","created_at":"2026-05-18T01:06:04Z"},{"alias_kind":"pith_short_12","alias_value":"COWVJI5SL2QM","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"COWVJI5SL2QMGW62","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"COWVJI5S","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:30a245b7990c63689ae6d0c5f72a864672cd59ad8c355d2dea42eaf63c500629","target":"graph","created_at":"2026-05-18T01:06:04Z","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":"The generalized form of the Kac formula for Verma modules associated with linear brackets of hydrodynamics type is proposed. Second cohomology groups of the generalized Virasoro algebras are calculated. Connection of the central extensions with the problem of quntization of hydrodynamics brackets is demonstrated.","authors_text":"A. A. Balinsky, A. I. Balinsky","cross_cats":["math.QA"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1993-11-22T19:15:01Z","title":"On the algebraic structures connected with the linear Poisson brackets of hydrodynamics type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9311134","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":"sha256:98b6f25a7927d15fcbe8dd5bcce3af6412c4d759e8b15c2d4bd163232c9f762a","target":"record","created_at":"2026-05-18T01:06:04Z","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":"c966a0e0580b43da6645e350bc5341d1f32013de585605c10e945f71ee2b9f93","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"hep-th","submitted_at":"1993-11-22T19:15:01Z","title_canon_sha256":"f6160a0a7ad499f127502cd90a30eb0f626768c5457f99af632a6c76fd279101"},"schema_version":"1.0","source":{"id":"hep-th/9311134","kind":"arxiv","version":1}},"canonical_sha256":"13ad54a3b25ea0c35bdaf3c176c74cb7e5f1e065d87c0c18ed5cd2068fa04e6f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13ad54a3b25ea0c35bdaf3c176c74cb7e5f1e065d87c0c18ed5cd2068fa04e6f","first_computed_at":"2026-05-18T01:06:04.725417Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:04.725417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3u1ZChavIa93CBHoLEAo7KeU/dZbEP62yndY0Ui7iKxX4YJnSDiOr92QShIMEzBQE7ZrHCHjidAG6ziWR0glDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:04.726125Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9311134","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98b6f25a7927d15fcbe8dd5bcce3af6412c4d759e8b15c2d4bd163232c9f762a","sha256:30a245b7990c63689ae6d0c5f72a864672cd59ad8c355d2dea42eaf63c500629"],"state_sha256":"2503f8289a353917ada892de95374459b80d04b7385ddff4ab81f89db407cb43"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eMsxYK7K/SkjySMlEvJPSQ+Vhx6YnLsL8RnxOU53Mes7azl42JWEwuAODt3ts1+puZW9q/zlq3FvjIM8alAxCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T05:51:46.332695Z","bundle_sha256":"01dbf5ecd530c20a32b82b2220affbd5c0f70f16bdf2d71a94d5b1a1ff8e01cf"}}