{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4O3MZXTARTIT4GHHZ4PQ6PENJ7","short_pith_number":"pith:4O3MZXTA","canonical_record":{"source":{"id":"1610.02638","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-10-09T07:31:04Z","cross_cats_sorted":["math.CA","math.MP","math.QA"],"title_canon_sha256":"134925c87de93603ede1f4e6a465a75c6d26932059988b28ae9fc6432d629c22","abstract_canon_sha256":"795b1b2040bc72d722252b5d6766738cd0316dc5eb030af1f68571c4b06f7cfd"},"schema_version":"1.0"},"canonical_sha256":"e3b6ccde608cd13e18e7cf1f0f3c8d4fdfe64b74c1286b1767514e6017820b2c","source":{"kind":"arxiv","id":"1610.02638","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.02638","created_at":"2026-05-18T00:06:26Z"},{"alias_kind":"arxiv_version","alias_value":"1610.02638v2","created_at":"2026-05-18T00:06:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02638","created_at":"2026-05-18T00:06:26Z"},{"alias_kind":"pith_short_12","alias_value":"4O3MZXTARTIT","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4O3MZXTARTIT4GHH","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4O3MZXTA","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4O3MZXTARTIT4GHHZ4PQ6PENJ7","target":"record","payload":{"canonical_record":{"source":{"id":"1610.02638","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-10-09T07:31:04Z","cross_cats_sorted":["math.CA","math.MP","math.QA"],"title_canon_sha256":"134925c87de93603ede1f4e6a465a75c6d26932059988b28ae9fc6432d629c22","abstract_canon_sha256":"795b1b2040bc72d722252b5d6766738cd0316dc5eb030af1f68571c4b06f7cfd"},"schema_version":"1.0"},"canonical_sha256":"e3b6ccde608cd13e18e7cf1f0f3c8d4fdfe64b74c1286b1767514e6017820b2c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:26.735361Z","signature_b64":"/VzMS0TAlaSmO7Ta0+iUZMo1Rv2+Gzte85Wd9Y/acXB+DYlXCXmYhIANV619Tr2PJUWAl257pLRqBuIYPGdRAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3b6ccde608cd13e18e7cf1f0f3c8d4fdfe64b74c1286b1767514e6017820b2c","last_reissued_at":"2026-05-18T00:06:26.734637Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:26.734637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.02638","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zAKXhI09fKBUgx1Yw2iNROMOQDQ3rhiRmgcZf7ICZihwT0lO5ON+8XMy15VHzsnl0fVXeIMtuGAoyz8YxHhjBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:28:51.455104Z"},"content_sha256":"30ecb1c623e581d632aab218558851291ee5853bfef9bcea4224128aa42c65d8","schema_version":"1.0","event_id":"sha256:30ecb1c623e581d632aab218558851291ee5853bfef9bcea4224128aa42c65d8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4O3MZXTARTIT4GHHZ4PQ6PENJ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A higher rank Racah algebra and the $\\mathbb{Z}_2^{n}$ Laplace-Dunkl operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP","math.QA"],"primary_cat":"math-ph","authors_text":"Hendrik De Bie, Luc Vinet, Vincent X. Genest, Wouter van de Vijver","submitted_at":"2016-10-09T07:31:04Z","abstract_excerpt":"A higher rank generalization of the (rank one) Racah algebra is obtained as the symmetry algebra of the Laplace-Dunkl operator associated to the $\\mathbb{Z}_2^n$ root system. This algebra is also the invariance algebra of the generic superintegrable model on the $n$-sphere. Bases of Dunkl harmonics are constructed explicitly using a Cauchy-Kovalevskaia theorem. These bases consist of joint eigenfunctions of maximal Abelian subalgebras of the higher rank Racah algebra. A method to obtain expressions for both the connection coefficients between these bases and the action of the symmetries on the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02638","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P5uujIjV2RJSN2D4cQPGMuxvz8kLWlXTY+XvxaUQqSDz/oja0aQwKnIGDzCAA1Acu+a34vxYJQ/f4SEaFo4/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:28:51.455698Z"},"content_sha256":"f8540055c18d15c5c2ed57ed0db79c98b507ac2965961d52e6dd00a3ca72ccb1","schema_version":"1.0","event_id":"sha256:f8540055c18d15c5c2ed57ed0db79c98b507ac2965961d52e6dd00a3ca72ccb1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4O3MZXTARTIT4GHHZ4PQ6PENJ7/bundle.json","state_url":"https://pith.science/pith/4O3MZXTARTIT4GHHZ4PQ6PENJ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4O3MZXTARTIT4GHHZ4PQ6PENJ7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T07:28:51Z","links":{"resolver":"https://pith.science/pith/4O3MZXTARTIT4GHHZ4PQ6PENJ7","bundle":"https://pith.science/pith/4O3MZXTARTIT4GHHZ4PQ6PENJ7/bundle.json","state":"https://pith.science/pith/4O3MZXTARTIT4GHHZ4PQ6PENJ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4O3MZXTARTIT4GHHZ4PQ6PENJ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4O3MZXTARTIT4GHHZ4PQ6PENJ7","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":"795b1b2040bc72d722252b5d6766738cd0316dc5eb030af1f68571c4b06f7cfd","cross_cats_sorted":["math.CA","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-10-09T07:31:04Z","title_canon_sha256":"134925c87de93603ede1f4e6a465a75c6d26932059988b28ae9fc6432d629c22"},"schema_version":"1.0","source":{"id":"1610.02638","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.02638","created_at":"2026-05-18T00:06:26Z"},{"alias_kind":"arxiv_version","alias_value":"1610.02638v2","created_at":"2026-05-18T00:06:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02638","created_at":"2026-05-18T00:06:26Z"},{"alias_kind":"pith_short_12","alias_value":"4O3MZXTARTIT","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4O3MZXTARTIT4GHH","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4O3MZXTA","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:f8540055c18d15c5c2ed57ed0db79c98b507ac2965961d52e6dd00a3ca72ccb1","target":"graph","created_at":"2026-05-18T00:06:26Z","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 higher rank generalization of the (rank one) Racah algebra is obtained as the symmetry algebra of the Laplace-Dunkl operator associated to the $\\mathbb{Z}_2^n$ root system. This algebra is also the invariance algebra of the generic superintegrable model on the $n$-sphere. Bases of Dunkl harmonics are constructed explicitly using a Cauchy-Kovalevskaia theorem. These bases consist of joint eigenfunctions of maximal Abelian subalgebras of the higher rank Racah algebra. A method to obtain expressions for both the connection coefficients between these bases and the action of the symmetries on the","authors_text":"Hendrik De Bie, Luc Vinet, Vincent X. Genest, Wouter van de Vijver","cross_cats":["math.CA","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-10-09T07:31:04Z","title":"A higher rank Racah algebra and the $\\mathbb{Z}_2^{n}$ Laplace-Dunkl operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02638","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":"sha256:30ecb1c623e581d632aab218558851291ee5853bfef9bcea4224128aa42c65d8","target":"record","created_at":"2026-05-18T00:06:26Z","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":"795b1b2040bc72d722252b5d6766738cd0316dc5eb030af1f68571c4b06f7cfd","cross_cats_sorted":["math.CA","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-10-09T07:31:04Z","title_canon_sha256":"134925c87de93603ede1f4e6a465a75c6d26932059988b28ae9fc6432d629c22"},"schema_version":"1.0","source":{"id":"1610.02638","kind":"arxiv","version":2}},"canonical_sha256":"e3b6ccde608cd13e18e7cf1f0f3c8d4fdfe64b74c1286b1767514e6017820b2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3b6ccde608cd13e18e7cf1f0f3c8d4fdfe64b74c1286b1767514e6017820b2c","first_computed_at":"2026-05-18T00:06:26.734637Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:26.734637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/VzMS0TAlaSmO7Ta0+iUZMo1Rv2+Gzte85Wd9Y/acXB+DYlXCXmYhIANV619Tr2PJUWAl257pLRqBuIYPGdRAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:26.735361Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.02638","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30ecb1c623e581d632aab218558851291ee5853bfef9bcea4224128aa42c65d8","sha256:f8540055c18d15c5c2ed57ed0db79c98b507ac2965961d52e6dd00a3ca72ccb1"],"state_sha256":"0d7c5060772a4286cb8c80f936cbff5e329ab033c27a2e4b3807831946502950"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fWe/fGQoRE0p235R7FVfpiQQSD2IkXP9Uxe09K28F6c8XjMYWPGrwXlvLUr5FNXawoHntz+L4Ss5Rd3a2zs1BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T07:28:51.458709Z","bundle_sha256":"18639622c285a15cfe429507def70750cd2baf56e9bc23a4efb6d88d3faac9c8"}}