{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:3ERDTERRNXSCZA6GT3RKBEBR33","short_pith_number":"pith:3ERDTERR","canonical_record":{"source":{"id":"1211.6552","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-11-28T09:27:16Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"a1031861fbfce821e60dff65f9417df4813d59bbbafaa75b173c231dfda40e9d","abstract_canon_sha256":"3305d055c02761cd8eaf3f36aaf788e23b8db14c97960383c3867bbe659b2f39"},"schema_version":"1.0"},"canonical_sha256":"d9223992316de42c83c69ee2a09031def96da842bf99bdbc75280d2cf26136e0","source":{"kind":"arxiv","id":"1211.6552","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.6552","created_at":"2026-05-17T23:55:30Z"},{"alias_kind":"arxiv_version","alias_value":"1211.6552v3","created_at":"2026-05-17T23:55:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.6552","created_at":"2026-05-17T23:55:30Z"},{"alias_kind":"pith_short_12","alias_value":"3ERDTERRNXSC","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3ERDTERRNXSCZA6G","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3ERDTERR","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:3ERDTERRNXSCZA6GT3RKBEBR33","target":"record","payload":{"canonical_record":{"source":{"id":"1211.6552","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-11-28T09:27:16Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"a1031861fbfce821e60dff65f9417df4813d59bbbafaa75b173c231dfda40e9d","abstract_canon_sha256":"3305d055c02761cd8eaf3f36aaf788e23b8db14c97960383c3867bbe659b2f39"},"schema_version":"1.0"},"canonical_sha256":"d9223992316de42c83c69ee2a09031def96da842bf99bdbc75280d2cf26136e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:30.354079Z","signature_b64":"dSq2VLb5/7XJqwo47WOY83+cylmd9Yhf8rQbDmG8HfaVp0NVE2asfPJaPLo+v3OOS+ar9HDNHklQLXIuynp3DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9223992316de42c83c69ee2a09031def96da842bf99bdbc75280d2cf26136e0","last_reissued_at":"2026-05-17T23:55:30.353638Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:30.353638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.6552","source_version":3,"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":"swnsK3mM2+IhGQcnx22/5EJ8V2p/zsoNeCGHom0ga1juzutyqqR4oZNSAVepnDRPoIGi/HuKZftKwdWa77FgAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:36:04.800004Z"},"content_sha256":"5af6eb3d0d9b3f4b25c8e5a2bb2060f14a554ea72fc39dc5cec3880e3a461bc2","schema_version":"1.0","event_id":"sha256:5af6eb3d0d9b3f4b25c8e5a2bb2060f14a554ea72fc39dc5cec3880e3a461bc2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:3ERDTERRNXSCZA6GT3RKBEBR33","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tannaka-Krein duality for compact quantum homogeneous spaces. I. General theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.OA","authors_text":"Kenny De Commer, Makoto Yamashita","submitted_at":"2012-11-28T09:27:16Z","abstract_excerpt":"An ergodic action of a compact quantum group G on an operator algebra A can be interpreted as a quantum homogeneous space for G. Such an action gives rise to the category of finite equivariant Hilbert modules over A, which has a module structure over the tensor category Rep(G) of finite dimensional representations of G. We show that there is a one-to-one correspondence between the quantum G-homogeneous spaces up to equivariant Morita equivalence, and indecomposable module C*-categories over Rep(G) up to natural equivalence. This gives a global approach to the duality theory for ergodic actions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6552","kind":"arxiv","version":3},"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":"DwmIaz/PVbTJLwd6ao42gdtvcH74LrsLqAcAR4sbLtwLG631g+bP/KCkclyioU2ISCQ+38D4VGpxJ5AabIfsDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:36:04.800679Z"},"content_sha256":"fad08996de65b125fe924c312a995ebed0f7b9b6abf55e91a4d249048757aea5","schema_version":"1.0","event_id":"sha256:fad08996de65b125fe924c312a995ebed0f7b9b6abf55e91a4d249048757aea5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3ERDTERRNXSCZA6GT3RKBEBR33/bundle.json","state_url":"https://pith.science/pith/3ERDTERRNXSCZA6GT3RKBEBR33/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3ERDTERRNXSCZA6GT3RKBEBR33/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":"2026-05-31T10:36:04Z","links":{"resolver":"https://pith.science/pith/3ERDTERRNXSCZA6GT3RKBEBR33","bundle":"https://pith.science/pith/3ERDTERRNXSCZA6GT3RKBEBR33/bundle.json","state":"https://pith.science/pith/3ERDTERRNXSCZA6GT3RKBEBR33/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3ERDTERRNXSCZA6GT3RKBEBR33/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3ERDTERRNXSCZA6GT3RKBEBR33","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":"3305d055c02761cd8eaf3f36aaf788e23b8db14c97960383c3867bbe659b2f39","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-11-28T09:27:16Z","title_canon_sha256":"a1031861fbfce821e60dff65f9417df4813d59bbbafaa75b173c231dfda40e9d"},"schema_version":"1.0","source":{"id":"1211.6552","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.6552","created_at":"2026-05-17T23:55:30Z"},{"alias_kind":"arxiv_version","alias_value":"1211.6552v3","created_at":"2026-05-17T23:55:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.6552","created_at":"2026-05-17T23:55:30Z"},{"alias_kind":"pith_short_12","alias_value":"3ERDTERRNXSC","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3ERDTERRNXSCZA6G","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3ERDTERR","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:fad08996de65b125fe924c312a995ebed0f7b9b6abf55e91a4d249048757aea5","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":"An ergodic action of a compact quantum group G on an operator algebra A can be interpreted as a quantum homogeneous space for G. Such an action gives rise to the category of finite equivariant Hilbert modules over A, which has a module structure over the tensor category Rep(G) of finite dimensional representations of G. We show that there is a one-to-one correspondence between the quantum G-homogeneous spaces up to equivariant Morita equivalence, and indecomposable module C*-categories over Rep(G) up to natural equivalence. This gives a global approach to the duality theory for ergodic actions","authors_text":"Kenny De Commer, Makoto Yamashita","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-11-28T09:27:16Z","title":"Tannaka-Krein duality for compact quantum homogeneous spaces. I. General theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6552","kind":"arxiv","version":3},"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":"sha256:5af6eb3d0d9b3f4b25c8e5a2bb2060f14a554ea72fc39dc5cec3880e3a461bc2","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":"3305d055c02761cd8eaf3f36aaf788e23b8db14c97960383c3867bbe659b2f39","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-11-28T09:27:16Z","title_canon_sha256":"a1031861fbfce821e60dff65f9417df4813d59bbbafaa75b173c231dfda40e9d"},"schema_version":"1.0","source":{"id":"1211.6552","kind":"arxiv","version":3}},"canonical_sha256":"d9223992316de42c83c69ee2a09031def96da842bf99bdbc75280d2cf26136e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9223992316de42c83c69ee2a09031def96da842bf99bdbc75280d2cf26136e0","first_computed_at":"2026-05-17T23:55:30.353638Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:30.353638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dSq2VLb5/7XJqwo47WOY83+cylmd9Yhf8rQbDmG8HfaVp0NVE2asfPJaPLo+v3OOS+ar9HDNHklQLXIuynp3DA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:30.354079Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.6552","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5af6eb3d0d9b3f4b25c8e5a2bb2060f14a554ea72fc39dc5cec3880e3a461bc2","sha256:fad08996de65b125fe924c312a995ebed0f7b9b6abf55e91a4d249048757aea5"],"state_sha256":"0330094295dae780c975a7a5446c602e619cb9c5d7bc9a412f123b9a0ce5ae11"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ftVrs7QuBfgeBU0+QVXiO9j3vQ4887QEYaNbyYfiVGtfCBz6iMbJqxcBAhJEUSV6FBZiturHYZbf8Dua+UTBCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T10:36:04.804414Z","bundle_sha256":"f6bcab95387decadd4df6068513aee8187fbd0ed35e0f5f67939b6a9d3fe7ca5"}}