{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IY7ZCAZRDZRSK5YZYN2V3BG5TP","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":"1acc8a23d2e3972a24d7f80c4c62c754e584b91cd5804c7a3ffb30b4c7e54f75","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-11-24T15:11:27Z","title_canon_sha256":"fe0554c2ddc579385b785027d70f19727e20a23729a85202021a44f04446c383"},"schema_version":"1.0","source":{"id":"1611.08213","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.08213","created_at":"2026-05-18T00:56:43Z"},{"alias_kind":"arxiv_version","alias_value":"1611.08213v1","created_at":"2026-05-18T00:56:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08213","created_at":"2026-05-18T00:56:43Z"},{"alias_kind":"pith_short_12","alias_value":"IY7ZCAZRDZRS","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IY7ZCAZRDZRSK5YZ","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IY7ZCAZR","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:930341a368dbcadafac8c32e106d73d7d3977ff752fd4cdca344bbb809a9021d","target":"graph","created_at":"2026-05-18T00:56:43Z","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":"Dunkl theory is a far reaching generalization of Fourier analysis and special function theory related to root systems. During the sixties and seventies, it became gradually clear that radial Fourier analysis on rank one symmetric spaces was closely connected with certain classes of special functions in one variable. During the eighties, several attempts were made, mainly by the Dutch school, to extend these results in higher rank (i.e. in several variables), until the discovery of Dunkl operators in the rational case and Cherednik operators in the trigonometric case. Together with q-special fu","authors_text":"Jean-Philippe Anker (MAPMO)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-11-24T15:11:27Z","title":"An introduction to Dunkl theory and its analytic aspects"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08213","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":"sha256:3bf7a6551135402b678a36a74c584668611cb3795591e4d5c2ebe15cdb64f909","target":"record","created_at":"2026-05-18T00:56:43Z","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":"1acc8a23d2e3972a24d7f80c4c62c754e584b91cd5804c7a3ffb30b4c7e54f75","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-11-24T15:11:27Z","title_canon_sha256":"fe0554c2ddc579385b785027d70f19727e20a23729a85202021a44f04446c383"},"schema_version":"1.0","source":{"id":"1611.08213","kind":"arxiv","version":1}},"canonical_sha256":"463f9103311e63257719c3755d84dd9bcb430b74f3820c7cdad84ef3159c7839","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"463f9103311e63257719c3755d84dd9bcb430b74f3820c7cdad84ef3159c7839","first_computed_at":"2026-05-18T00:56:43.979218Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:43.979218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bfU/DXqf0Ra8bmujA6IHHqN91qimK4ilTDhvyEFtTdFAiYZQ/edqjs8yjsuSgn5wJZVMXRhRelj2+UgxkznfDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:43.979828Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.08213","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3bf7a6551135402b678a36a74c584668611cb3795591e4d5c2ebe15cdb64f909","sha256:930341a368dbcadafac8c32e106d73d7d3977ff752fd4cdca344bbb809a9021d"],"state_sha256":"416e9abc4315efcc04ed22a808bf83b7f12aa199e014efa01455811a90afcb9b"}