{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:LDBBMNCZLQFXTKO62CPZOYA6WW","short_pith_number":"pith:LDBBMNCZ","canonical_record":{"source":{"id":"0912.4350","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-12-22T09:53:14Z","cross_cats_sorted":[],"title_canon_sha256":"aa6ecaecc4f1fa3676f256720f56703e1cf2d1ee6400cc2b5ec9d2036f247fc3","abstract_canon_sha256":"00ce255afab27be216a5c761a2a5f978e46baf1bf326441e7cd82b8eac8acb4a"},"schema_version":"1.0"},"canonical_sha256":"58c21634595c0b79a9ded09f97601eb59c479d00930ddf8c6979569b2400d121","source":{"kind":"arxiv","id":"0912.4350","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.4350","created_at":"2026-05-18T03:16:17Z"},{"alias_kind":"arxiv_version","alias_value":"0912.4350v2","created_at":"2026-05-18T03:16:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.4350","created_at":"2026-05-18T03:16:17Z"},{"alias_kind":"pith_short_12","alias_value":"LDBBMNCZLQFX","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"LDBBMNCZLQFXTKO6","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"LDBBMNCZ","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:LDBBMNCZLQFXTKO62CPZOYA6WW","target":"record","payload":{"canonical_record":{"source":{"id":"0912.4350","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-12-22T09:53:14Z","cross_cats_sorted":[],"title_canon_sha256":"aa6ecaecc4f1fa3676f256720f56703e1cf2d1ee6400cc2b5ec9d2036f247fc3","abstract_canon_sha256":"00ce255afab27be216a5c761a2a5f978e46baf1bf326441e7cd82b8eac8acb4a"},"schema_version":"1.0"},"canonical_sha256":"58c21634595c0b79a9ded09f97601eb59c479d00930ddf8c6979569b2400d121","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:17.861692Z","signature_b64":"dEAzREJnpV56zxWGnVGsvM/viRsVoOzm0vTEjsrWBMyUn21/DOP3scGZp5HHIdmLyhsYvXJsc95ToEAtIx98DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58c21634595c0b79a9ded09f97601eb59c479d00930ddf8c6979569b2400d121","last_reissued_at":"2026-05-18T03:16:17.861206Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:17.861206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0912.4350","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":"2026-05-18T03:16:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xvER5sM1oKPMrdqTPsBnOMbBufgRIN9JWRVg9lChiNPTBmjMYkLtBIMxPrOD63cohaZSdcYjVgUtGwBp7zBnCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:10:38.514417Z"},"content_sha256":"da76590af260286ee1cbec5c067b9665e8068ffb19e7c49d4313d3bf92acc9e3","schema_version":"1.0","event_id":"sha256:da76590af260286ee1cbec5c067b9665e8068ffb19e7c49d4313d3bf92acc9e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:LDBBMNCZLQFXTKO62CPZOYA6WW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a Morita equivalence between the duals of quantum SU(2) and quantum E(2)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"K. De Commer","submitted_at":"2009-12-22T09:53:14Z","abstract_excerpt":"Let SU_q(2) and E_q(2) be Woronowicz' q-deformations of respectively the compact Lie group SU(2) and the non-trivial double cover of the Lie group E(2) of Euclidian transformations of the plane. We prove that, in some sense, their duals are `Morita equivalent locally compact quantum groups'. In more concrete terms, we prove that the von Neumann algebraic quantum groups of `bounded measurable functions' on SU_q(2) and E_q(2) are unitary cocycle deformations of each other."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.4350","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":"2026-05-18T03:16:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UCKFnMDRLRzMcO83zltITnpWMojSOwTX51TCm2IXzNRfYtgpYirWDO3d26VLDZgtT0F7On4xfIACzAzQ5XIDBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:10:38.514764Z"},"content_sha256":"88ac6a652539461ba6759a1e9ffe08270d9f3c6787280d2d60423af651548c13","schema_version":"1.0","event_id":"sha256:88ac6a652539461ba6759a1e9ffe08270d9f3c6787280d2d60423af651548c13"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LDBBMNCZLQFXTKO62CPZOYA6WW/bundle.json","state_url":"https://pith.science/pith/LDBBMNCZLQFXTKO62CPZOYA6WW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LDBBMNCZLQFXTKO62CPZOYA6WW/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":"2026-06-24T07:10:38Z","links":{"resolver":"https://pith.science/pith/LDBBMNCZLQFXTKO62CPZOYA6WW","bundle":"https://pith.science/pith/LDBBMNCZLQFXTKO62CPZOYA6WW/bundle.json","state":"https://pith.science/pith/LDBBMNCZLQFXTKO62CPZOYA6WW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LDBBMNCZLQFXTKO62CPZOYA6WW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:LDBBMNCZLQFXTKO62CPZOYA6WW","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":"00ce255afab27be216a5c761a2a5f978e46baf1bf326441e7cd82b8eac8acb4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-12-22T09:53:14Z","title_canon_sha256":"aa6ecaecc4f1fa3676f256720f56703e1cf2d1ee6400cc2b5ec9d2036f247fc3"},"schema_version":"1.0","source":{"id":"0912.4350","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.4350","created_at":"2026-05-18T03:16:17Z"},{"alias_kind":"arxiv_version","alias_value":"0912.4350v2","created_at":"2026-05-18T03:16:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.4350","created_at":"2026-05-18T03:16:17Z"},{"alias_kind":"pith_short_12","alias_value":"LDBBMNCZLQFX","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"LDBBMNCZLQFXTKO6","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"LDBBMNCZ","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:88ac6a652539461ba6759a1e9ffe08270d9f3c6787280d2d60423af651548c13","target":"graph","created_at":"2026-05-18T03:16:17Z","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":"Let SU_q(2) and E_q(2) be Woronowicz' q-deformations of respectively the compact Lie group SU(2) and the non-trivial double cover of the Lie group E(2) of Euclidian transformations of the plane. We prove that, in some sense, their duals are `Morita equivalent locally compact quantum groups'. In more concrete terms, we prove that the von Neumann algebraic quantum groups of `bounded measurable functions' on SU_q(2) and E_q(2) are unitary cocycle deformations of each other.","authors_text":"K. De Commer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-12-22T09:53:14Z","title":"On a Morita equivalence between the duals of quantum SU(2) and quantum E(2)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.4350","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:da76590af260286ee1cbec5c067b9665e8068ffb19e7c49d4313d3bf92acc9e3","target":"record","created_at":"2026-05-18T03:16:17Z","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":"00ce255afab27be216a5c761a2a5f978e46baf1bf326441e7cd82b8eac8acb4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-12-22T09:53:14Z","title_canon_sha256":"aa6ecaecc4f1fa3676f256720f56703e1cf2d1ee6400cc2b5ec9d2036f247fc3"},"schema_version":"1.0","source":{"id":"0912.4350","kind":"arxiv","version":2}},"canonical_sha256":"58c21634595c0b79a9ded09f97601eb59c479d00930ddf8c6979569b2400d121","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58c21634595c0b79a9ded09f97601eb59c479d00930ddf8c6979569b2400d121","first_computed_at":"2026-05-18T03:16:17.861206Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:17.861206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dEAzREJnpV56zxWGnVGsvM/viRsVoOzm0vTEjsrWBMyUn21/DOP3scGZp5HHIdmLyhsYvXJsc95ToEAtIx98DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:17.861692Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.4350","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da76590af260286ee1cbec5c067b9665e8068ffb19e7c49d4313d3bf92acc9e3","sha256:88ac6a652539461ba6759a1e9ffe08270d9f3c6787280d2d60423af651548c13"],"state_sha256":"a85b0a41809c022d3f37c98a46fbc791c439cec185b7094cfbeffe6b9f8ba4a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bB4pq2OQpJboq3OwMlcMNYRM7gXhpcIbUsRfxQEiWUDJj42CUToIfxL9w4kGYd6p9WB1vyHgUinfvYEEzNdTDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T07:10:38.516689Z","bundle_sha256":"99690c502fe8af3a568a391907147adf009e11ab402bf3a676467a01775e5f5b"}}