{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:XJ2Q756GUCZ5K34U3QT4KWHBXX","short_pith_number":"pith:XJ2Q756G","canonical_record":{"source":{"id":"1206.2806","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-06-13T13:46:48Z","cross_cats_sorted":["math.QA","math.RA","math.RT"],"title_canon_sha256":"439722a4eb4ebfce4614bda38f46bb8706c52947417c805b5457a450f825d70a","abstract_canon_sha256":"e1d8b8f8532d681673198d741883349d1b0b015e28efed7a44095d03359a1ac3"},"schema_version":"1.0"},"canonical_sha256":"ba750ff7c6a0b3d56f94dc27c558e1bdd7c505536b82d9a1d541056e9598df38","source":{"kind":"arxiv","id":"1206.2806","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.2806","created_at":"2026-05-18T03:53:43Z"},{"alias_kind":"arxiv_version","alias_value":"1206.2806v1","created_at":"2026-05-18T03:53:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.2806","created_at":"2026-05-18T03:53:43Z"},{"alias_kind":"pith_short_12","alias_value":"XJ2Q756GUCZ5","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XJ2Q756GUCZ5K34U","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XJ2Q756G","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:XJ2Q756GUCZ5K34U3QT4KWHBXX","target":"record","payload":{"canonical_record":{"source":{"id":"1206.2806","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-06-13T13:46:48Z","cross_cats_sorted":["math.QA","math.RA","math.RT"],"title_canon_sha256":"439722a4eb4ebfce4614bda38f46bb8706c52947417c805b5457a450f825d70a","abstract_canon_sha256":"e1d8b8f8532d681673198d741883349d1b0b015e28efed7a44095d03359a1ac3"},"schema_version":"1.0"},"canonical_sha256":"ba750ff7c6a0b3d56f94dc27c558e1bdd7c505536b82d9a1d541056e9598df38","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:43.073659Z","signature_b64":"m0KiudqjFcLxo0WYdy1AHyT8uGBRLBveInHQOMmmiXtvPpm1Xrz1XR0B/YUXt9LigJRxM/B9jh1plDcoPm+zCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba750ff7c6a0b3d56f94dc27c558e1bdd7c505536b82d9a1d541056e9598df38","last_reissued_at":"2026-05-18T03:53:43.073150Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:43.073150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.2806","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":"2026-05-18T03:53:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nOxZDgVzNSFggyl2PfLAKpVqVcJSExxbc7F+8ylxR1obfZncCe8FJUPQ0JUj6BMeEeWFWA9pMJWF72rWcdtyAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:30:04.804159Z"},"content_sha256":"e272901e6560967e4c493922a0b8fb4a28be2e3cec0844984a7d6ea19e575799","schema_version":"1.0","event_id":"sha256:e272901e6560967e4c493922a0b8fb4a28be2e3cec0844984a7d6ea19e575799"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:XJ2Q756GUCZ5K34U3QT4KWHBXX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Induced *-representations and $C^*$-envelopes of some quantum $*$-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RA","math.RT"],"primary_cat":"math.OA","authors_text":"Philip A. Dowerk, Yurii Savchuk","submitted_at":"2012-06-13T13:46:48Z","abstract_excerpt":"We consider three quantum algebras: the q-oscillator algebra, the Podles' sphere and the q-deformed enveloping algebra of $su(2).$ To each of these *-algebras we associate certain partial dynamical system and perform the \"Mackey analysis\" of *-representations developed in [SS]. As a result we get the description of \"standard\" irreducible *-representations. Further, for each of these examples we show the existence of a \"$C^*$-envelope\" which is canonically isomorphic to the covariance $C^*$-algebra of the partial dynamical system. Finally, for the q-oscillator algebra and the q-deformed $\\cU(su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2806","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":"2026-05-18T03:53:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MnpgBeYXtS9sUOqpq7ttk2yD6Gs1ziTgkfqRW9WhNPNOTgpOpBs2zFZaS0ft1V3SLBhHGVN+tjNf8xhA4p+SCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:30:04.804526Z"},"content_sha256":"b9b94d0f3abd9c81795abb0b23ca1e23a84d3419f7ad2af0fe0508854af14705","schema_version":"1.0","event_id":"sha256:b9b94d0f3abd9c81795abb0b23ca1e23a84d3419f7ad2af0fe0508854af14705"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XJ2Q756GUCZ5K34U3QT4KWHBXX/bundle.json","state_url":"https://pith.science/pith/XJ2Q756GUCZ5K34U3QT4KWHBXX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XJ2Q756GUCZ5K34U3QT4KWHBXX/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":"2026-06-22T14:30:04Z","links":{"resolver":"https://pith.science/pith/XJ2Q756GUCZ5K34U3QT4KWHBXX","bundle":"https://pith.science/pith/XJ2Q756GUCZ5K34U3QT4KWHBXX/bundle.json","state":"https://pith.science/pith/XJ2Q756GUCZ5K34U3QT4KWHBXX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XJ2Q756GUCZ5K34U3QT4KWHBXX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XJ2Q756GUCZ5K34U3QT4KWHBXX","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":"e1d8b8f8532d681673198d741883349d1b0b015e28efed7a44095d03359a1ac3","cross_cats_sorted":["math.QA","math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-06-13T13:46:48Z","title_canon_sha256":"439722a4eb4ebfce4614bda38f46bb8706c52947417c805b5457a450f825d70a"},"schema_version":"1.0","source":{"id":"1206.2806","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.2806","created_at":"2026-05-18T03:53:43Z"},{"alias_kind":"arxiv_version","alias_value":"1206.2806v1","created_at":"2026-05-18T03:53:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.2806","created_at":"2026-05-18T03:53:43Z"},{"alias_kind":"pith_short_12","alias_value":"XJ2Q756GUCZ5","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XJ2Q756GUCZ5K34U","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XJ2Q756G","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:b9b94d0f3abd9c81795abb0b23ca1e23a84d3419f7ad2af0fe0508854af14705","target":"graph","created_at":"2026-05-18T03:53:43Z","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 three quantum algebras: the q-oscillator algebra, the Podles' sphere and the q-deformed enveloping algebra of $su(2).$ To each of these *-algebras we associate certain partial dynamical system and perform the \"Mackey analysis\" of *-representations developed in [SS]. As a result we get the description of \"standard\" irreducible *-representations. Further, for each of these examples we show the existence of a \"$C^*$-envelope\" which is canonically isomorphic to the covariance $C^*$-algebra of the partial dynamical system. Finally, for the q-oscillator algebra and the q-deformed $\\cU(su","authors_text":"Philip A. Dowerk, Yurii Savchuk","cross_cats":["math.QA","math.RA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-06-13T13:46:48Z","title":"Induced *-representations and $C^*$-envelopes of some quantum $*$-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2806","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:e272901e6560967e4c493922a0b8fb4a28be2e3cec0844984a7d6ea19e575799","target":"record","created_at":"2026-05-18T03:53:43Z","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":"e1d8b8f8532d681673198d741883349d1b0b015e28efed7a44095d03359a1ac3","cross_cats_sorted":["math.QA","math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-06-13T13:46:48Z","title_canon_sha256":"439722a4eb4ebfce4614bda38f46bb8706c52947417c805b5457a450f825d70a"},"schema_version":"1.0","source":{"id":"1206.2806","kind":"arxiv","version":1}},"canonical_sha256":"ba750ff7c6a0b3d56f94dc27c558e1bdd7c505536b82d9a1d541056e9598df38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba750ff7c6a0b3d56f94dc27c558e1bdd7c505536b82d9a1d541056e9598df38","first_computed_at":"2026-05-18T03:53:43.073150Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:43.073150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m0KiudqjFcLxo0WYdy1AHyT8uGBRLBveInHQOMmmiXtvPpm1Xrz1XR0B/YUXt9LigJRxM/B9jh1plDcoPm+zCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:43.073659Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.2806","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e272901e6560967e4c493922a0b8fb4a28be2e3cec0844984a7d6ea19e575799","sha256:b9b94d0f3abd9c81795abb0b23ca1e23a84d3419f7ad2af0fe0508854af14705"],"state_sha256":"7124bf79e777e12a68de55960b6dd54d48a89b146b044d69ac12f6a4476761b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IURMTaIYmDNm4Ibsfvl8no41LZ6Ea2NjPWLWf3d1g68jvVIFqq2HXNGxcOiEdTzo/BsswCTYXGkkvcav+ue4DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T14:30:04.806634Z","bundle_sha256":"b407eebb9ce2dd752a00b2e4dd84a9124bdc82309fff63bc945518a70dc1cca1"}}