{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1995:BFYHZ5DZXVZPID6U3KW4PN4VV4","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":"ddc512e7039b0becdbc9700b0ff5798649466f605ced7346dae0699189d116da","cross_cats_sorted":["hep-th","math.QA"],"license":"","primary_cat":"q-alg","submitted_at":"1995-05-18T18:49:18Z","title_canon_sha256":"6fd55a26c177acca5881f7bcf109abd179235d12290b82add888d51c8dace261"},"schema_version":"1.0","source":{"id":"q-alg/9505023","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"q-alg/9505023","created_at":"2026-07-04T15:59:55Z"},{"alias_kind":"arxiv_version","alias_value":"q-alg/9505023v1","created_at":"2026-07-04T15:59:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.q-alg/9505023","created_at":"2026-07-04T15:59:55Z"},{"alias_kind":"pith_short_12","alias_value":"BFYHZ5DZXVZP","created_at":"2026-07-04T15:59:55Z"},{"alias_kind":"pith_short_16","alias_value":"BFYHZ5DZXVZPID6U","created_at":"2026-07-04T15:59:55Z"},{"alias_kind":"pith_short_8","alias_value":"BFYHZ5DZ","created_at":"2026-07-04T15:59:55Z"}],"graph_snapshots":[{"event_id":"sha256:4e4ba4bf77712e29a562319be08f32c280c4fc2dcd37f75baede9c17d1e960f7","target":"graph","created_at":"2026-07-04T15:59:55Z","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/q-alg/9505023/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct the space of vector fields on a generic quantum group. Its elements are products of elements of the quantum group itself with left invariant vector fields. We study the duality between vector fields and 1-forms and generalize the construction to tensor fields. A Lie derivative along any (also non left invariant) vector field is proposed and a puzzling ambiguity in its definition discussed. These results hold for a generic Hopf algebra.","authors_text":"Paolo Aschieri, Peter Schupp","cross_cats":["hep-th","math.QA"],"headline":"","license":"","primary_cat":"q-alg","submitted_at":"1995-05-18T18:49:18Z","title":"Vector Fields on Quantum Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-alg/9505023","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":"sha256:1ee6735fa9b94cbdaf6e89cd0ef1a6d141d01e8485a0954d8a7e9c454e958f75","target":"record","created_at":"2026-07-04T15:59:55Z","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":"ddc512e7039b0becdbc9700b0ff5798649466f605ced7346dae0699189d116da","cross_cats_sorted":["hep-th","math.QA"],"license":"","primary_cat":"q-alg","submitted_at":"1995-05-18T18:49:18Z","title_canon_sha256":"6fd55a26c177acca5881f7bcf109abd179235d12290b82add888d51c8dace261"},"schema_version":"1.0","source":{"id":"q-alg/9505023","kind":"arxiv","version":1}},"canonical_sha256":"09707cf479bd72f40fd4daadc7b795af30d5aa9482458fe3fb9b77555e0d8c26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"09707cf479bd72f40fd4daadc7b795af30d5aa9482458fe3fb9b77555e0d8c26","first_computed_at":"2026-07-04T15:59:55.308938Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:59:55.308938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lQHK4Q4OUjmhNTEC1NgLz3S5fFiws4SgDZ4bR2KaIJI+9k09+5UHOjaJ34JyFF7k+a5+OteIblyrjycvWMqsDw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:59:55.309301Z","signed_message":"canonical_sha256_bytes"},"source_id":"q-alg/9505023","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ee6735fa9b94cbdaf6e89cd0ef1a6d141d01e8485a0954d8a7e9c454e958f75","sha256:4e4ba4bf77712e29a562319be08f32c280c4fc2dcd37f75baede9c17d1e960f7"],"state_sha256":"c97bd9de15146990fd471ef1925f7b45e785eeaa858926b26ba034fe19e3d66b"}