{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RXB42CE2QHSYAM6NSVII5GGIXC","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":"ca8a315ae3df719f94a34192d6d166fda28c66a12c22d3400b233a3d776abe9a","cross_cats_sorted":["math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-13T18:55:27Z","title_canon_sha256":"c1f77d082dcd1a2567c505bfdc236409b36d3313e31e83efdcb078564a3dec47"},"schema_version":"1.0","source":{"id":"1501.03108","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.03108","created_at":"2026-05-18T01:11:00Z"},{"alias_kind":"arxiv_version","alias_value":"1501.03108v1","created_at":"2026-05-18T01:11:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03108","created_at":"2026-05-18T01:11:00Z"},{"alias_kind":"pith_short_12","alias_value":"RXB42CE2QHSY","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RXB42CE2QHSYAM6N","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RXB42CE2","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:49e0280957723b896b9fe4d6da4d9464288bbd0e0d1c456a8273ece00d0c46ab","target":"graph","created_at":"2026-05-18T01:11:00Z","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":"The Dirac-Dunkl operator on the 2-sphere associated to the $\\mathbb{Z}_2^3$ reflection group is considered. Its symmetries are found and are shown to generate the Bannai-Ito algebra. Representations of the Bannai-Ito algebra are constructed using ladder operators. Eigenfunctions of the spherical Dirac-Dunkl operator are obtained using a Cauchy-Kovalevskaia extension theorem. These eigenfunctions, which correspond to Dunkl monogenics, are seen to support finite-dimensional irreducible representations of the Bannai-Ito algebra.","authors_text":"Hendrik De Bie, Luc Vinet, Vincent X. Genest","cross_cats":["math.CA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-13T18:55:27Z","title":"A Dirac-Dunkl equation on $S^2$ and the Bannai-Ito algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03108","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":"sha256:201d3488448cc11e5f2ab01e5d893cfee168f76b9382909d68bb30682ca1fa08","target":"record","created_at":"2026-05-18T01:11:00Z","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":"ca8a315ae3df719f94a34192d6d166fda28c66a12c22d3400b233a3d776abe9a","cross_cats_sorted":["math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-13T18:55:27Z","title_canon_sha256":"c1f77d082dcd1a2567c505bfdc236409b36d3313e31e83efdcb078564a3dec47"},"schema_version":"1.0","source":{"id":"1501.03108","kind":"arxiv","version":1}},"canonical_sha256":"8dc3cd089a81e58033cd95508e98c8b88d4da212c2443db66a1a535f7a297d4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8dc3cd089a81e58033cd95508e98c8b88d4da212c2443db66a1a535f7a297d4b","first_computed_at":"2026-05-18T01:11:00.303376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:00.303376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ibIzaNHV2D/bs9V4K/jggCH2ylB4PCKFTL/w6X68h1tLMOaNaKFYjYQdzS2PCd4KX6ybrusN/+4JxNySF80KBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:00.304006Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.03108","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:201d3488448cc11e5f2ab01e5d893cfee168f76b9382909d68bb30682ca1fa08","sha256:49e0280957723b896b9fe4d6da4d9464288bbd0e0d1c456a8273ece00d0c46ab"],"state_sha256":"c5ee0546d609d71ac9742ed77c8ac033ede036ee89646789a54eef5128af360e"}