{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:N44YIPKKPHBJWI63WLHK4N255P","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":"f431b929a89ea421bf97f7820cf77ba569491063234919617787a0cd60ec147b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-04-18T05:43:57Z","title_canon_sha256":"7cd6021b06432d7fd84a1c6a5c9c7a92d6b771c39c684557fcd7a6d800630e5b"},"schema_version":"1.0","source":{"id":"1304.5024","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5024","created_at":"2026-05-18T03:27:42Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5024v1","created_at":"2026-05-18T03:27:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5024","created_at":"2026-05-18T03:27:42Z"},{"alias_kind":"pith_short_12","alias_value":"N44YIPKKPHBJ","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"N44YIPKKPHBJWI63","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"N44YIPKK","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:e32547c274e4ef5e910f045bc0af1532a2ce7a69fa0bd42b4284d5363e6e5f97","target":"graph","created_at":"2026-05-18T03:27:42Z","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":"The jet bundle $J^kG$ of $k$-jets of curves in a Lie group $G$ has a natural Lie group structure. We present an explicit formula for the group multiplication in the right trivialization and for the group 2-cocycle describing the abelian Lie group extension $\\mathfrak{g}\\to J^{k}G\\to J^{k-1}G$.","authors_text":"Cornelia Vizman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-04-18T05:43:57Z","title":"The group structure for jet bundles over Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5024","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":"sha256:47e4921b19ad41d2e077fa6e019dae4ed7bfc830170a51fbf3bc730c6d3fe180","target":"record","created_at":"2026-05-18T03:27:42Z","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":"f431b929a89ea421bf97f7820cf77ba569491063234919617787a0cd60ec147b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-04-18T05:43:57Z","title_canon_sha256":"7cd6021b06432d7fd84a1c6a5c9c7a92d6b771c39c684557fcd7a6d800630e5b"},"schema_version":"1.0","source":{"id":"1304.5024","kind":"arxiv","version":1}},"canonical_sha256":"6f39843d4a79c29b23dbb2ceae375debc60efa3e5f8702a65b6e069c536664b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f39843d4a79c29b23dbb2ceae375debc60efa3e5f8702a65b6e069c536664b5","first_computed_at":"2026-05-18T03:27:42.006780Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:42.006780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N85V8tciTdeAt5By46RfoiRb3L1dLNuuRVGXURdko5cUju4YZwi9RgHh8gYreNKgeliZlEiG0H9BdW0Cg3wjCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:42.007522Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5024","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47e4921b19ad41d2e077fa6e019dae4ed7bfc830170a51fbf3bc730c6d3fe180","sha256:e32547c274e4ef5e910f045bc0af1532a2ce7a69fa0bd42b4284d5363e6e5f97"],"state_sha256":"712b81e1f2d86afabc5f27bcc3eacd381f3057f6da18273c349d1115a9603fab"}