{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:3NJ3PSYSO4VKAJSHWTZFC6BYMI","short_pith_number":"pith:3NJ3PSYS","canonical_record":{"source":{"id":"1002.1122","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2010-02-05T05:24:45Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"925beb3d0c405fd2c3ee71b6f2f755b314a51f07957ac458976c1e1ec2bc5688","abstract_canon_sha256":"5abbf7c05d2279865bc845b3af8d7ec77a2464cc648e0c8eb0d5dbb96e591ca8"},"schema_version":"1.0"},"canonical_sha256":"db53b7cb12772aa02647b4f25178386235e851b11927a857b5b9fe769a26863e","source":{"kind":"arxiv","id":"1002.1122","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.1122","created_at":"2026-05-18T04:24:35Z"},{"alias_kind":"arxiv_version","alias_value":"1002.1122v2","created_at":"2026-05-18T04:24:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.1122","created_at":"2026-05-18T04:24:35Z"},{"alias_kind":"pith_short_12","alias_value":"3NJ3PSYSO4VK","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3NJ3PSYSO4VKAJSH","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3NJ3PSYS","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:3NJ3PSYSO4VKAJSHWTZFC6BYMI","target":"record","payload":{"canonical_record":{"source":{"id":"1002.1122","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2010-02-05T05:24:45Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"925beb3d0c405fd2c3ee71b6f2f755b314a51f07957ac458976c1e1ec2bc5688","abstract_canon_sha256":"5abbf7c05d2279865bc845b3af8d7ec77a2464cc648e0c8eb0d5dbb96e591ca8"},"schema_version":"1.0"},"canonical_sha256":"db53b7cb12772aa02647b4f25178386235e851b11927a857b5b9fe769a26863e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:35.264062Z","signature_b64":"hg+xS/CJZnT0SV/8zm1c4/gG8CisntpIieXM8dvGK5AWyJnQbFJ1JejoG0AO69Q622gNsgxZeQ8PFjo7L/lkDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db53b7cb12772aa02647b4f25178386235e851b11927a857b5b9fe769a26863e","last_reissued_at":"2026-05-18T04:24:35.263657Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:35.263657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.1122","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":"2026-05-18T04:24:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G7CZkV7Xw7/Ep5N6jQjIEwpqLjUVZokDIs1SDujs57IC5sNKVaXxrqTY7akzGy+14CGM7rwYtafeOci13LnYBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:31:18.232811Z"},"content_sha256":"292876d6fc23d1450e48ba1d73f61ae1d9d8805543fc5e76c62b9df402c9bf1c","schema_version":"1.0","event_id":"sha256:292876d6fc23d1450e48ba1d73f61ae1d9d8805543fc5e76c62b9df402c9bf1c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:3NJ3PSYSO4VKAJSHWTZFC6BYMI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hopf monoidal comonads","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.CT","authors_text":"Dimitri Chikhladze, Ross Street, Stephen Lack","submitted_at":"2010-02-05T05:24:45Z","abstract_excerpt":"Alain Bruguieres, in his talk [1], announced his work [2] with Alexis Virelizier and the second author which dealt with lifting closed structure on a monoidal category to the category of Eilenberg-Moore algebras for an opmonoidal monad. Our purpose here is to generalize that work to the context internal to an autonomous monoidal bicategory. The result then applies to quantum categories and bialgebroids."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1122","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":"2026-05-18T04:24:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eDbT8FQJ59IBZ9YnDlTnFHpZ7tGdWjGsadeYNhZ6JyK2e9oS6pZwbMgZOHnrXbdvsKNUfOB8yypgBd6QS2RBCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:31:18.233155Z"},"content_sha256":"b60baac3d02a8c23dc786cabc44d499ebdd17cca9b8bc37e2def067421a81e0a","schema_version":"1.0","event_id":"sha256:b60baac3d02a8c23dc786cabc44d499ebdd17cca9b8bc37e2def067421a81e0a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3NJ3PSYSO4VKAJSHWTZFC6BYMI/bundle.json","state_url":"https://pith.science/pith/3NJ3PSYSO4VKAJSHWTZFC6BYMI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3NJ3PSYSO4VKAJSHWTZFC6BYMI/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":"2026-06-03T17:31:18Z","links":{"resolver":"https://pith.science/pith/3NJ3PSYSO4VKAJSHWTZFC6BYMI","bundle":"https://pith.science/pith/3NJ3PSYSO4VKAJSHWTZFC6BYMI/bundle.json","state":"https://pith.science/pith/3NJ3PSYSO4VKAJSHWTZFC6BYMI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3NJ3PSYSO4VKAJSHWTZFC6BYMI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:3NJ3PSYSO4VKAJSHWTZFC6BYMI","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":"5abbf7c05d2279865bc845b3af8d7ec77a2464cc648e0c8eb0d5dbb96e591ca8","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2010-02-05T05:24:45Z","title_canon_sha256":"925beb3d0c405fd2c3ee71b6f2f755b314a51f07957ac458976c1e1ec2bc5688"},"schema_version":"1.0","source":{"id":"1002.1122","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.1122","created_at":"2026-05-18T04:24:35Z"},{"alias_kind":"arxiv_version","alias_value":"1002.1122v2","created_at":"2026-05-18T04:24:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.1122","created_at":"2026-05-18T04:24:35Z"},{"alias_kind":"pith_short_12","alias_value":"3NJ3PSYSO4VK","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3NJ3PSYSO4VKAJSH","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3NJ3PSYS","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:b60baac3d02a8c23dc786cabc44d499ebdd17cca9b8bc37e2def067421a81e0a","target":"graph","created_at":"2026-05-18T04:24:35Z","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":"Alain Bruguieres, in his talk [1], announced his work [2] with Alexis Virelizier and the second author which dealt with lifting closed structure on a monoidal category to the category of Eilenberg-Moore algebras for an opmonoidal monad. Our purpose here is to generalize that work to the context internal to an autonomous monoidal bicategory. The result then applies to quantum categories and bialgebroids.","authors_text":"Dimitri Chikhladze, Ross Street, Stephen Lack","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2010-02-05T05:24:45Z","title":"Hopf monoidal comonads"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1122","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":"sha256:292876d6fc23d1450e48ba1d73f61ae1d9d8805543fc5e76c62b9df402c9bf1c","target":"record","created_at":"2026-05-18T04:24:35Z","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":"5abbf7c05d2279865bc845b3af8d7ec77a2464cc648e0c8eb0d5dbb96e591ca8","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2010-02-05T05:24:45Z","title_canon_sha256":"925beb3d0c405fd2c3ee71b6f2f755b314a51f07957ac458976c1e1ec2bc5688"},"schema_version":"1.0","source":{"id":"1002.1122","kind":"arxiv","version":2}},"canonical_sha256":"db53b7cb12772aa02647b4f25178386235e851b11927a857b5b9fe769a26863e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db53b7cb12772aa02647b4f25178386235e851b11927a857b5b9fe769a26863e","first_computed_at":"2026-05-18T04:24:35.263657Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:35.263657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hg+xS/CJZnT0SV/8zm1c4/gG8CisntpIieXM8dvGK5AWyJnQbFJ1JejoG0AO69Q622gNsgxZeQ8PFjo7L/lkDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:35.264062Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.1122","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:292876d6fc23d1450e48ba1d73f61ae1d9d8805543fc5e76c62b9df402c9bf1c","sha256:b60baac3d02a8c23dc786cabc44d499ebdd17cca9b8bc37e2def067421a81e0a"],"state_sha256":"c3adda10f854edf09bef04188319997e1cbaae3fdaa5b3c594d7b52e54561b59"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s+jpX3mSAUHnj0UiR/nrob7bKYIOR7yQwgK1mAqM4M5vgLeBUWOZeiunmOtZrXUEC9bTe0W6UskkZ2DvqlwgCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T17:31:18.235071Z","bundle_sha256":"3449803b6778d2bf10f2bfc0f305a76a60ab6dcabdcc4d3a0e6b1d3d906aeee0"}}