{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:BNTQOKKK6NCRX5QJY3BLOGOAH2","short_pith_number":"pith:BNTQOKKK","canonical_record":{"source":{"id":"1802.03037","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-02-08T20:22:35Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"9fb5cb821106c6c758d67680d1bea9336e9152e47ee65bc61f6ce5fd2be4eca9","abstract_canon_sha256":"b8b8ba49c05de3740b9c024ea2a636963a398c8a131d5976bba21c470fadc446"},"schema_version":"1.0"},"canonical_sha256":"0b6707294af3451bf609c6c2b719c03e8e4127f2b9bd863d45c1fba31bf62e9d","source":{"kind":"arxiv","id":"1802.03037","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.03037","created_at":"2026-05-17T23:51:34Z"},{"alias_kind":"arxiv_version","alias_value":"1802.03037v2","created_at":"2026-05-17T23:51:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.03037","created_at":"2026-05-17T23:51:34Z"},{"alias_kind":"pith_short_12","alias_value":"BNTQOKKK6NCR","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BNTQOKKK6NCRX5QJ","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BNTQOKKK","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:BNTQOKKK6NCRX5QJY3BLOGOAH2","target":"record","payload":{"canonical_record":{"source":{"id":"1802.03037","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-02-08T20:22:35Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"9fb5cb821106c6c758d67680d1bea9336e9152e47ee65bc61f6ce5fd2be4eca9","abstract_canon_sha256":"b8b8ba49c05de3740b9c024ea2a636963a398c8a131d5976bba21c470fadc446"},"schema_version":"1.0"},"canonical_sha256":"0b6707294af3451bf609c6c2b719c03e8e4127f2b9bd863d45c1fba31bf62e9d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:34.177430Z","signature_b64":"+gmiYfTgfpivDcf+GzTRQkStvlI0nHtBTxbnJc8qZ9tAG18V72SiYnY10QyxQ6d5+bQ4myLm9/MomQgGBnXwBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b6707294af3451bf609c6c2b719c03e8e4127f2b9bd863d45c1fba31bf62e9d","last_reissued_at":"2026-05-17T23:51:34.176830Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:34.176830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.03037","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":"2026-05-17T23:51:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dWy5jg1rg4kp3Gl0HHA3WclqZtQF4oQSgtgG5sXIs0Phrvc1weDy+2sWmQcRtNuJmzLcr8BVBFLxBRvQKQ4GAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:52:18.629597Z"},"content_sha256":"b2ed6354348358b4fd680538a6651aac73ac1b3173d90e77cdb5d79415b7e677","schema_version":"1.0","event_id":"sha256:b2ed6354348358b4fd680538a6651aac73ac1b3173d90e77cdb5d79415b7e677"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:BNTQOKKK6NCRX5QJY3BLOGOAH2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dilations of partial representations of Hopf algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Eliezer Batista, Joost Vercruysse, Marcelo Muniz S. Alves","submitted_at":"2018-02-08T20:22:35Z","abstract_excerpt":"We introduce the notion of a dilation for a partial representation (i.e. a partial module) of a Hopf algebra, which in case the partial representation origins from a partial action (i.e.a partial module algebra) coincides with the enveloping action (or globalization). This construction leads to categorical equivalences between the category of partial $H$-modules, a category of (global) $H$-modules endowed with a projection satisfying a suitable commutation relation and the category of modules over a (global) smash product constructed upon $H$, from which we deduce the structure of a Hopfish al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03037","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":"2026-05-17T23:51:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DyR/vZhwr1BQG8VwD0WIVXMsodjFYfuikj8W+vxiDkAsy4EiBFzcTmtFPtWjFe1J1l2zhXa1bm9XVRFu9ERTBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:52:18.629945Z"},"content_sha256":"bbf4f1e6341a2aa79920309614a269bc23b9360a4bcfbfa2328048b8d5d03242","schema_version":"1.0","event_id":"sha256:bbf4f1e6341a2aa79920309614a269bc23b9360a4bcfbfa2328048b8d5d03242"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BNTQOKKK6NCRX5QJY3BLOGOAH2/bundle.json","state_url":"https://pith.science/pith/BNTQOKKK6NCRX5QJY3BLOGOAH2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BNTQOKKK6NCRX5QJY3BLOGOAH2/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":"2026-06-05T12:52:18Z","links":{"resolver":"https://pith.science/pith/BNTQOKKK6NCRX5QJY3BLOGOAH2","bundle":"https://pith.science/pith/BNTQOKKK6NCRX5QJY3BLOGOAH2/bundle.json","state":"https://pith.science/pith/BNTQOKKK6NCRX5QJY3BLOGOAH2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BNTQOKKK6NCRX5QJY3BLOGOAH2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BNTQOKKK6NCRX5QJY3BLOGOAH2","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":"b8b8ba49c05de3740b9c024ea2a636963a398c8a131d5976bba21c470fadc446","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-02-08T20:22:35Z","title_canon_sha256":"9fb5cb821106c6c758d67680d1bea9336e9152e47ee65bc61f6ce5fd2be4eca9"},"schema_version":"1.0","source":{"id":"1802.03037","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.03037","created_at":"2026-05-17T23:51:34Z"},{"alias_kind":"arxiv_version","alias_value":"1802.03037v2","created_at":"2026-05-17T23:51:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.03037","created_at":"2026-05-17T23:51:34Z"},{"alias_kind":"pith_short_12","alias_value":"BNTQOKKK6NCR","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BNTQOKKK6NCRX5QJ","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BNTQOKKK","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:bbf4f1e6341a2aa79920309614a269bc23b9360a4bcfbfa2328048b8d5d03242","target":"graph","created_at":"2026-05-17T23:51:34Z","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 the notion of a dilation for a partial representation (i.e. a partial module) of a Hopf algebra, which in case the partial representation origins from a partial action (i.e.a partial module algebra) coincides with the enveloping action (or globalization). This construction leads to categorical equivalences between the category of partial $H$-modules, a category of (global) $H$-modules endowed with a projection satisfying a suitable commutation relation and the category of modules over a (global) smash product constructed upon $H$, from which we deduce the structure of a Hopfish al","authors_text":"Eliezer Batista, Joost Vercruysse, Marcelo Muniz S. Alves","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-02-08T20:22:35Z","title":"Dilations of partial representations of Hopf algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03037","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:b2ed6354348358b4fd680538a6651aac73ac1b3173d90e77cdb5d79415b7e677","target":"record","created_at":"2026-05-17T23:51:34Z","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":"b8b8ba49c05de3740b9c024ea2a636963a398c8a131d5976bba21c470fadc446","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-02-08T20:22:35Z","title_canon_sha256":"9fb5cb821106c6c758d67680d1bea9336e9152e47ee65bc61f6ce5fd2be4eca9"},"schema_version":"1.0","source":{"id":"1802.03037","kind":"arxiv","version":2}},"canonical_sha256":"0b6707294af3451bf609c6c2b719c03e8e4127f2b9bd863d45c1fba31bf62e9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b6707294af3451bf609c6c2b719c03e8e4127f2b9bd863d45c1fba31bf62e9d","first_computed_at":"2026-05-17T23:51:34.176830Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:34.176830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+gmiYfTgfpivDcf+GzTRQkStvlI0nHtBTxbnJc8qZ9tAG18V72SiYnY10QyxQ6d5+bQ4myLm9/MomQgGBnXwBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:34.177430Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.03037","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2ed6354348358b4fd680538a6651aac73ac1b3173d90e77cdb5d79415b7e677","sha256:bbf4f1e6341a2aa79920309614a269bc23b9360a4bcfbfa2328048b8d5d03242"],"state_sha256":"e48f59d86dd3d01d262bca28840013430ce3912dacf3bb78cd0c7bdff65c99ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7BSFsdBbhnCinXaxejYhwSFgjlDKD5dG0I+1x9eq1vs33e1UKoLQ3lTRmCjtFts4MbNsDU2r/UxIaaNRVDD4BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T12:52:18.631912Z","bundle_sha256":"4f6de51ea87ee4f157963ae5500666930c7dab32cc649f273cd1d8cb45a55ca0"}}