{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4K6VBKUPA5SKVRFPWZK74DXJTS","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":"aa5b0d3a02983c3f79b8917444f43529ce29f9a287ef6b0ae9522aa28b7f1dbd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-12-23T09:21:00Z","title_canon_sha256":"ecb8dc9a63b316b71c8edb743fbbb1d751c889740432b6bda4a7adb91e46d628"},"schema_version":"1.0","source":{"id":"1612.07910","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07910","created_at":"2026-05-18T00:54:05Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07910v1","created_at":"2026-05-18T00:54:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07910","created_at":"2026-05-18T00:54:05Z"},{"alias_kind":"pith_short_12","alias_value":"4K6VBKUPA5SK","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4K6VBKUPA5SKVRFP","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4K6VBKUP","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:3a0aa241de2c42fb4cfa01bef60f7cc15516ed6a4cac68c534b74aeea38b338c","target":"graph","created_at":"2026-05-18T00:54:05Z","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 a non-abelian exterior product of two crossed modules of Leibniz algebra and investigate its relation to the low dimensional Leibniz homology. Later this non-abelian exterior product is applied to the construction of eight term exact sequence in Leibniz homology. Also its relationship to the universal quadratic functor is established, which is applied to the comparison of the second Lie and Leibniz homologies of a Lie algebra.","authors_text":"Emzar Khmaladze, Guram Donadze, Xabier Garc\\'ia-Mart\\'inez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-12-23T09:21:00Z","title":"A non-abelian exterior product and homology of Leibniz algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07910","kind":"arxiv","version":1},"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:c293d28b8660c6812d6ac41224dd9a96098d27bc7c03c5ff5892f2ff5b292a1c","target":"record","created_at":"2026-05-18T00:54:05Z","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":"aa5b0d3a02983c3f79b8917444f43529ce29f9a287ef6b0ae9522aa28b7f1dbd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-12-23T09:21:00Z","title_canon_sha256":"ecb8dc9a63b316b71c8edb743fbbb1d751c889740432b6bda4a7adb91e46d628"},"schema_version":"1.0","source":{"id":"1612.07910","kind":"arxiv","version":1}},"canonical_sha256":"e2bd50aa8f0764aac4afb655fe0ee99c861327343ba26a8a99d91e8c1e1d4241","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2bd50aa8f0764aac4afb655fe0ee99c861327343ba26a8a99d91e8c1e1d4241","first_computed_at":"2026-05-18T00:54:05.365052Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:05.365052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0MGW4Z6YBIQnSU1QOBXXdhaCD32ndFhk5F9xE817+UcWF/OKt0duDfUws6Tw7ET8+hghjXz0kM2zORi3qB/FBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:05.365546Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.07910","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c293d28b8660c6812d6ac41224dd9a96098d27bc7c03c5ff5892f2ff5b292a1c","sha256:3a0aa241de2c42fb4cfa01bef60f7cc15516ed6a4cac68c534b74aeea38b338c"],"state_sha256":"ad88603b4f33a3123a4b1604845130f0ceaa1124304ac12c16d82c342eb77c82"}