{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XWUAUJFWLOSYXWVWRQJXIN2FCI","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":"2fedd0f4b6325608e3adf7098bcf6eac70591ca1f6f3f0f5cb9245204ef30f29","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-04-19T01:21:13Z","title_canon_sha256":"5f1aa1cbb9cf6b648ef2887a1fc84b7559d9eb81f6431dafe1ef23690d25c9bb"},"schema_version":"1.0","source":{"id":"1504.04780","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04780","created_at":"2026-05-18T01:44:11Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04780v3","created_at":"2026-05-18T01:44:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04780","created_at":"2026-05-18T01:44:11Z"},{"alias_kind":"pith_short_12","alias_value":"XWUAUJFWLOSY","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XWUAUJFWLOSYXWVW","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XWUAUJFW","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:3ebdd71d94e38c6800f5cf7d0dd4c25dfbcde6236d0a1562cd6baacf71ebe917","target":"graph","created_at":"2026-05-18T01:44:11Z","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":"We develop the generalized Cartan Calculus for the groups $G=$SL$(2,\\mathbb{R})\\times\\mathbb{R}^+$, SL$(5,\\mathbb{R})$ and SO(5,5). They are the underlying algebraic structures of $d=9,7,6$ exceptional field theory, respectively. These algebraic identities are needed for the \"tensor hierarchy\" structure in exceptional field theory. The validity of Poincar\\'e lemmas in this new differential geometry is also discussed. Finally we explore some possible extension of the generalized Cartan calculus beyond the exceptional series.","authors_text":"Yi-Nan Wang","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-04-19T01:21:13Z","title":"Generalized Cartan Calculus in general dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04780","kind":"arxiv","version":3},"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":"sha256:48d5e30f23d2e0a6e2434e53e1ff26bfdf9d4c0f9a436cc57cfb41e122294ab0","target":"record","created_at":"2026-05-18T01:44:11Z","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":"2fedd0f4b6325608e3adf7098bcf6eac70591ca1f6f3f0f5cb9245204ef30f29","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-04-19T01:21:13Z","title_canon_sha256":"5f1aa1cbb9cf6b648ef2887a1fc84b7559d9eb81f6431dafe1ef23690d25c9bb"},"schema_version":"1.0","source":{"id":"1504.04780","kind":"arxiv","version":3}},"canonical_sha256":"bda80a24b65ba58bdab68c13743745122dcec017140d85f1f222d0e356b907e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bda80a24b65ba58bdab68c13743745122dcec017140d85f1f222d0e356b907e0","first_computed_at":"2026-05-18T01:44:11.057585Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:44:11.057585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iFjm0t86TkASxkdogstScY4fIOoer6oT9mgawrhJNlGIx4/3Aj7zSC36TE9oJzddHeUNOd8kG8JJU9y8S0JzCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:44:11.058382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.04780","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48d5e30f23d2e0a6e2434e53e1ff26bfdf9d4c0f9a436cc57cfb41e122294ab0","sha256:3ebdd71d94e38c6800f5cf7d0dd4c25dfbcde6236d0a1562cd6baacf71ebe917"],"state_sha256":"fe9c9816caacd0ec289792350fb3bff5faa695ef0a9f7c7d2f5dd6b002af08bf"}