{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SHKPJHLNHSHV6BOOK753Q45SZQ","short_pith_number":"pith:SHKPJHLN","canonical_record":{"source":{"id":"1702.08191","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-02-27T08:51:39Z","cross_cats_sorted":["math.QA","math.RT"],"title_canon_sha256":"88905655314f8a36679698a7971f0f89f5aeb26912218a462643a5a73e27e78e","abstract_canon_sha256":"2387914f2bd83a73af75953ee78608e16e4cbc9f955f93cf28803769bd9ab1d9"},"schema_version":"1.0"},"canonical_sha256":"91d4f49d6d3c8f5f05ce57fbb873b2cc19afaa6872f69ab815e77f0884872ec2","source":{"kind":"arxiv","id":"1702.08191","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.08191","created_at":"2026-05-17T23:55:30Z"},{"alias_kind":"arxiv_version","alias_value":"1702.08191v1","created_at":"2026-05-17T23:55:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08191","created_at":"2026-05-17T23:55:30Z"},{"alias_kind":"pith_short_12","alias_value":"SHKPJHLNHSHV","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SHKPJHLNHSHV6BOO","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SHKPJHLN","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SHKPJHLNHSHV6BOOK753Q45SZQ","target":"record","payload":{"canonical_record":{"source":{"id":"1702.08191","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-02-27T08:51:39Z","cross_cats_sorted":["math.QA","math.RT"],"title_canon_sha256":"88905655314f8a36679698a7971f0f89f5aeb26912218a462643a5a73e27e78e","abstract_canon_sha256":"2387914f2bd83a73af75953ee78608e16e4cbc9f955f93cf28803769bd9ab1d9"},"schema_version":"1.0"},"canonical_sha256":"91d4f49d6d3c8f5f05ce57fbb873b2cc19afaa6872f69ab815e77f0884872ec2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:30.047062Z","signature_b64":"4dVgCJ0nKYYh9ksijg64wGszUOiaW2PaQol3WbckjSLPsYda27cDojP3mUH3DqeWVakMBlw647NDT1fN+MCdBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91d4f49d6d3c8f5f05ce57fbb873b2cc19afaa6872f69ab815e77f0884872ec2","last_reissued_at":"2026-05-17T23:55:30.046565Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:30.046565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.08191","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":"2026-05-17T23:55:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"podClKZruGWKwPx4yRnPLALbz8RXp70EpNo1cdmr4zQyzn+4c3xNciW5ehvHSiU+yeLGywHAXRO5D/bO82/3Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:29:33.579872Z"},"content_sha256":"5b2b61696b03a9b603e0cc798cc2a8f7b29ceaa4f60eadcd5b30740ca800679d","schema_version":"1.0","event_id":"sha256:5b2b61696b03a9b603e0cc798cc2a8f7b29ceaa4f60eadcd5b30740ca800679d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SHKPJHLNHSHV6BOOK753Q45SZQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"I-factorial quantum torsors and Heisenberg algebras of quantized universal enveloping type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RT"],"primary_cat":"math.OA","authors_text":"Kenny De Commer","submitted_at":"2017-02-27T08:51:39Z","abstract_excerpt":"We introduce a notion of I-factorial quantum torsor, which consists of an integrable ergodic action of a locally compact quantum group on a type I-factor such that also the crossed product is a type I-factor. We show that any such I-factorial quantum torsor is at the same time a I-factorial quantum torsor for the dual locally compact quantum group, in such a way that the construction is involutive. As a motivating example, we show that quantized compact semisimple Lie groups, when amplified via a crossed product construction with the function algebra on the associated weight lattice, admit I-f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08191","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":"2026-05-17T23:55:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WmvTL4OoWgF2wJeAIgmxLaDLMB1lbjJQiI4Ovg3iA5jut/0TWZvPLfqxvUsqCEyhqtQLyYcOlD0Fx3Pgb75FDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:29:33.580222Z"},"content_sha256":"93873b3ec1750f132f90a1c1e4d3073f1aa1c9a298825df81be3a192f52b21c5","schema_version":"1.0","event_id":"sha256:93873b3ec1750f132f90a1c1e4d3073f1aa1c9a298825df81be3a192f52b21c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SHKPJHLNHSHV6BOOK753Q45SZQ/bundle.json","state_url":"https://pith.science/pith/SHKPJHLNHSHV6BOOK753Q45SZQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SHKPJHLNHSHV6BOOK753Q45SZQ/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":"2026-06-25T12:29:33Z","links":{"resolver":"https://pith.science/pith/SHKPJHLNHSHV6BOOK753Q45SZQ","bundle":"https://pith.science/pith/SHKPJHLNHSHV6BOOK753Q45SZQ/bundle.json","state":"https://pith.science/pith/SHKPJHLNHSHV6BOOK753Q45SZQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SHKPJHLNHSHV6BOOK753Q45SZQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SHKPJHLNHSHV6BOOK753Q45SZQ","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":"2387914f2bd83a73af75953ee78608e16e4cbc9f955f93cf28803769bd9ab1d9","cross_cats_sorted":["math.QA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-02-27T08:51:39Z","title_canon_sha256":"88905655314f8a36679698a7971f0f89f5aeb26912218a462643a5a73e27e78e"},"schema_version":"1.0","source":{"id":"1702.08191","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.08191","created_at":"2026-05-17T23:55:30Z"},{"alias_kind":"arxiv_version","alias_value":"1702.08191v1","created_at":"2026-05-17T23:55:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08191","created_at":"2026-05-17T23:55:30Z"},{"alias_kind":"pith_short_12","alias_value":"SHKPJHLNHSHV","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SHKPJHLNHSHV6BOO","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SHKPJHLN","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:93873b3ec1750f132f90a1c1e4d3073f1aa1c9a298825df81be3a192f52b21c5","target":"graph","created_at":"2026-05-17T23:55:30Z","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 introduce a notion of I-factorial quantum torsor, which consists of an integrable ergodic action of a locally compact quantum group on a type I-factor such that also the crossed product is a type I-factor. We show that any such I-factorial quantum torsor is at the same time a I-factorial quantum torsor for the dual locally compact quantum group, in such a way that the construction is involutive. As a motivating example, we show that quantized compact semisimple Lie groups, when amplified via a crossed product construction with the function algebra on the associated weight lattice, admit I-f","authors_text":"Kenny De Commer","cross_cats":["math.QA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-02-27T08:51:39Z","title":"I-factorial quantum torsors and Heisenberg algebras of quantized universal enveloping type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08191","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":"sha256:5b2b61696b03a9b603e0cc798cc2a8f7b29ceaa4f60eadcd5b30740ca800679d","target":"record","created_at":"2026-05-17T23:55:30Z","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":"2387914f2bd83a73af75953ee78608e16e4cbc9f955f93cf28803769bd9ab1d9","cross_cats_sorted":["math.QA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-02-27T08:51:39Z","title_canon_sha256":"88905655314f8a36679698a7971f0f89f5aeb26912218a462643a5a73e27e78e"},"schema_version":"1.0","source":{"id":"1702.08191","kind":"arxiv","version":1}},"canonical_sha256":"91d4f49d6d3c8f5f05ce57fbb873b2cc19afaa6872f69ab815e77f0884872ec2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91d4f49d6d3c8f5f05ce57fbb873b2cc19afaa6872f69ab815e77f0884872ec2","first_computed_at":"2026-05-17T23:55:30.046565Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:30.046565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4dVgCJ0nKYYh9ksijg64wGszUOiaW2PaQol3WbckjSLPsYda27cDojP3mUH3DqeWVakMBlw647NDT1fN+MCdBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:30.047062Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.08191","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b2b61696b03a9b603e0cc798cc2a8f7b29ceaa4f60eadcd5b30740ca800679d","sha256:93873b3ec1750f132f90a1c1e4d3073f1aa1c9a298825df81be3a192f52b21c5"],"state_sha256":"ca0c05459b210d316415bfdabedec42b80adfefcecf90621e600e7c320ba72a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"irCZP8ewBKFCjQu/YTPeai/vPLwZ01qH9MpqXHGaz8AdYiL8Sq5/RPO+JOC60ZfRlsPrvT+BqVcnNsG4cZcBBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T12:29:33.582130Z","bundle_sha256":"4f46d23f332fda37eb42930a5c27908239cf674a5f18146d7a4dd46c2e1e7bab"}}