{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:XBX4R4MNZ36HFE7FSE3UMHFNZ4","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":"4daf117dfe371dcd902cad87b7486382037a4d6b34a9d570fcf376ea5a2b1fb9","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.QA","submitted_at":"2020-06-04T10:38:45Z","title_canon_sha256":"4aa16033109eb9753c4f59d60d5b5ed34cfbe12c5df22cfc07a0e7867caa1b7f"},"schema_version":"1.0","source":{"id":"2006.02761","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.02761","created_at":"2026-05-25T02:00:59Z"},{"alias_kind":"arxiv_version","alias_value":"2006.02761v3","created_at":"2026-05-25T02:00:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.02761","created_at":"2026-05-25T02:00:59Z"},{"alias_kind":"pith_short_12","alias_value":"XBX4R4MNZ36H","created_at":"2026-05-25T02:00:59Z"},{"alias_kind":"pith_short_16","alias_value":"XBX4R4MNZ36HFE7F","created_at":"2026-05-25T02:00:59Z"},{"alias_kind":"pith_short_8","alias_value":"XBX4R4MN","created_at":"2026-05-25T02:00:59Z"}],"graph_snapshots":[{"event_id":"sha256:9fdc1767e8f965105898495baea1f6455926818f06ce79840259442a8e9c21ff","target":"graph","created_at":"2026-05-25T02:00:59Z","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/2006.02761/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the differential and Riemannian geometry of algebras $A$ endowed with an action of a triangular Hopf algebra $H$ and noncommutativity compatible with the associated braiding. The modules of one forms and of braided derivations are modules in a compact closed category of $H$-equivariant $A$-bimodules, whose internal morphisms correspond to tensor fields. Vector fields and forms approaches to curvature and torsion are proven to be equivalent by extending the Cartan calculus to left (right) $A$-module (not necessarily $A$-bimodule) connections. The Cartan structure equations and the Bian","authors_text":"Paolo Aschieri","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.QA","submitted_at":"2020-06-04T10:38:45Z","title":"Cartan structure equations and Levi-Civita connection in noncommutative geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.02761","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":"sha256:4f84f230ef795f6d1e6c229e8558aa9a7687beaf10ea4521d97b998d5aa462de","target":"record","created_at":"2026-05-25T02:00:59Z","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":"4daf117dfe371dcd902cad87b7486382037a4d6b34a9d570fcf376ea5a2b1fb9","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.QA","submitted_at":"2020-06-04T10:38:45Z","title_canon_sha256":"4aa16033109eb9753c4f59d60d5b5ed34cfbe12c5df22cfc07a0e7867caa1b7f"},"schema_version":"1.0","source":{"id":"2006.02761","kind":"arxiv","version":3}},"canonical_sha256":"b86fc8f18dcefc7293e59137461cadcf1f4109ba5b82a10acebc7139134c5504","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b86fc8f18dcefc7293e59137461cadcf1f4109ba5b82a10acebc7139134c5504","first_computed_at":"2026-05-25T02:00:59.531946Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-25T02:00:59.531946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HbrgCC58hKCOxQgXwkd7ByK21mtUON8OBbKR+zF2+Kp/3Ox6PtxH22qqqMeY5mc3vP3KfPwqwWXW8+3B1T5vBQ==","signature_status":"signed_v1","signed_at":"2026-05-25T02:00:59.532642Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.02761","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f84f230ef795f6d1e6c229e8558aa9a7687beaf10ea4521d97b998d5aa462de","sha256:9fdc1767e8f965105898495baea1f6455926818f06ce79840259442a8e9c21ff"],"state_sha256":"664073605e7f780c8fc72f8e3206b5a1a00bc9f1b3dcda41f4050f58f78db6ae"}