{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MSKXCECASGR6WNQ62M2SZRAUVH","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":"6f677a436b05067e9d3a6851824ac2dfada52dc73779382f5bdc4ed02ccb845a","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-08-26T12:39:54Z","title_canon_sha256":"280f65fa042fba62360f0fe113f645d282e31dea417c16d8c9611820f2adafd6"},"schema_version":"1.0","source":{"id":"1308.5559","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5559","created_at":"2026-05-18T01:37:08Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5559v1","created_at":"2026-05-18T01:37:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5559","created_at":"2026-05-18T01:37:08Z"},{"alias_kind":"pith_short_12","alias_value":"MSKXCECASGR6","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MSKXCECASGR6WNQ6","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MSKXCECA","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:bdb97c3f9822c72ae85b3869fcf87ad0978bf32428bc27b3b6c155eb84bc3e98","target":"graph","created_at":"2026-05-18T01:37:08Z","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":"Let $\\mathfrak{L}$ be a Leibniz algebra, $E$ a vector space and $\\pi : E \\to \\mathfrak{L}$ an epimorphism of vector spaces with $ \\mathfrak{g} = {\\rm Ker} (\\pi)$. The global extension problem asks for the classification of all Leibniz algebra structures that can be defined on $E$ such that $\\pi : E \\to \\mathfrak{L}$ is a morphism of Leibniz algebras: from a geometrical viewpoint this means to give the decomposition of the groupoid of all such structures in its connected components and to indicate a point in each component. All such Leibniz algebra structures on $E$ are classified by a global c","authors_text":"Gigel Militaru","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-08-26T12:39:54Z","title":"The global extension problem, co-flag and metabelian Leibniz algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5559","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":"sha256:4a3e66bfff0402ce475c7d82d9d2868963b607615c2ab00563fde4c052649e48","target":"record","created_at":"2026-05-18T01:37:08Z","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":"6f677a436b05067e9d3a6851824ac2dfada52dc73779382f5bdc4ed02ccb845a","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-08-26T12:39:54Z","title_canon_sha256":"280f65fa042fba62360f0fe113f645d282e31dea417c16d8c9611820f2adafd6"},"schema_version":"1.0","source":{"id":"1308.5559","kind":"arxiv","version":1}},"canonical_sha256":"649571104091a3eb361ed3352cc414a9ed00d13167ead2210dae406f7a1090ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"649571104091a3eb361ed3352cc414a9ed00d13167ead2210dae406f7a1090ce","first_computed_at":"2026-05-18T01:37:08.084656Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:08.084656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bgl2fYgp5vtCK+h5jYrPEIhFMoUy1x5XE/pNfMEfWINVoGsUlsK0ivbLGVA6+y9fPQGHdGaxNvjbs2aXRp8RBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:08.085482Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.5559","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a3e66bfff0402ce475c7d82d9d2868963b607615c2ab00563fde4c052649e48","sha256:bdb97c3f9822c72ae85b3869fcf87ad0978bf32428bc27b3b6c155eb84bc3e98"],"state_sha256":"7768bfef50b0c847a820fbc7cff0c30e6c871fd99e6d1b7bde839b8b195d2491"}