{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:AGZCTVRORLMXWD5SYAEUBZIDRJ","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":"b1876d0dcd4fa02939ff50d1e14e2c2c0279b5053f96a638d7ea6b08ebe16f80","cross_cats_sorted":["math.RA"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2008-06-05T14:24:17Z","title_canon_sha256":"d36c936469f590a28448056acbca7ee87ed6a3f449363470a689172e17bc1145"},"schema_version":"1.0","source":{"id":"0806.0978","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.0978","created_at":"2026-07-05T01:27:15Z"},{"alias_kind":"arxiv_version","alias_value":"0806.0978v4","created_at":"2026-07-05T01:27:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.0978","created_at":"2026-07-05T01:27:15Z"},{"alias_kind":"pith_short_12","alias_value":"AGZCTVRORLMX","created_at":"2026-07-05T01:27:15Z"},{"alias_kind":"pith_short_16","alias_value":"AGZCTVRORLMXWD5S","created_at":"2026-07-05T01:27:15Z"},{"alias_kind":"pith_short_8","alias_value":"AGZCTVRO","created_at":"2026-07-05T01:27:15Z"}],"graph_snapshots":[{"event_id":"sha256:0abb7f9635fd6250a84d33f1acf2b55e351bbbb1be2112922283ef8a8b9c2cb8","target":"graph","created_at":"2026-07-05T01:27:15Z","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/0806.0978/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Consider any representation $\\phi$ of a finite-dimensional Lie algebra $g$ by derivations of the completed symmetric algebra $\\hat{S}(g^*)$ of its dual. Consider the tensor product of $\\hat{S}(g^*)$ and the exterior algebra $\\Lambda(g)$. We show that the representation $\\phi$ extends canonically to the representation $\\tilde\\phi$ of that tensor product algebra. We construct an exterior derivative on that algebra, giving rise to a twisted version of the exterior differential calculus with the enveloping algebra in the role of the coordinate algebra. In this twisted version, the commutators betw","authors_text":"Zoran \\v{S}koda","cross_cats":["math.RA"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2008-06-05T14:24:17Z","title":"Twisted exterior derivatives for universal enveloping algebras I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.0978","kind":"arxiv","version":4},"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":"sha256:08a716226e16ee5009b262661e55e5ba32fbb26308c9f8e04c2da3369c92c970","target":"record","created_at":"2026-07-05T01:27:15Z","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":"b1876d0dcd4fa02939ff50d1e14e2c2c0279b5053f96a638d7ea6b08ebe16f80","cross_cats_sorted":["math.RA"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2008-06-05T14:24:17Z","title_canon_sha256":"d36c936469f590a28448056acbca7ee87ed6a3f449363470a689172e17bc1145"},"schema_version":"1.0","source":{"id":"0806.0978","kind":"arxiv","version":4}},"canonical_sha256":"01b229d62e8ad97b0fb2c00940e5038a5355e94907a187773496941eaff8498e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01b229d62e8ad97b0fb2c00940e5038a5355e94907a187773496941eaff8498e","first_computed_at":"2026-07-05T01:27:15.804860Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:27:15.804860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YqahHagSPtHFLtY2gE3kFx9Jxhn3HSsjO7ZoiHoPwHFD8DE6/CA20X8FM1e/5PO2FCMehTY7k22bf+e23qFVBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:27:15.805267Z","signed_message":"canonical_sha256_bytes"},"source_id":"0806.0978","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08a716226e16ee5009b262661e55e5ba32fbb26308c9f8e04c2da3369c92c970","sha256:0abb7f9635fd6250a84d33f1acf2b55e351bbbb1be2112922283ef8a8b9c2cb8"],"state_sha256":"5920e55bd6af9c11094659d615606f2176b94b0a3ab02e093df279c60e0ba138"}