{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7OR6E2GQI3276W2H24UNLPCOD5","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":"937262931d85c3ed9e5c7b5b4451d29192bc5f49eaf9330f7f90c92ba5e6e303","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-04T18:37:22Z","title_canon_sha256":"07dfc93953f65f25c5d5fe5dadf9324600881a4501c291a0fe4b3e37477f7ab8"},"schema_version":"1.0","source":{"id":"1308.0835","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0835","created_at":"2026-05-18T01:24:14Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0835v2","created_at":"2026-05-18T01:24:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0835","created_at":"2026-05-18T01:24:14Z"},{"alias_kind":"pith_short_12","alias_value":"7OR6E2GQI327","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7OR6E2GQI3276W2H","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7OR6E2GQ","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:902ca089b5a7cc152280136f26275694b7557573c1d7d9dc7c0f37a8a1ccb10c","target":"graph","created_at":"2026-05-18T01:24:14Z","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 $\\omega_\\mathfrak{g}$ be a Lie algebra valued differential $1$-form on a manifold $M$ satisfying the structure equations $d \\omega_\\mathfrak{g} + \\frac{1}{2} \\omega_\\mathfrak{g}\\wedge \\omega_\\mathfrak{g}=0$ where $\\mathfrak{g}$ is solvable. We show that the problem of finding a smooth map $\\rho:M\\to G$, where $G$ is an $n$-dimensional solvable Lie group with Lie algebra $\\mathfrak{g}$ and left invariant Maurer-Cartan form $\\tau$, such that $\\rho^* \\tau= \\omega_\\mathfrak{g}$ can be solved by quadratures and the matrix exponential. In the process we give a closed form formula for the vector ","authors_text":"Mark E. Fels","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-04T18:37:22Z","title":"On the Construction of Simply Connected Solvable Lie Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0835","kind":"arxiv","version":2},"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":"sha256:638d495e2813f883d1e5fad67c80f14b75fc61cf7659a01a877110501f684a18","target":"record","created_at":"2026-05-18T01:24:14Z","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":"937262931d85c3ed9e5c7b5b4451d29192bc5f49eaf9330f7f90c92ba5e6e303","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-04T18:37:22Z","title_canon_sha256":"07dfc93953f65f25c5d5fe5dadf9324600881a4501c291a0fe4b3e37477f7ab8"},"schema_version":"1.0","source":{"id":"1308.0835","kind":"arxiv","version":2}},"canonical_sha256":"fba3e268d046f5ff5b47d728d5bc4e1f4f08f5a61b9e433c9c852774370eed37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fba3e268d046f5ff5b47d728d5bc4e1f4f08f5a61b9e433c9c852774370eed37","first_computed_at":"2026-05-18T01:24:14.892646Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:14.892646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tj6hHR/dJpBuDbybZaHRSnlwvWETWH3sVeAXakjkAri1AKcbScNMWzc3IoDBXg6e7NcLBITDEscpQit5WTdwBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:14.893149Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.0835","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:638d495e2813f883d1e5fad67c80f14b75fc61cf7659a01a877110501f684a18","sha256:902ca089b5a7cc152280136f26275694b7557573c1d7d9dc7c0f37a8a1ccb10c"],"state_sha256":"a9ff39d3bc57141b44925e7b06f0c8c5a2a6fddd7a52e855f45d9f5ba6760dc2"}