{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FKPIQT6SMCXTC5R67YSBIQH2JK","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":"11e72918877ce408ad3edb6c2c639ae13195e4d0026c940f980f8ec5db6e4e0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-06-26T05:16:00Z","title_canon_sha256":"32c45539581d7c859250f87e5dda771813f748841c58e218864f710a5406c85f"},"schema_version":"1.0","source":{"id":"1706.08235","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.08235","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"arxiv_version","alias_value":"1706.08235v1","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.08235","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"pith_short_12","alias_value":"FKPIQT6SMCXT","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FKPIQT6SMCXTC5R6","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FKPIQT6S","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:bde506dcdd3a763f3cfd20f47b4c463bee33ad036dd6779aa3f64f475b371d2e","target":"graph","created_at":"2026-05-18T00:02:02Z","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 establish a universal approach to solution of the word problem in the varieties of di- and tri-algebras. This approach, for example, allows to apply Groebner---Shirshov bases method for Lie algebras to solve the ideal membership problem in free Leibniz algebras (Lie di-algebras). As another application, we prove an analogue of the Poincare---Birkhoff---Witt Theorem for universal enveloping associative tri-algebra of a Lie tri-algebra (CTD^!-algebra).","authors_text":"Pavel Kolesnikov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-06-26T05:16:00Z","title":"Groebner---Shirshov bases for replicated algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08235","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":"sha256:4270fc9b3f9e65dfb15c641b6e3e5cf6c05ae957221e02663d9c35ac133af3ce","target":"record","created_at":"2026-05-18T00:02:02Z","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":"11e72918877ce408ad3edb6c2c639ae13195e4d0026c940f980f8ec5db6e4e0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-06-26T05:16:00Z","title_canon_sha256":"32c45539581d7c859250f87e5dda771813f748841c58e218864f710a5406c85f"},"schema_version":"1.0","source":{"id":"1706.08235","kind":"arxiv","version":1}},"canonical_sha256":"2a9e884fd260af31763efe241440fa4a8d625a788613cd78a8569976a6e6d17f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a9e884fd260af31763efe241440fa4a8d625a788613cd78a8569976a6e6d17f","first_computed_at":"2026-05-18T00:02:02.132051Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:02.132051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XJSxQ39dmb88D6JWgWrtWlkLD40J+sNTo/llePmnL1K7JOt6cv6UX1HokDliIVRlsmxnsjIMiB2OijrpVtocBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:02.132548Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.08235","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4270fc9b3f9e65dfb15c641b6e3e5cf6c05ae957221e02663d9c35ac133af3ce","sha256:bde506dcdd3a763f3cfd20f47b4c463bee33ad036dd6779aa3f64f475b371d2e"],"state_sha256":"84f521fca904f425568e8c77d4a793c2b51ba3de866008f9e518e5580968a588"}