{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:PV76KDWDKG6G4MYOFAAATPGPNH","short_pith_number":"pith:PV76KDWD","canonical_record":{"source":{"id":"2411.19238","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2024-11-28T16:18:53Z","cross_cats_sorted":["math.CT","math.QA","math.RT"],"title_canon_sha256":"5fd8bd9ae340a32f7bcb4866090a895eb2c8eb9b8bf846aee004788d69510f8f","abstract_canon_sha256":"b25f961254c28b14f2195bf9024226ddabf704ededa9343a0a0d6b8384433680"},"schema_version":"1.0"},"canonical_sha256":"7d7fe50ec351bc6e330e280009bccf69efc3d327efc99210ac4b5fcd47abd847","source":{"kind":"arxiv","id":"2411.19238","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.19238","created_at":"2026-07-05T11:02:14Z"},{"alias_kind":"arxiv_version","alias_value":"2411.19238v2","created_at":"2026-07-05T11:02:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.19238","created_at":"2026-07-05T11:02:14Z"},{"alias_kind":"pith_short_12","alias_value":"PV76KDWDKG6G","created_at":"2026-07-05T11:02:14Z"},{"alias_kind":"pith_short_16","alias_value":"PV76KDWDKG6G4MYO","created_at":"2026-07-05T11:02:14Z"},{"alias_kind":"pith_short_8","alias_value":"PV76KDWD","created_at":"2026-07-05T11:02:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:PV76KDWDKG6G4MYOFAAATPGPNH","target":"record","payload":{"canonical_record":{"source":{"id":"2411.19238","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2024-11-28T16:18:53Z","cross_cats_sorted":["math.CT","math.QA","math.RT"],"title_canon_sha256":"5fd8bd9ae340a32f7bcb4866090a895eb2c8eb9b8bf846aee004788d69510f8f","abstract_canon_sha256":"b25f961254c28b14f2195bf9024226ddabf704ededa9343a0a0d6b8384433680"},"schema_version":"1.0"},"canonical_sha256":"7d7fe50ec351bc6e330e280009bccf69efc3d327efc99210ac4b5fcd47abd847","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:02:14.801894Z","signature_b64":"BAQ8FK7S9y3uZoiWI6aFOt+t6yoVXXcLYjJyU/0TgR6hlyxe6XsRP66dXYVu6wkVuQCp6SlOdn4t5Ir8RHIjCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d7fe50ec351bc6e330e280009bccf69efc3d327efc99210ac4b5fcd47abd847","last_reissued_at":"2026-07-05T11:02:14.801450Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:02:14.801450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.19238","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":"2026-07-05T11:02:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T+YlxYA3H0jTxXyZkERhr4WphPdmUsvrXxbRD287e3K5rMOySRBL10od0HZvz/p61Cspt2xNBVS6irogBJoODw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T01:00:56.418153Z"},"content_sha256":"4b9f2437b1b350859bf078912098c77ae7f6d72ee15db5519353f5828a0f7107","schema_version":"1.0","event_id":"sha256:4b9f2437b1b350859bf078912098c77ae7f6d72ee15db5519353f5828a0f7107"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:PV76KDWDKG6G4MYOFAAATPGPNH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hopf braces and semi-abelian categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.QA","math.RT"],"primary_cat":"math.RA","authors_text":"Andrea Sciandra, Marino Gran","submitted_at":"2024-11-28T16:18:53Z","abstract_excerpt":"Hopf braces have been introduced as a Hopf-theoretic generalization of skew braces. Under the assumption of cocommutativity, these algebraic structures are equivalent to matched pairs of actions on Hopf algebras, that can be used to produce solutions of the quantum Yang-Baxter equation. We prove that the category of cocommutative Hopf braces is semi-abelian and strongly protomodular. In particular, this implies that the main homological lemmas known for groups, Lie algebras and other classical algebraic structures also hold for cocommutative Hopf braces. Abelian objects are commutative and coc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.19238","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.19238/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:02:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h6/pv7nW/9GDAeI1C4/lrrsnN/iS+3sjLzHrjrOiu+8aC7gQaLWC6MdK8WZJhG8MqsynwawGlDNW5wNLsqePAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T01:00:56.419154Z"},"content_sha256":"a89f90e8f72d50cee1d0a88a719a8d6a821e95b346f99d0ac00a13175fa81e36","schema_version":"1.0","event_id":"sha256:a89f90e8f72d50cee1d0a88a719a8d6a821e95b346f99d0ac00a13175fa81e36"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PV76KDWDKG6G4MYOFAAATPGPNH/bundle.json","state_url":"https://pith.science/pith/PV76KDWDKG6G4MYOFAAATPGPNH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PV76KDWDKG6G4MYOFAAATPGPNH/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":"2026-08-13T01:00:56Z","links":{"resolver":"https://pith.science/pith/PV76KDWDKG6G4MYOFAAATPGPNH","bundle":"https://pith.science/pith/PV76KDWDKG6G4MYOFAAATPGPNH/bundle.json","state":"https://pith.science/pith/PV76KDWDKG6G4MYOFAAATPGPNH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PV76KDWDKG6G4MYOFAAATPGPNH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:PV76KDWDKG6G4MYOFAAATPGPNH","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":"b25f961254c28b14f2195bf9024226ddabf704ededa9343a0a0d6b8384433680","cross_cats_sorted":["math.CT","math.QA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2024-11-28T16:18:53Z","title_canon_sha256":"5fd8bd9ae340a32f7bcb4866090a895eb2c8eb9b8bf846aee004788d69510f8f"},"schema_version":"1.0","source":{"id":"2411.19238","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.19238","created_at":"2026-07-05T11:02:14Z"},{"alias_kind":"arxiv_version","alias_value":"2411.19238v2","created_at":"2026-07-05T11:02:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.19238","created_at":"2026-07-05T11:02:14Z"},{"alias_kind":"pith_short_12","alias_value":"PV76KDWDKG6G","created_at":"2026-07-05T11:02:14Z"},{"alias_kind":"pith_short_16","alias_value":"PV76KDWDKG6G4MYO","created_at":"2026-07-05T11:02:14Z"},{"alias_kind":"pith_short_8","alias_value":"PV76KDWD","created_at":"2026-07-05T11:02:14Z"}],"graph_snapshots":[{"event_id":"sha256:a89f90e8f72d50cee1d0a88a719a8d6a821e95b346f99d0ac00a13175fa81e36","target":"graph","created_at":"2026-07-05T11:02:14Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.19238/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Hopf braces have been introduced as a Hopf-theoretic generalization of skew braces. Under the assumption of cocommutativity, these algebraic structures are equivalent to matched pairs of actions on Hopf algebras, that can be used to produce solutions of the quantum Yang-Baxter equation. We prove that the category of cocommutative Hopf braces is semi-abelian and strongly protomodular. In particular, this implies that the main homological lemmas known for groups, Lie algebras and other classical algebraic structures also hold for cocommutative Hopf braces. Abelian objects are commutative and coc","authors_text":"Andrea Sciandra, Marino Gran","cross_cats":["math.CT","math.QA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2024-11-28T16:18:53Z","title":"Hopf braces and semi-abelian categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.19238","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":"sha256:4b9f2437b1b350859bf078912098c77ae7f6d72ee15db5519353f5828a0f7107","target":"record","created_at":"2026-07-05T11:02:14Z","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":"b25f961254c28b14f2195bf9024226ddabf704ededa9343a0a0d6b8384433680","cross_cats_sorted":["math.CT","math.QA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2024-11-28T16:18:53Z","title_canon_sha256":"5fd8bd9ae340a32f7bcb4866090a895eb2c8eb9b8bf846aee004788d69510f8f"},"schema_version":"1.0","source":{"id":"2411.19238","kind":"arxiv","version":2}},"canonical_sha256":"7d7fe50ec351bc6e330e280009bccf69efc3d327efc99210ac4b5fcd47abd847","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d7fe50ec351bc6e330e280009bccf69efc3d327efc99210ac4b5fcd47abd847","first_computed_at":"2026-07-05T11:02:14.801450Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:02:14.801450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BAQ8FK7S9y3uZoiWI6aFOt+t6yoVXXcLYjJyU/0TgR6hlyxe6XsRP66dXYVu6wkVuQCp6SlOdn4t5Ir8RHIjCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:02:14.801894Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.19238","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b9f2437b1b350859bf078912098c77ae7f6d72ee15db5519353f5828a0f7107","sha256:a89f90e8f72d50cee1d0a88a719a8d6a821e95b346f99d0ac00a13175fa81e36"],"state_sha256":"98b32999a520b8934b1c0934b7e0e100109602ade09a4f13db813b0d2712a5f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1hqDNnYON7hfrc5yDn2ZrQgWIqW0B9cZ8Le4KEl2isVqLSZDG7FfUIObBmFXg5sALWihmNO0PVf7lda8Z73fDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T01:00:56.425554Z","bundle_sha256":"66b23d202b35a0c76e5a5492ad17baf3b953d8df19df7253fb77a258e4e29529"}}