{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1997:5EKZVR5LUGLF5FZ42Q5JJZTW3R","short_pith_number":"pith:5EKZVR5L","canonical_record":{"source":{"id":"q-alg/9710022","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"q-alg","submitted_at":"1997-10-17T14:50:46Z","cross_cats_sorted":["gr-qc","hep-th","math.QA"],"title_canon_sha256":"2e5ca7c110815f1926c067eecbac8e12444852c8e264c76a46c1077eb70d1bea","abstract_canon_sha256":"0c6d556e15c66095aa66a4fc47d06acee49502b7b26ef08fddb171586308cf0c"},"schema_version":"1.0"},"canonical_sha256":"e9159ac7aba1965e973cd43a94e676dc4e80b7283d85434720dc88741487e183","source":{"kind":"arxiv","id":"q-alg/9710022","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"q-alg/9710022","created_at":"2026-07-04T16:06:27Z"},{"alias_kind":"arxiv_version","alias_value":"q-alg/9710022v2","created_at":"2026-07-04T16:06:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.q-alg/9710022","created_at":"2026-07-04T16:06:27Z"},{"alias_kind":"pith_short_12","alias_value":"5EKZVR5LUGLF","created_at":"2026-07-04T16:06:27Z"},{"alias_kind":"pith_short_16","alias_value":"5EKZVR5LUGLF5FZ4","created_at":"2026-07-04T16:06:27Z"},{"alias_kind":"pith_short_8","alias_value":"5EKZVR5L","created_at":"2026-07-04T16:06:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1997:5EKZVR5LUGLF5FZ42Q5JJZTW3R","target":"record","payload":{"canonical_record":{"source":{"id":"q-alg/9710022","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"q-alg","submitted_at":"1997-10-17T14:50:46Z","cross_cats_sorted":["gr-qc","hep-th","math.QA"],"title_canon_sha256":"2e5ca7c110815f1926c067eecbac8e12444852c8e264c76a46c1077eb70d1bea","abstract_canon_sha256":"0c6d556e15c66095aa66a4fc47d06acee49502b7b26ef08fddb171586308cf0c"},"schema_version":"1.0"},"canonical_sha256":"e9159ac7aba1965e973cd43a94e676dc4e80b7283d85434720dc88741487e183","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:06:27.664860Z","signature_b64":"Ql3oy3fZFVh6AvBaZ1Zn4Un7+Kq2Ti5l5+E+50bRewnXyAgC7k+LoEKFKilc2oZmsOnFO2TosyBIEuLMsELdCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9159ac7aba1965e973cd43a94e676dc4e80b7283d85434720dc88741487e183","last_reissued_at":"2026-07-04T16:06:27.664512Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:06:27.664512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"q-alg/9710022","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":"2026-07-04T16:06:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hv+nMAJNbLf7CqTwh/moHA1M1qBJQymaHVlh/EJjIWDz0swEeMBrm+buAk+OA45+qgAdoom+vnhDq3VjOClrCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T21:42:51.631373Z"},"content_sha256":"aa379c56a1e46262ff4fdf17c8128a5b9005f5f0dc463a73530208e36a7627f5","schema_version":"1.0","event_id":"sha256:aa379c56a1e46262ff4fdf17c8128a5b9005f5f0dc463a73530208e36a7627f5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1997:5EKZVR5LUGLF5FZ42Q5JJZTW3R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Harmonic Analysis on the quantum Lorentz group","license":"","headline":"","cross_cats":["gr-qc","hep-th","math.QA"],"primary_cat":"q-alg","authors_text":"E.Buffenoir, Ph.Roche","submitted_at":"1997-10-17T14:50:46Z","abstract_excerpt":"This work begins with a review of complexification and realification of Hopf algebras. We emphasize the notion of multiplier Hopf algebras for the description of different classes of functions (compact supported, bounded, unbounded) on complex quantum groups and the construction of the associated left and right Haar measure. Using a continuation of $6j$ symbols of $SU_q (2)$ with complex spins, we give a new description of the unitary representations of $SL_q (2,\\CC)_{\\RR}$ and find explicit expressions for the characters of $SL_q (2,\\CC)_{\\RR}$. The major theorem of this article is the Planch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-alg/9710022","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/q-alg/9710022/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T16:06:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QT6IGutzmTFTDAQJpt+8sBLZpE5sw3xO3oT8Ui+WPqyodeG+TaUlpToSlM/W6zLO0abtIGqg8rY6YontXPL1Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T21:42:51.631743Z"},"content_sha256":"918b0a5daa9bf5477a9f7bb6fb1312ff51f9cc0f8c1e8db909a57a2d26e4a699","schema_version":"1.0","event_id":"sha256:918b0a5daa9bf5477a9f7bb6fb1312ff51f9cc0f8c1e8db909a57a2d26e4a699"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5EKZVR5LUGLF5FZ42Q5JJZTW3R/bundle.json","state_url":"https://pith.science/pith/5EKZVR5LUGLF5FZ42Q5JJZTW3R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5EKZVR5LUGLF5FZ42Q5JJZTW3R/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":"2026-07-04T21:42:51Z","links":{"resolver":"https://pith.science/pith/5EKZVR5LUGLF5FZ42Q5JJZTW3R","bundle":"https://pith.science/pith/5EKZVR5LUGLF5FZ42Q5JJZTW3R/bundle.json","state":"https://pith.science/pith/5EKZVR5LUGLF5FZ42Q5JJZTW3R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5EKZVR5LUGLF5FZ42Q5JJZTW3R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:5EKZVR5LUGLF5FZ42Q5JJZTW3R","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":"0c6d556e15c66095aa66a4fc47d06acee49502b7b26ef08fddb171586308cf0c","cross_cats_sorted":["gr-qc","hep-th","math.QA"],"license":"","primary_cat":"q-alg","submitted_at":"1997-10-17T14:50:46Z","title_canon_sha256":"2e5ca7c110815f1926c067eecbac8e12444852c8e264c76a46c1077eb70d1bea"},"schema_version":"1.0","source":{"id":"q-alg/9710022","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"q-alg/9710022","created_at":"2026-07-04T16:06:27Z"},{"alias_kind":"arxiv_version","alias_value":"q-alg/9710022v2","created_at":"2026-07-04T16:06:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.q-alg/9710022","created_at":"2026-07-04T16:06:27Z"},{"alias_kind":"pith_short_12","alias_value":"5EKZVR5LUGLF","created_at":"2026-07-04T16:06:27Z"},{"alias_kind":"pith_short_16","alias_value":"5EKZVR5LUGLF5FZ4","created_at":"2026-07-04T16:06:27Z"},{"alias_kind":"pith_short_8","alias_value":"5EKZVR5L","created_at":"2026-07-04T16:06:27Z"}],"graph_snapshots":[{"event_id":"sha256:918b0a5daa9bf5477a9f7bb6fb1312ff51f9cc0f8c1e8db909a57a2d26e4a699","target":"graph","created_at":"2026-07-04T16:06:27Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/q-alg/9710022/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This work begins with a review of complexification and realification of Hopf algebras. We emphasize the notion of multiplier Hopf algebras for the description of different classes of functions (compact supported, bounded, unbounded) on complex quantum groups and the construction of the associated left and right Haar measure. Using a continuation of $6j$ symbols of $SU_q (2)$ with complex spins, we give a new description of the unitary representations of $SL_q (2,\\CC)_{\\RR}$ and find explicit expressions for the characters of $SL_q (2,\\CC)_{\\RR}$. The major theorem of this article is the Planch","authors_text":"E.Buffenoir, Ph.Roche","cross_cats":["gr-qc","hep-th","math.QA"],"headline":"","license":"","primary_cat":"q-alg","submitted_at":"1997-10-17T14:50:46Z","title":"Harmonic Analysis on the quantum Lorentz group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-alg/9710022","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:aa379c56a1e46262ff4fdf17c8128a5b9005f5f0dc463a73530208e36a7627f5","target":"record","created_at":"2026-07-04T16:06:27Z","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":"0c6d556e15c66095aa66a4fc47d06acee49502b7b26ef08fddb171586308cf0c","cross_cats_sorted":["gr-qc","hep-th","math.QA"],"license":"","primary_cat":"q-alg","submitted_at":"1997-10-17T14:50:46Z","title_canon_sha256":"2e5ca7c110815f1926c067eecbac8e12444852c8e264c76a46c1077eb70d1bea"},"schema_version":"1.0","source":{"id":"q-alg/9710022","kind":"arxiv","version":2}},"canonical_sha256":"e9159ac7aba1965e973cd43a94e676dc4e80b7283d85434720dc88741487e183","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9159ac7aba1965e973cd43a94e676dc4e80b7283d85434720dc88741487e183","first_computed_at":"2026-07-04T16:06:27.664512Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:06:27.664512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ql3oy3fZFVh6AvBaZ1Zn4Un7+Kq2Ti5l5+E+50bRewnXyAgC7k+LoEKFKilc2oZmsOnFO2TosyBIEuLMsELdCA==","signature_status":"signed_v1","signed_at":"2026-07-04T16:06:27.664860Z","signed_message":"canonical_sha256_bytes"},"source_id":"q-alg/9710022","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa379c56a1e46262ff4fdf17c8128a5b9005f5f0dc463a73530208e36a7627f5","sha256:918b0a5daa9bf5477a9f7bb6fb1312ff51f9cc0f8c1e8db909a57a2d26e4a699"],"state_sha256":"d4ebf89038bc6a8ee79714eba6e97804b2bfdffb4575dcf6a7122e587832f60e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"79vpwd8OQV7R1lMUXwlDiWqmJpoR8X71HYTeMfpmPeNl9jV9MbvGVBhw30NOSukv9WiDs2I0taisnxRMwMuKBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T21:42:51.633603Z","bundle_sha256":"95f4ee461a0b3a4f2a45056fef533f3b60bbf866cb22d1c14db875ee96a63e68"}}