{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:A7STCGCLKJM7JLDQCN73MWZTWY","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":"15d9e02f933e0412c7cc79962a8a47d305b793edbbc0bb2cce3f51c3dfdd8c9b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-04-06T15:35:07Z","title_canon_sha256":"9c28b6bb9438ea7518d2b0f939120dfb9cadea64456b9613d2fce690fc60fb6f"},"schema_version":"1.0","source":{"id":"0804.0914","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0804.0914","created_at":"2026-05-18T02:15:53Z"},{"alias_kind":"arxiv_version","alias_value":"0804.0914v1","created_at":"2026-05-18T02:15:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0804.0914","created_at":"2026-05-18T02:15:53Z"},{"alias_kind":"pith_short_12","alias_value":"A7STCGCLKJM7","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"A7STCGCLKJM7JLDQ","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"A7STCGCL","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:d772fb2063192870099fcdfa83c0ae81473acca7bbc1b1797b8af2842fee3467","target":"graph","created_at":"2026-05-18T02:15:53Z","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":"One of the natural ways to prove that the Hall words (Philip Hall, 1933) consist of a basis of a free Lie algebra is a direct construction: to start with a linear space spanned by Hall words, to define the Lie product of Hall words, and then to check that the product yields the Lie identities (Marshall Hall, 1950). Here we suggest another way using the Composition-Diamond lemma for free anti-commutative (non-associative) algebras (A.I. Shirshov, 1962).","authors_text":"L. A. Bokut, Yu Li, Yuqun Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-04-06T15:35:07Z","title":"Anti-commutative Groebner-Shirshov basis of a free Lie algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.0914","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":"sha256:0f590a68eea69092b209e550cbdd018c9b68e2920e3e6de11bb3654851554e75","target":"record","created_at":"2026-05-18T02:15:53Z","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":"15d9e02f933e0412c7cc79962a8a47d305b793edbbc0bb2cce3f51c3dfdd8c9b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-04-06T15:35:07Z","title_canon_sha256":"9c28b6bb9438ea7518d2b0f939120dfb9cadea64456b9613d2fce690fc60fb6f"},"schema_version":"1.0","source":{"id":"0804.0914","kind":"arxiv","version":1}},"canonical_sha256":"07e531184b5259f4ac70137fb65b33b624da92212eddbe9bfb3efda44cfe69ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07e531184b5259f4ac70137fb65b33b624da92212eddbe9bfb3efda44cfe69ae","first_computed_at":"2026-05-18T02:15:53.947036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:53.947036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9JXoToPVX1S77fgSZC4chvxp1ICc8Zg0zJfnjMe/tAvzDkb/Zsl3xeIo4r0o5ZFepuJzV1ZqshqkcGY4RYxvDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:53.947567Z","signed_message":"canonical_sha256_bytes"},"source_id":"0804.0914","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f590a68eea69092b209e550cbdd018c9b68e2920e3e6de11bb3654851554e75","sha256:d772fb2063192870099fcdfa83c0ae81473acca7bbc1b1797b8af2842fee3467"],"state_sha256":"9dea79b69145e635b439ee83a24e7728622593b505c59464169bba084e4e7f0c"}