{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:EAO2ZRNGDLATMWAB34ACQNEHOK","short_pith_number":"pith:EAO2ZRNG","canonical_record":{"source":{"id":"1810.00130","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-09-29T01:28:02Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"a2757470426777fba9abe28bf6558695f6fb9a481e1dbfd8196e4ed72f938fb5","abstract_canon_sha256":"ecca72faaf45ed3ecb7029f485fa27ae35bd38542c932d0b9652acf750efc287"},"schema_version":"1.0"},"canonical_sha256":"201dacc5a61ac1365801df00283487729024c9d0d35c5c49d30ef6a5a7a212fc","source":{"kind":"arxiv","id":"1810.00130","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.00130","created_at":"2026-05-18T00:00:47Z"},{"alias_kind":"arxiv_version","alias_value":"1810.00130v1","created_at":"2026-05-18T00:00:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00130","created_at":"2026-05-18T00:00:47Z"},{"alias_kind":"pith_short_12","alias_value":"EAO2ZRNGDLAT","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EAO2ZRNGDLATMWAB","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EAO2ZRNG","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:EAO2ZRNGDLATMWAB34ACQNEHOK","target":"record","payload":{"canonical_record":{"source":{"id":"1810.00130","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-09-29T01:28:02Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"a2757470426777fba9abe28bf6558695f6fb9a481e1dbfd8196e4ed72f938fb5","abstract_canon_sha256":"ecca72faaf45ed3ecb7029f485fa27ae35bd38542c932d0b9652acf750efc287"},"schema_version":"1.0"},"canonical_sha256":"201dacc5a61ac1365801df00283487729024c9d0d35c5c49d30ef6a5a7a212fc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:47.756632Z","signature_b64":"TvTGFsUX2I33wEe8PWIt5QAJnlXArLuSF9gSe3K+Svkq8zZp435whz4qoYgAZJJ2s2SvUjDPFA7jfvT6LLlUCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"201dacc5a61ac1365801df00283487729024c9d0d35c5c49d30ef6a5a7a212fc","last_reissued_at":"2026-05-18T00:00:47.756160Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:47.756160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.00130","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:00:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DRJhvwaDiFXm5tiU8GpS06XaMZngQxNEXM4S562W/g27wCdkqsSZA7KwYUkFEcWRALsHF77anvGuqX8lU2msCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T01:50:34.248803Z"},"content_sha256":"23c1dc0047620b9e27d5a4f3c5e6381758642ef0dc0b9151bf25fa1de0f172b4","schema_version":"1.0","event_id":"sha256:23c1dc0047620b9e27d5a4f3c5e6381758642ef0dc0b9151bf25fa1de0f172b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:EAO2ZRNGDLATMWAB34ACQNEHOK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The dual pair $Pin(2n)\\times\\mathfrak{osp}(1|2)$, the Dirac equation and the Bannai-Ito algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alexei Zhedanov, Julien Gaboriaud, Luc Vinet, St\\'ephane Vinet","submitted_at":"2018-09-29T01:28:02Z","abstract_excerpt":"The Bannai-Ito algebra can be defined as the centralizer of the coproduct embedding of $\\mathfrak{osp}(1|2)$ in $\\mathfrak{osp}(1|2)^{\\otimes n}$. It will be shown that it is also the commutant of a maximal Abelian subalgebra of $\\mathfrak{o}(2n)$ in a spinorial representation and an embedding of the Racah algebra in this commutant will emerge. The connection between the two pictures for the Bannai-Ito algebra will be traced to the Howe duality which is embodied in the $Pin(2n)\\times\\mathfrak{osp}(1|2)$ symmetry of the massless Dirac equation in $\\mathbb{R}^{2n}$. Dimensional reduction to $\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00130","kind":"arxiv","version":1},"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":"2026-05-18T00:00:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LYsNE8qUWRKbgHZTY+JbOWV//VeAO8tfJRs8VCMdWZRlU3rFtsjSxEzKPJydocdRa7RUzIb4qk0O+kXLV6sKDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T01:50:34.249157Z"},"content_sha256":"cae3295eaefa30c1428777bed1f8bfcf155fd959a8a1c48a8fb71e3a3b389ec1","schema_version":"1.0","event_id":"sha256:cae3295eaefa30c1428777bed1f8bfcf155fd959a8a1c48a8fb71e3a3b389ec1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EAO2ZRNGDLATMWAB34ACQNEHOK/bundle.json","state_url":"https://pith.science/pith/EAO2ZRNGDLATMWAB34ACQNEHOK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EAO2ZRNGDLATMWAB34ACQNEHOK/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":"2026-06-29T01:50:34Z","links":{"resolver":"https://pith.science/pith/EAO2ZRNGDLATMWAB34ACQNEHOK","bundle":"https://pith.science/pith/EAO2ZRNGDLATMWAB34ACQNEHOK/bundle.json","state":"https://pith.science/pith/EAO2ZRNGDLATMWAB34ACQNEHOK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EAO2ZRNGDLATMWAB34ACQNEHOK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EAO2ZRNGDLATMWAB34ACQNEHOK","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":"ecca72faaf45ed3ecb7029f485fa27ae35bd38542c932d0b9652acf750efc287","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-09-29T01:28:02Z","title_canon_sha256":"a2757470426777fba9abe28bf6558695f6fb9a481e1dbfd8196e4ed72f938fb5"},"schema_version":"1.0","source":{"id":"1810.00130","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.00130","created_at":"2026-05-18T00:00:47Z"},{"alias_kind":"arxiv_version","alias_value":"1810.00130v1","created_at":"2026-05-18T00:00:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00130","created_at":"2026-05-18T00:00:47Z"},{"alias_kind":"pith_short_12","alias_value":"EAO2ZRNGDLAT","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EAO2ZRNGDLATMWAB","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EAO2ZRNG","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:cae3295eaefa30c1428777bed1f8bfcf155fd959a8a1c48a8fb71e3a3b389ec1","target":"graph","created_at":"2026-05-18T00:00:47Z","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 Bannai-Ito algebra can be defined as the centralizer of the coproduct embedding of $\\mathfrak{osp}(1|2)$ in $\\mathfrak{osp}(1|2)^{\\otimes n}$. It will be shown that it is also the commutant of a maximal Abelian subalgebra of $\\mathfrak{o}(2n)$ in a spinorial representation and an embedding of the Racah algebra in this commutant will emerge. The connection between the two pictures for the Bannai-Ito algebra will be traced to the Howe duality which is embodied in the $Pin(2n)\\times\\mathfrak{osp}(1|2)$ symmetry of the massless Dirac equation in $\\mathbb{R}^{2n}$. Dimensional reduction to $\\ma","authors_text":"Alexei Zhedanov, Julien Gaboriaud, Luc Vinet, St\\'ephane Vinet","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-09-29T01:28:02Z","title":"The dual pair $Pin(2n)\\times\\mathfrak{osp}(1|2)$, the Dirac equation and the Bannai-Ito algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00130","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":"sha256:23c1dc0047620b9e27d5a4f3c5e6381758642ef0dc0b9151bf25fa1de0f172b4","target":"record","created_at":"2026-05-18T00:00:47Z","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":"ecca72faaf45ed3ecb7029f485fa27ae35bd38542c932d0b9652acf750efc287","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-09-29T01:28:02Z","title_canon_sha256":"a2757470426777fba9abe28bf6558695f6fb9a481e1dbfd8196e4ed72f938fb5"},"schema_version":"1.0","source":{"id":"1810.00130","kind":"arxiv","version":1}},"canonical_sha256":"201dacc5a61ac1365801df00283487729024c9d0d35c5c49d30ef6a5a7a212fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"201dacc5a61ac1365801df00283487729024c9d0d35c5c49d30ef6a5a7a212fc","first_computed_at":"2026-05-18T00:00:47.756160Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:47.756160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TvTGFsUX2I33wEe8PWIt5QAJnlXArLuSF9gSe3K+Svkq8zZp435whz4qoYgAZJJ2s2SvUjDPFA7jfvT6LLlUCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:47.756632Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.00130","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23c1dc0047620b9e27d5a4f3c5e6381758642ef0dc0b9151bf25fa1de0f172b4","sha256:cae3295eaefa30c1428777bed1f8bfcf155fd959a8a1c48a8fb71e3a3b389ec1"],"state_sha256":"618ffeec7d0717e8bf9c4c89363285377c65b34297d55d660324cde2c53f5c6a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Gbc9ZlTS3hCER1D1vqg0raP4Kf8FevlZ/VQ5YYamlMSVMHGPItvIN0s6qu/zqeeHtjHG5xyVwPYlv8EF2mFDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T01:50:34.251283Z","bundle_sha256":"ee9e38ab9a8089bcd12b6a80030df2c54e651f57f75f9fcd6388a6620b6ab6ca"}}