{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:LPKBUPDOTLB5BQZYXW4AZYXHBI","short_pith_number":"pith:LPKBUPDO","canonical_record":{"source":{"id":"1711.02755","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-11-07T22:41:29Z","cross_cats_sorted":[],"title_canon_sha256":"3ae87827a55acd19633622cb0838b00d008de4e58f8814b7a1b9de36d512e77a","abstract_canon_sha256":"ad56fa125eadbddaba774098f6108d707a2faf44f7185507a82a7d5241dc851d"},"schema_version":"1.0"},"canonical_sha256":"5bd41a3c6e9ac3d0c338bdb80ce2e70a2f49d6e2e3bdf1c501668ccd723187b9","source":{"kind":"arxiv","id":"1711.02755","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02755","created_at":"2026-05-18T00:04:13Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02755v4","created_at":"2026-05-18T00:04:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02755","created_at":"2026-05-18T00:04:13Z"},{"alias_kind":"pith_short_12","alias_value":"LPKBUPDOTLB5","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LPKBUPDOTLB5BQZY","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LPKBUPDO","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:LPKBUPDOTLB5BQZYXW4AZYXHBI","target":"record","payload":{"canonical_record":{"source":{"id":"1711.02755","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-11-07T22:41:29Z","cross_cats_sorted":[],"title_canon_sha256":"3ae87827a55acd19633622cb0838b00d008de4e58f8814b7a1b9de36d512e77a","abstract_canon_sha256":"ad56fa125eadbddaba774098f6108d707a2faf44f7185507a82a7d5241dc851d"},"schema_version":"1.0"},"canonical_sha256":"5bd41a3c6e9ac3d0c338bdb80ce2e70a2f49d6e2e3bdf1c501668ccd723187b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:13.506694Z","signature_b64":"GMCc2cjCqhBCD30vs7kB4AWYeoRvpNxzgpbNM8KoK6hxyjVVw2EF1OendnL0GigBtWXmW3Y9Nknu3S4Y1IBPCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5bd41a3c6e9ac3d0c338bdb80ce2e70a2f49d6e2e3bdf1c501668ccd723187b9","last_reissued_at":"2026-05-18T00:04:13.505888Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:13.505888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.02755","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:04:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iKCa2dEwB4gq2uyPodJ1rVX2EW3fBw9ZQC/oDdm92F+evyGy6MsyzTuouywsV68fzaTDR15k3n06UhkVDVpeAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:36:45.590307Z"},"content_sha256":"7af4e0de38165e740c2343d81604b15113348d77e9ab62c9aca8c688fa2e5e0b","schema_version":"1.0","event_id":"sha256:7af4e0de38165e740c2343d81604b15113348d77e9ab62c9aca8c688fa2e5e0b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:LPKBUPDOTLB5BQZYXW4AZYXHBI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"L\\'evy-Khintchine decompositions for generating functionals on algebras associated to universal compact quantum groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Adam Skalski, Anna Kula, Biswarup Das, Uwe Franz","submitted_at":"2017-11-07T22:41:29Z","abstract_excerpt":"We study the first and second cohomology groups of the $^*$-algebras of the universal unitary and orthogonal quantum groups $U_F^+$ and $O_F^+$. This provides valuable information for constructing and classifying L\\'evy processes on these quantum groups, as pointed out by Sch\\\"urmann. In the case when all eigenvalues of $F^*F$ are distinct, we show that these $^*$-algebras have the properties (GC), (NC), and (LK) introduced by Sch\\\"urmann and studied recently by Franz, Gerhold and Thom. In the degenerate case $F=I_d$, we show that they do not have any of these properties. We also compute the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02755","kind":"arxiv","version":4},"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":"2026-05-18T00:04:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4AvsO/Y9ENiZNQLBDVl5mZkOO9cTbRuC6UTPUd1e8YIOiY/ZmWs3ZPmFcltR7unrBmRJTXxwwjuWcnSOYGjyDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:36:45.590982Z"},"content_sha256":"e2f50f00bf3726ab36657336d906bf55f27ad30feaba282335dee1cc18f6db15","schema_version":"1.0","event_id":"sha256:e2f50f00bf3726ab36657336d906bf55f27ad30feaba282335dee1cc18f6db15"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LPKBUPDOTLB5BQZYXW4AZYXHBI/bundle.json","state_url":"https://pith.science/pith/LPKBUPDOTLB5BQZYXW4AZYXHBI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LPKBUPDOTLB5BQZYXW4AZYXHBI/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":"2026-05-28T23:36:45Z","links":{"resolver":"https://pith.science/pith/LPKBUPDOTLB5BQZYXW4AZYXHBI","bundle":"https://pith.science/pith/LPKBUPDOTLB5BQZYXW4AZYXHBI/bundle.json","state":"https://pith.science/pith/LPKBUPDOTLB5BQZYXW4AZYXHBI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LPKBUPDOTLB5BQZYXW4AZYXHBI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LPKBUPDOTLB5BQZYXW4AZYXHBI","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":"ad56fa125eadbddaba774098f6108d707a2faf44f7185507a82a7d5241dc851d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-11-07T22:41:29Z","title_canon_sha256":"3ae87827a55acd19633622cb0838b00d008de4e58f8814b7a1b9de36d512e77a"},"schema_version":"1.0","source":{"id":"1711.02755","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02755","created_at":"2026-05-18T00:04:13Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02755v4","created_at":"2026-05-18T00:04:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02755","created_at":"2026-05-18T00:04:13Z"},{"alias_kind":"pith_short_12","alias_value":"LPKBUPDOTLB5","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LPKBUPDOTLB5BQZY","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LPKBUPDO","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:e2f50f00bf3726ab36657336d906bf55f27ad30feaba282335dee1cc18f6db15","target":"graph","created_at":"2026-05-18T00:04:13Z","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 study the first and second cohomology groups of the $^*$-algebras of the universal unitary and orthogonal quantum groups $U_F^+$ and $O_F^+$. This provides valuable information for constructing and classifying L\\'evy processes on these quantum groups, as pointed out by Sch\\\"urmann. In the case when all eigenvalues of $F^*F$ are distinct, we show that these $^*$-algebras have the properties (GC), (NC), and (LK) introduced by Sch\\\"urmann and studied recently by Franz, Gerhold and Thom. In the degenerate case $F=I_d$, we show that they do not have any of these properties. We also compute the s","authors_text":"Adam Skalski, Anna Kula, Biswarup Das, Uwe Franz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-11-07T22:41:29Z","title":"L\\'evy-Khintchine decompositions for generating functionals on algebras associated to universal compact quantum groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02755","kind":"arxiv","version":4},"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":"sha256:7af4e0de38165e740c2343d81604b15113348d77e9ab62c9aca8c688fa2e5e0b","target":"record","created_at":"2026-05-18T00:04:13Z","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":"ad56fa125eadbddaba774098f6108d707a2faf44f7185507a82a7d5241dc851d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-11-07T22:41:29Z","title_canon_sha256":"3ae87827a55acd19633622cb0838b00d008de4e58f8814b7a1b9de36d512e77a"},"schema_version":"1.0","source":{"id":"1711.02755","kind":"arxiv","version":4}},"canonical_sha256":"5bd41a3c6e9ac3d0c338bdb80ce2e70a2f49d6e2e3bdf1c501668ccd723187b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5bd41a3c6e9ac3d0c338bdb80ce2e70a2f49d6e2e3bdf1c501668ccd723187b9","first_computed_at":"2026-05-18T00:04:13.505888Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:13.505888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GMCc2cjCqhBCD30vs7kB4AWYeoRvpNxzgpbNM8KoK6hxyjVVw2EF1OendnL0GigBtWXmW3Y9Nknu3S4Y1IBPCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:13.506694Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.02755","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7af4e0de38165e740c2343d81604b15113348d77e9ab62c9aca8c688fa2e5e0b","sha256:e2f50f00bf3726ab36657336d906bf55f27ad30feaba282335dee1cc18f6db15"],"state_sha256":"2b4aa303991a3e55ed697b999ff84ca7a93eb3500aee6609d1beaa60f279e62f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lcPiCrOE/cRRdyr0PvfWLZmgCqzNw4GBN6ybsPxdykcHYfxOLe8Y8tvYcvvjcc3BVaJk6Y9RXurrbAE7W0vsCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T23:36:45.594487Z","bundle_sha256":"f6a1ab2cb2f59bc8df8c8eb18f5b913d250b2d50753d86cf6cb6bfafd1ce7d07"}}