{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:7JKA3IAS3HHRA75UU3EZRVMT55","short_pith_number":"pith:7JKA3IAS","canonical_record":{"source":{"id":"1309.1659","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-09-06T14:46:16Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"c9d350f5f51ecbe54b9e1108c703a1f3e8ee4518d04e6947eaf1ef2dd763e5e8","abstract_canon_sha256":"2eb40cf8de3522ba9567e09abb7380490a03aab30529cbe387506e16e7b48fa6"},"schema_version":"1.0"},"canonical_sha256":"fa540da012d9cf107fb4a6c998d593ef5c47f3c6d5856e8e6028770260eb2e77","source":{"kind":"arxiv","id":"1309.1659","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1659","created_at":"2026-05-18T03:12:47Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1659v2","created_at":"2026-05-18T03:12:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1659","created_at":"2026-05-18T03:12:47Z"},{"alias_kind":"pith_short_12","alias_value":"7JKA3IAS3HHR","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7JKA3IAS3HHRA75U","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7JKA3IAS","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:7JKA3IAS3HHRA75UU3EZRVMT55","target":"record","payload":{"canonical_record":{"source":{"id":"1309.1659","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-09-06T14:46:16Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"c9d350f5f51ecbe54b9e1108c703a1f3e8ee4518d04e6947eaf1ef2dd763e5e8","abstract_canon_sha256":"2eb40cf8de3522ba9567e09abb7380490a03aab30529cbe387506e16e7b48fa6"},"schema_version":"1.0"},"canonical_sha256":"fa540da012d9cf107fb4a6c998d593ef5c47f3c6d5856e8e6028770260eb2e77","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:47.911812Z","signature_b64":"TprgmS9zzvwSLKNirmw/KF6q0zKnuidKU5NlSRVepV+sD1WsV2Vrk3UL8dEXFei7DDvhCBq66shWJrLzkMh6DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa540da012d9cf107fb4a6c998d593ef5c47f3c6d5856e8e6028770260eb2e77","last_reissued_at":"2026-05-18T03:12:47.911399Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:47.911399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.1659","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":"2026-05-18T03:12:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2iFXW2YxjphPKVL+Gwt/6JiBcFCmOcN74CGgqkWf+csREDpVrZW3F+xan2EwV+e17MTmwZB2g3lIV70M0cvYDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:19:14.828236Z"},"content_sha256":"414dd457806cb5d12dc357051f0895afe54c73c565108f025f713f44221f0761","schema_version":"1.0","event_id":"sha256:414dd457806cb5d12dc357051f0895afe54c73c565108f025f713f44221f0761"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:7JKA3IAS3HHRA75UU3EZRVMT55","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Partial Representations of Hopf Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RA","authors_text":"Eliezer Batista, Joost Vercruysse, Marcelo Muniz S. Alves","submitted_at":"2013-09-06T14:46:16Z","abstract_excerpt":"In this work, the notion of partial representation of a Hopf algebra is introduced and its relationship with partial actions of Hopf algebras is explored. Given a Hopf algebra $H$, one can associate it to a Hopf algebroid $H_{par}$ which has the universal property that each partial representation of $H$ can be factorized by an algebra morphism from $H_{par}$. We define also the category of partial modules over a Hopf algebra $H$, which is the category of modules over its associated Hopf algebroid $H_{par}$. The Hopf algebroid structure of $H_{par}$ enables us to enhance the category of partial"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1659","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":"2026-05-18T03:12:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fNNq8uA3kO8mjxNfaQEk4tDm645cq6UdSGq2IzkGCKYTGwx/5ZXyWbQMCa564E3fNsZKaVMyiZRtWUGiBh6qCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:19:14.828595Z"},"content_sha256":"93925a343bb76fe13ef20b2875368ec9bd20ac6215334027936817b134566d51","schema_version":"1.0","event_id":"sha256:93925a343bb76fe13ef20b2875368ec9bd20ac6215334027936817b134566d51"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7JKA3IAS3HHRA75UU3EZRVMT55/bundle.json","state_url":"https://pith.science/pith/7JKA3IAS3HHRA75UU3EZRVMT55/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7JKA3IAS3HHRA75UU3EZRVMT55/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":"2026-06-05T00:19:14Z","links":{"resolver":"https://pith.science/pith/7JKA3IAS3HHRA75UU3EZRVMT55","bundle":"https://pith.science/pith/7JKA3IAS3HHRA75UU3EZRVMT55/bundle.json","state":"https://pith.science/pith/7JKA3IAS3HHRA75UU3EZRVMT55/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7JKA3IAS3HHRA75UU3EZRVMT55/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7JKA3IAS3HHRA75UU3EZRVMT55","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":"2eb40cf8de3522ba9567e09abb7380490a03aab30529cbe387506e16e7b48fa6","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-09-06T14:46:16Z","title_canon_sha256":"c9d350f5f51ecbe54b9e1108c703a1f3e8ee4518d04e6947eaf1ef2dd763e5e8"},"schema_version":"1.0","source":{"id":"1309.1659","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1659","created_at":"2026-05-18T03:12:47Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1659v2","created_at":"2026-05-18T03:12:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1659","created_at":"2026-05-18T03:12:47Z"},{"alias_kind":"pith_short_12","alias_value":"7JKA3IAS3HHR","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7JKA3IAS3HHRA75U","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7JKA3IAS","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:93925a343bb76fe13ef20b2875368ec9bd20ac6215334027936817b134566d51","target":"graph","created_at":"2026-05-18T03:12:47Z","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":"In this work, the notion of partial representation of a Hopf algebra is introduced and its relationship with partial actions of Hopf algebras is explored. Given a Hopf algebra $H$, one can associate it to a Hopf algebroid $H_{par}$ which has the universal property that each partial representation of $H$ can be factorized by an algebra morphism from $H_{par}$. We define also the category of partial modules over a Hopf algebra $H$, which is the category of modules over its associated Hopf algebroid $H_{par}$. The Hopf algebroid structure of $H_{par}$ enables us to enhance the category of partial","authors_text":"Eliezer Batista, Joost Vercruysse, Marcelo Muniz S. Alves","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-09-06T14:46:16Z","title":"Partial Representations of Hopf Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1659","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":"sha256:414dd457806cb5d12dc357051f0895afe54c73c565108f025f713f44221f0761","target":"record","created_at":"2026-05-18T03:12:47Z","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":"2eb40cf8de3522ba9567e09abb7380490a03aab30529cbe387506e16e7b48fa6","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-09-06T14:46:16Z","title_canon_sha256":"c9d350f5f51ecbe54b9e1108c703a1f3e8ee4518d04e6947eaf1ef2dd763e5e8"},"schema_version":"1.0","source":{"id":"1309.1659","kind":"arxiv","version":2}},"canonical_sha256":"fa540da012d9cf107fb4a6c998d593ef5c47f3c6d5856e8e6028770260eb2e77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa540da012d9cf107fb4a6c998d593ef5c47f3c6d5856e8e6028770260eb2e77","first_computed_at":"2026-05-18T03:12:47.911399Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:47.911399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TprgmS9zzvwSLKNirmw/KF6q0zKnuidKU5NlSRVepV+sD1WsV2Vrk3UL8dEXFei7DDvhCBq66shWJrLzkMh6DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:47.911812Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1659","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:414dd457806cb5d12dc357051f0895afe54c73c565108f025f713f44221f0761","sha256:93925a343bb76fe13ef20b2875368ec9bd20ac6215334027936817b134566d51"],"state_sha256":"7ada59a216c3f6cf8ec771eeb964bd1109587f8c8ec79e7cf93ffc7c9a6c8545"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wtkIUrBujhXrk5TMrwQHyeYDsCtyBQVU+CLruq/ZsSi5/wRCamF41b2Of5KzvDOYaqVuUvpsdF/2Zsmw9HlgDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T00:19:14.830565Z","bundle_sha256":"a772aefa7eb51fc0a942aebc9714e966ab473845f711f3ba1dc0975867bf63d6"}}