{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OYQHQIPBWTTI27JIYDTFE75XGI","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":"7433577c725fe6d4bf3c7e723a4a7c9ba97f8a0c9f9516f049a302849cca6b10","cross_cats_sorted":["math.CA","math.MP","math.RA"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2011-08-18T14:42:15Z","title_canon_sha256":"af66180804a87a9c7c2dd0b8bfa5e3c64c0d171277cb4f5c77826be7892c7b09"},"schema_version":"1.0","source":{"id":"1108.3769","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.3769","created_at":"2026-05-18T03:22:17Z"},{"alias_kind":"arxiv_version","alias_value":"1108.3769v2","created_at":"2026-05-18T03:22:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3769","created_at":"2026-05-18T03:22:17Z"},{"alias_kind":"pith_short_12","alias_value":"OYQHQIPBWTTI","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OYQHQIPBWTTI27JI","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OYQHQIPB","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:4ac928deb6a6a3fe959115d36f636ae15b281a8d9480ee47c556429c0100460c","target":"graph","created_at":"2026-05-18T03:22:17Z","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":"A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space $E$, and then a connection is also defined on this bundle. The covariant derivatives associated to this connection are the Dunkl operators, originally introduced as part of a program to generalize harmonic analysis in Euclidean spaces. This gives us a new, geometric way of viewing the Dunkl operators. In particular, we present a new proof of the commutativity of these operators among themselves as a consequence of a geometric property, namely, that the connection has curvature zero.","authors_text":"Micho Durdevich, Stephen Bruce Sontz","cross_cats":["math.CA","math.MP","math.RA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2011-08-18T14:42:15Z","title":"Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3769","kind":"arxiv","version":2},"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:dad5bee7218d26008a95780701122c5f309bad558a833943d0ab6f573df6b516","target":"record","created_at":"2026-05-18T03:22:17Z","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":"7433577c725fe6d4bf3c7e723a4a7c9ba97f8a0c9f9516f049a302849cca6b10","cross_cats_sorted":["math.CA","math.MP","math.RA"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2011-08-18T14:42:15Z","title_canon_sha256":"af66180804a87a9c7c2dd0b8bfa5e3c64c0d171277cb4f5c77826be7892c7b09"},"schema_version":"1.0","source":{"id":"1108.3769","kind":"arxiv","version":2}},"canonical_sha256":"76207821e1b4e68d7d28c0e6527fb7323de882a5f219718c94d2b7565bae7d15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76207821e1b4e68d7d28c0e6527fb7323de882a5f219718c94d2b7565bae7d15","first_computed_at":"2026-05-18T03:22:17.570163Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:22:17.570163Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cGWRNigwJ4T/QN8pN8Vq9gGq1lXNJwzASIHrFFhK2Pu+x0PI+hRhrbtZjnmlFXgrTt0eQApD+uOkspk355qMAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:22:17.570716Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.3769","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dad5bee7218d26008a95780701122c5f309bad558a833943d0ab6f573df6b516","sha256:4ac928deb6a6a3fe959115d36f636ae15b281a8d9480ee47c556429c0100460c"],"state_sha256":"2cef8273d7493efe186071d17c8e2a42aa62679d9414cf62a97431824cb276e1"}