{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:73R35FSYT7DG3EMSNNDOMYU6MD","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":"14c320ab08300ba09d7c2ab1f3e0964e15ba9bba065d2488abdf55e2ea5c7370","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-12-19T11:29:57Z","title_canon_sha256":"2472aec585bc23c4073deea5dd0ed656688e2cd7784fbd671ab6900b7470e8e9"},"schema_version":"1.0","source":{"id":"1712.07302","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.07302","created_at":"2026-05-18T00:27:34Z"},{"alias_kind":"arxiv_version","alias_value":"1712.07302v1","created_at":"2026-05-18T00:27:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.07302","created_at":"2026-05-18T00:27:34Z"},{"alias_kind":"pith_short_12","alias_value":"73R35FSYT7DG","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"73R35FSYT7DG3EMS","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"73R35FSY","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:6e3cdd893e3b401baea72070ccf41b2aebe8b4d09a0bc60f2816568548fd2df7","target":"graph","created_at":"2026-05-18T00:27:34Z","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 prove that an arbitrary countable dimensional Lie algebra over a field of characteristic $\\neq 2$ that is locally of subexponential growth is embeddable in a finitely generated Lie algebra of subexponential growth.","authors_text":"Adel Alahmadi, Hamed Alsulami","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-12-19T11:29:57Z","title":"Embeddings in Lie algebras of subexponential growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.07302","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:ca56485e4094a1197ae345eff46cc93b04c48f4a103eff7545cf6852734150fc","target":"record","created_at":"2026-05-18T00:27:34Z","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":"14c320ab08300ba09d7c2ab1f3e0964e15ba9bba065d2488abdf55e2ea5c7370","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-12-19T11:29:57Z","title_canon_sha256":"2472aec585bc23c4073deea5dd0ed656688e2cd7784fbd671ab6900b7470e8e9"},"schema_version":"1.0","source":{"id":"1712.07302","kind":"arxiv","version":1}},"canonical_sha256":"fee3be96589fc66d91926b46e6629e60f691ea7dfe29f30b21ca6a5dbbd67253","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fee3be96589fc66d91926b46e6629e60f691ea7dfe29f30b21ca6a5dbbd67253","first_computed_at":"2026-05-18T00:27:34.895969Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:34.895969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zahuPaxWbVAfwfUsaNHP1AytTl3SUs83bVdHJ3IK7udxxwntUdOHJwN6u84X0mGWHCpVYJKFqehyqZ6qX8yeBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:34.896719Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.07302","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca56485e4094a1197ae345eff46cc93b04c48f4a103eff7545cf6852734150fc","sha256:6e3cdd893e3b401baea72070ccf41b2aebe8b4d09a0bc60f2816568548fd2df7"],"state_sha256":"6f82a50922d0757ce53b2e405c09474dea735a050de5062e11be9a8a9dd49c94"}