{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:Y4XQZWVSNUN424GJET4L22ZCI2","short_pith_number":"pith:Y4XQZWVS","canonical_record":{"source":{"id":"1003.5526","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-03-29T12:51:39Z","cross_cats_sorted":[],"title_canon_sha256":"15f403a9021fe155fb88aa7c63449a825d1e66023724bcdb9d2adea98d866f65","abstract_canon_sha256":"9e0fcf0fddd6d29e05eb400cda0d95b0988d8ddeae68bbfe5881076028603902"},"schema_version":"1.0"},"canonical_sha256":"c72f0cdab26d1bcd70c924f8bd6b2246b42cbec845115acb22b833deafb35426","source":{"kind":"arxiv","id":"1003.5526","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.5526","created_at":"2026-05-18T03:18:38Z"},{"alias_kind":"arxiv_version","alias_value":"1003.5526v2","created_at":"2026-05-18T03:18:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.5526","created_at":"2026-05-18T03:18:38Z"},{"alias_kind":"pith_short_12","alias_value":"Y4XQZWVSNUN4","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"Y4XQZWVSNUN424GJ","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"Y4XQZWVS","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:Y4XQZWVSNUN424GJET4L22ZCI2","target":"record","payload":{"canonical_record":{"source":{"id":"1003.5526","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-03-29T12:51:39Z","cross_cats_sorted":[],"title_canon_sha256":"15f403a9021fe155fb88aa7c63449a825d1e66023724bcdb9d2adea98d866f65","abstract_canon_sha256":"9e0fcf0fddd6d29e05eb400cda0d95b0988d8ddeae68bbfe5881076028603902"},"schema_version":"1.0"},"canonical_sha256":"c72f0cdab26d1bcd70c924f8bd6b2246b42cbec845115acb22b833deafb35426","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:38.850006Z","signature_b64":"m5OOYTz+i2e8LSPUpEbDMGHUXSuCuTtBB1cyWYFX0mSPsVkJxuz69FbIx1msviXhCp7pOuXclkcVRLZN6aLXAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c72f0cdab26d1bcd70c924f8bd6b2246b42cbec845115acb22b833deafb35426","last_reissued_at":"2026-05-18T03:18:38.849530Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:38.849530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.5526","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":"2026-05-18T03:18:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0nqZEEyA/0AstyJ/L/8lAcCMTe2e6chjQli0TrDFAwPui/CEr9xRovbw8DQMJCq0wDjKsrcxVsct7XhRSb2tAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:05:51.781340Z"},"content_sha256":"e01129a8d03f95eaadb49bfccee0b98fc86f90ca6b2ded2098395cb4abe20e67","schema_version":"1.0","event_id":"sha256:e01129a8d03f95eaadb49bfccee0b98fc86f90ca6b2ded2098395cb4abe20e67"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:Y4XQZWVSNUN424GJET4L22ZCI2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On actions of compact quantum groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Piotr M. So{\\l}tan","submitted_at":"2010-03-29T12:51:39Z","abstract_excerpt":"We compare algebraic objects related to a compact quantum group action on a unital C*-algebra in the sense of Podle\\'s and Baum et al. and show that they differ by the kernel of the morphism describing the action. Then we address ways to remove the kernel without changing the Podle\\'s algebraic core. A minimal such procedure is described. We end the paper with a natural example of an action of a reduced compact quantum group with non-trivial kernel."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5526","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":"2026-05-18T03:18:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zyynjTh8775Vs0L9CKoJbqnFuCCWNdW1NLaAaXtypNh19l3ug6I6Q1cdBsRJnfoH0+0COIwnXXlli1H39NrzDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:05:51.781687Z"},"content_sha256":"fab571f4ad05244b6542d9405c3211a20e77684cb9c2c8b0f8048a9c053fb4c2","schema_version":"1.0","event_id":"sha256:fab571f4ad05244b6542d9405c3211a20e77684cb9c2c8b0f8048a9c053fb4c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y4XQZWVSNUN424GJET4L22ZCI2/bundle.json","state_url":"https://pith.science/pith/Y4XQZWVSNUN424GJET4L22ZCI2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y4XQZWVSNUN424GJET4L22ZCI2/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":"2026-06-26T11:05:51Z","links":{"resolver":"https://pith.science/pith/Y4XQZWVSNUN424GJET4L22ZCI2","bundle":"https://pith.science/pith/Y4XQZWVSNUN424GJET4L22ZCI2/bundle.json","state":"https://pith.science/pith/Y4XQZWVSNUN424GJET4L22ZCI2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y4XQZWVSNUN424GJET4L22ZCI2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:Y4XQZWVSNUN424GJET4L22ZCI2","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":"9e0fcf0fddd6d29e05eb400cda0d95b0988d8ddeae68bbfe5881076028603902","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-03-29T12:51:39Z","title_canon_sha256":"15f403a9021fe155fb88aa7c63449a825d1e66023724bcdb9d2adea98d866f65"},"schema_version":"1.0","source":{"id":"1003.5526","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.5526","created_at":"2026-05-18T03:18:38Z"},{"alias_kind":"arxiv_version","alias_value":"1003.5526v2","created_at":"2026-05-18T03:18:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.5526","created_at":"2026-05-18T03:18:38Z"},{"alias_kind":"pith_short_12","alias_value":"Y4XQZWVSNUN4","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"Y4XQZWVSNUN424GJ","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"Y4XQZWVS","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:fab571f4ad05244b6542d9405c3211a20e77684cb9c2c8b0f8048a9c053fb4c2","target":"graph","created_at":"2026-05-18T03:18:38Z","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 compare algebraic objects related to a compact quantum group action on a unital C*-algebra in the sense of Podle\\'s and Baum et al. and show that they differ by the kernel of the morphism describing the action. Then we address ways to remove the kernel without changing the Podle\\'s algebraic core. A minimal such procedure is described. We end the paper with a natural example of an action of a reduced compact quantum group with non-trivial kernel.","authors_text":"Piotr M. So{\\l}tan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-03-29T12:51:39Z","title":"On actions of compact quantum groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5526","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:e01129a8d03f95eaadb49bfccee0b98fc86f90ca6b2ded2098395cb4abe20e67","target":"record","created_at":"2026-05-18T03:18:38Z","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":"9e0fcf0fddd6d29e05eb400cda0d95b0988d8ddeae68bbfe5881076028603902","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-03-29T12:51:39Z","title_canon_sha256":"15f403a9021fe155fb88aa7c63449a825d1e66023724bcdb9d2adea98d866f65"},"schema_version":"1.0","source":{"id":"1003.5526","kind":"arxiv","version":2}},"canonical_sha256":"c72f0cdab26d1bcd70c924f8bd6b2246b42cbec845115acb22b833deafb35426","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c72f0cdab26d1bcd70c924f8bd6b2246b42cbec845115acb22b833deafb35426","first_computed_at":"2026-05-18T03:18:38.849530Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:38.849530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m5OOYTz+i2e8LSPUpEbDMGHUXSuCuTtBB1cyWYFX0mSPsVkJxuz69FbIx1msviXhCp7pOuXclkcVRLZN6aLXAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:38.850006Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.5526","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e01129a8d03f95eaadb49bfccee0b98fc86f90ca6b2ded2098395cb4abe20e67","sha256:fab571f4ad05244b6542d9405c3211a20e77684cb9c2c8b0f8048a9c053fb4c2"],"state_sha256":"cc8f741ea796e01d3f946c7eacccefb55757dec9959f76081470b21b0a7b8f90"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7SY20orT+id/KsLtufyDtR8rFN/omeHU/3qzSplNCcHFRrE0G1oMn9xCSLiqxPNjhWDTOAwkbJNykIIhiRL2Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T11:05:51.783619Z","bundle_sha256":"0656f863edc4aa36370ba97933332fd306deb20d40820f39f967570a898c34bb"}}