{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:YQ6FWIYRX333IXFKIFVUDKNBGA","short_pith_number":"pith:YQ6FWIYR","canonical_record":{"source":{"id":"1810.03335","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-08T09:08:37Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"47cef8834c24140bbb8828ab91f80b91ede0c4e632931be2eb7b38b9ad6756ee","abstract_canon_sha256":"78373469faf78aa1e9502a858fd59345538a536f6625401597bfa49c13ffcfce"},"schema_version":"1.0"},"canonical_sha256":"c43c5b2311bef7b45caa416b41a9a1302559892b1968540533bcf80b5ca70822","source":{"kind":"arxiv","id":"1810.03335","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03335","created_at":"2026-05-18T00:03:36Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03335v2","created_at":"2026-05-18T00:03:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03335","created_at":"2026-05-18T00:03:36Z"},{"alias_kind":"pith_short_12","alias_value":"YQ6FWIYRX333","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YQ6FWIYRX333IXFK","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YQ6FWIYR","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:YQ6FWIYRX333IXFKIFVUDKNBGA","target":"record","payload":{"canonical_record":{"source":{"id":"1810.03335","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-08T09:08:37Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"47cef8834c24140bbb8828ab91f80b91ede0c4e632931be2eb7b38b9ad6756ee","abstract_canon_sha256":"78373469faf78aa1e9502a858fd59345538a536f6625401597bfa49c13ffcfce"},"schema_version":"1.0"},"canonical_sha256":"c43c5b2311bef7b45caa416b41a9a1302559892b1968540533bcf80b5ca70822","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:36.382980Z","signature_b64":"fEOJHFzIif+EKr3zIfx637UNK2G/NkZgSu95bWRdRFHT5crmPj143Ndxm0uPp2849WiTbH6/H5FHK6evnVIYDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c43c5b2311bef7b45caa416b41a9a1302559892b1968540533bcf80b5ca70822","last_reissued_at":"2026-05-18T00:03:36.381323Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:36.381323Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.03335","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":"2026-05-18T00:03:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SnI6WKSCPN6Pu3+BM1Fr0nvjZJaejrFes1bgq8aX/phZrKDugJeArv7jOGVU1ZXNNvfLCaUFRehso7cc1efeCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:25:12.976710Z"},"content_sha256":"bc19b0ab8ce81ccaa815491aaa3769c916a6eb4b9ae30fc1e9c10f9d605cc6ff","schema_version":"1.0","event_id":"sha256:bc19b0ab8ce81ccaa815491aaa3769c916a6eb4b9ae30fc1e9c10f9d605cc6ff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:YQ6FWIYRX333IXFKIFVUDKNBGA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A universal enveloping algebra for cocommutative rack bialgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.AT","authors_text":"Friedrich Wagemann (LMJL), Ulrich Kraehmer","submitted_at":"2018-10-08T09:08:37Z","abstract_excerpt":"We construct a bialgebra object in the category of linear maps LM from a cocommutative rack bialgebra. The construction does extend to some non-cocommutative rack bialgebras, as is illustrated by a concrete example. As a separate result, we show that the Loday complex with adjoint coefficients embeds into the rack bialgebra deformation complex for the rack bialgebra defined by a Leibniz algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03335","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":"2026-05-18T00:03:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F+s9uOPdBSfOWx5iKriTqyqVRB6BLx3Jyui97mxxVl5RbLdRuS/fs7UgghC+1o96iTuXYMaMeHH9OnLZam2QCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:25:12.977057Z"},"content_sha256":"4ab698d8213d9c11cebbca15b460c6e80daca82a8b6e1d0b8b2468a94b7cce68","schema_version":"1.0","event_id":"sha256:4ab698d8213d9c11cebbca15b460c6e80daca82a8b6e1d0b8b2468a94b7cce68"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YQ6FWIYRX333IXFKIFVUDKNBGA/bundle.json","state_url":"https://pith.science/pith/YQ6FWIYRX333IXFKIFVUDKNBGA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YQ6FWIYRX333IXFKIFVUDKNBGA/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":"2026-05-28T07:25:12Z","links":{"resolver":"https://pith.science/pith/YQ6FWIYRX333IXFKIFVUDKNBGA","bundle":"https://pith.science/pith/YQ6FWIYRX333IXFKIFVUDKNBGA/bundle.json","state":"https://pith.science/pith/YQ6FWIYRX333IXFKIFVUDKNBGA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YQ6FWIYRX333IXFKIFVUDKNBGA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YQ6FWIYRX333IXFKIFVUDKNBGA","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":"78373469faf78aa1e9502a858fd59345538a536f6625401597bfa49c13ffcfce","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-08T09:08:37Z","title_canon_sha256":"47cef8834c24140bbb8828ab91f80b91ede0c4e632931be2eb7b38b9ad6756ee"},"schema_version":"1.0","source":{"id":"1810.03335","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03335","created_at":"2026-05-18T00:03:36Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03335v2","created_at":"2026-05-18T00:03:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03335","created_at":"2026-05-18T00:03:36Z"},{"alias_kind":"pith_short_12","alias_value":"YQ6FWIYRX333","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YQ6FWIYRX333IXFK","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YQ6FWIYR","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:4ab698d8213d9c11cebbca15b460c6e80daca82a8b6e1d0b8b2468a94b7cce68","target":"graph","created_at":"2026-05-18T00:03:36Z","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 construct a bialgebra object in the category of linear maps LM from a cocommutative rack bialgebra. The construction does extend to some non-cocommutative rack bialgebras, as is illustrated by a concrete example. As a separate result, we show that the Loday complex with adjoint coefficients embeds into the rack bialgebra deformation complex for the rack bialgebra defined by a Leibniz algebra.","authors_text":"Friedrich Wagemann (LMJL), Ulrich Kraehmer","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-08T09:08:37Z","title":"A universal enveloping algebra for cocommutative rack bialgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03335","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:bc19b0ab8ce81ccaa815491aaa3769c916a6eb4b9ae30fc1e9c10f9d605cc6ff","target":"record","created_at":"2026-05-18T00:03:36Z","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":"78373469faf78aa1e9502a858fd59345538a536f6625401597bfa49c13ffcfce","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-08T09:08:37Z","title_canon_sha256":"47cef8834c24140bbb8828ab91f80b91ede0c4e632931be2eb7b38b9ad6756ee"},"schema_version":"1.0","source":{"id":"1810.03335","kind":"arxiv","version":2}},"canonical_sha256":"c43c5b2311bef7b45caa416b41a9a1302559892b1968540533bcf80b5ca70822","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c43c5b2311bef7b45caa416b41a9a1302559892b1968540533bcf80b5ca70822","first_computed_at":"2026-05-18T00:03:36.381323Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:36.381323Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fEOJHFzIif+EKr3zIfx637UNK2G/NkZgSu95bWRdRFHT5crmPj143Ndxm0uPp2849WiTbH6/H5FHK6evnVIYDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:36.382980Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.03335","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc19b0ab8ce81ccaa815491aaa3769c916a6eb4b9ae30fc1e9c10f9d605cc6ff","sha256:4ab698d8213d9c11cebbca15b460c6e80daca82a8b6e1d0b8b2468a94b7cce68"],"state_sha256":"4fb4d8470b99cf31c7234e4eebe20a4a76f432e84acf8e54bac818dd3b238fac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6f4FxlGRgXXObAYLY8yori5jdjnL8blT6qtOSoyQSi70XUEtEz0JFePbi/TuLXK9aj1/tdeULrBTplvy9wEwAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T07:25:12.979943Z","bundle_sha256":"f6360288e3a2370ec761217d8db5c1aa1a8115e2655304b6de8ee392b9ae055a"}}