{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:QJJUZBLJM6HHKSXEL7UBJCKI35","short_pith_number":"pith:QJJUZBLJ","canonical_record":{"source":{"id":"1106.3512","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-06-17T15:13:32Z","cross_cats_sorted":[],"title_canon_sha256":"1e66d3007f54cc0332e55cccbcbc96165a4714ff98291f38261afba7497ed72d","abstract_canon_sha256":"d627bae45ac9bbc0e91184f58a72f590a8ddfa94a8aa623914118a9dd5fc58e5"},"schema_version":"1.0"},"canonical_sha256":"82534c8569678e754ae45fe8148948df545c78ee0bd76afa78ae38d441a15af4","source":{"kind":"arxiv","id":"1106.3512","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.3512","created_at":"2026-05-18T04:05:03Z"},{"alias_kind":"arxiv_version","alias_value":"1106.3512v2","created_at":"2026-05-18T04:05:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.3512","created_at":"2026-05-18T04:05:03Z"},{"alias_kind":"pith_short_12","alias_value":"QJJUZBLJM6HH","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QJJUZBLJM6HHKSXE","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QJJUZBLJ","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:QJJUZBLJM6HHKSXEL7UBJCKI35","target":"record","payload":{"canonical_record":{"source":{"id":"1106.3512","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-06-17T15:13:32Z","cross_cats_sorted":[],"title_canon_sha256":"1e66d3007f54cc0332e55cccbcbc96165a4714ff98291f38261afba7497ed72d","abstract_canon_sha256":"d627bae45ac9bbc0e91184f58a72f590a8ddfa94a8aa623914118a9dd5fc58e5"},"schema_version":"1.0"},"canonical_sha256":"82534c8569678e754ae45fe8148948df545c78ee0bd76afa78ae38d441a15af4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:03.885815Z","signature_b64":"mFh/alRmbUExhJY0xyJG+KVVipgkx/lKHnrhJ496A8E7FBN4rxK+FZ5kRNtBfmLzrFf/Xi52qAI9vlwi4DSnAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82534c8569678e754ae45fe8148948df545c78ee0bd76afa78ae38d441a15af4","last_reissued_at":"2026-05-18T04:05:03.884991Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:03.884991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.3512","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":"2026-05-18T04:05:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cXmt6AQmxozvk8HpeRiC/MejGcXgBt8DFq9INRzR60DrV7Ni6LfRz5TXuZx2hKO1cSN3ykraO0OuE/XEyku2Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T17:18:40.536344Z"},"content_sha256":"9d818f5b7939ef28d8a689f6ba94971355a435535a1603e2e963850d5b8e092c","schema_version":"1.0","event_id":"sha256:9d818f5b7939ef28d8a689f6ba94971355a435535a1603e2e963850d5b8e092c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:QJJUZBLJM6HHKSXEL7UBJCKI35","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dunkl shift operators and Bannai-Ito polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alexei Zhedanov, Luc Vinet, Satoshi Tsujimoto","submitted_at":"2011-06-17T15:13:32Z","abstract_excerpt":"We consider the most general Dunkl shift operator $L$ with the following properties: (i) $L$ is of first order in the shift operator and involves reflections; (ii) $L$ preserves the space of polynomials of a given degree; (iii) $L$ is potentially self-adjoint. We show that under these conditions, the operator $L$ has eigenfunctions which coincide with the Bannai-Ito polynomials. We construct a polynomial basis which is lower-triangular and two-diagonal with respect to the action of the operator $L$. This allows to express the BI polynomials explicitly. We also present an anti-commutator AW(3) "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3512","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":"2026-05-18T04:05:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q+bPEoH87DF+pAchLGw1cPuAdwiV5+Ocg3hyI5sADrA2PQSK/pchV5UjsXDadfnRPeZxMV5p4ws1YjdCgzScAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T17:18:40.536832Z"},"content_sha256":"b242e806f61c8c22106094612b42310224822d153f8527cbe75e75186c9a6125","schema_version":"1.0","event_id":"sha256:b242e806f61c8c22106094612b42310224822d153f8527cbe75e75186c9a6125"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QJJUZBLJM6HHKSXEL7UBJCKI35/bundle.json","state_url":"https://pith.science/pith/QJJUZBLJM6HHKSXEL7UBJCKI35/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QJJUZBLJM6HHKSXEL7UBJCKI35/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":"2026-08-16T17:18:40Z","links":{"resolver":"https://pith.science/pith/QJJUZBLJM6HHKSXEL7UBJCKI35","bundle":"https://pith.science/pith/QJJUZBLJM6HHKSXEL7UBJCKI35/bundle.json","state":"https://pith.science/pith/QJJUZBLJM6HHKSXEL7UBJCKI35/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QJJUZBLJM6HHKSXEL7UBJCKI35/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QJJUZBLJM6HHKSXEL7UBJCKI35","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":"d627bae45ac9bbc0e91184f58a72f590a8ddfa94a8aa623914118a9dd5fc58e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-06-17T15:13:32Z","title_canon_sha256":"1e66d3007f54cc0332e55cccbcbc96165a4714ff98291f38261afba7497ed72d"},"schema_version":"1.0","source":{"id":"1106.3512","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.3512","created_at":"2026-05-18T04:05:03Z"},{"alias_kind":"arxiv_version","alias_value":"1106.3512v2","created_at":"2026-05-18T04:05:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.3512","created_at":"2026-05-18T04:05:03Z"},{"alias_kind":"pith_short_12","alias_value":"QJJUZBLJM6HH","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QJJUZBLJM6HHKSXE","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QJJUZBLJ","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:b242e806f61c8c22106094612b42310224822d153f8527cbe75e75186c9a6125","target":"graph","created_at":"2026-05-18T04:05:03Z","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":"We consider the most general Dunkl shift operator $L$ with the following properties: (i) $L$ is of first order in the shift operator and involves reflections; (ii) $L$ preserves the space of polynomials of a given degree; (iii) $L$ is potentially self-adjoint. We show that under these conditions, the operator $L$ has eigenfunctions which coincide with the Bannai-Ito polynomials. We construct a polynomial basis which is lower-triangular and two-diagonal with respect to the action of the operator $L$. This allows to express the BI polynomials explicitly. We also present an anti-commutator AW(3) ","authors_text":"Alexei Zhedanov, Luc Vinet, Satoshi Tsujimoto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-06-17T15:13:32Z","title":"Dunkl shift operators and Bannai-Ito polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3512","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":"sha256:9d818f5b7939ef28d8a689f6ba94971355a435535a1603e2e963850d5b8e092c","target":"record","created_at":"2026-05-18T04:05:03Z","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":"d627bae45ac9bbc0e91184f58a72f590a8ddfa94a8aa623914118a9dd5fc58e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-06-17T15:13:32Z","title_canon_sha256":"1e66d3007f54cc0332e55cccbcbc96165a4714ff98291f38261afba7497ed72d"},"schema_version":"1.0","source":{"id":"1106.3512","kind":"arxiv","version":2}},"canonical_sha256":"82534c8569678e754ae45fe8148948df545c78ee0bd76afa78ae38d441a15af4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82534c8569678e754ae45fe8148948df545c78ee0bd76afa78ae38d441a15af4","first_computed_at":"2026-05-18T04:05:03.884991Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:03.884991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mFh/alRmbUExhJY0xyJG+KVVipgkx/lKHnrhJ496A8E7FBN4rxK+FZ5kRNtBfmLzrFf/Xi52qAI9vlwi4DSnAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:03.885815Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.3512","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d818f5b7939ef28d8a689f6ba94971355a435535a1603e2e963850d5b8e092c","sha256:b242e806f61c8c22106094612b42310224822d153f8527cbe75e75186c9a6125"],"state_sha256":"e03c927549a6fa45116bd22c6cba01c68aef4640d71b13e027f6e3db444371c6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6jaVW9JbwJMA5u0Pf5khhu/ze5Sw7R1fTzmsARtXPm+yMB5rAUTXZUCRyK2eS+YrGwYED/qMUGQksfoOlV4SAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T17:18:40.542547Z","bundle_sha256":"2b8f1f51740384034ea7482eba7452f6ffd505f94fb25b8dbaa3dd54075692d4"}}