{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VDFC3OIMHBZQ6RRRFPSSWVFN7C","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":"e78d184fcf4a7d991f388c1f6c1f2656b92e70b4e8c46ad0812093ad347ce155","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-12-23T15:43:40Z","title_canon_sha256":"5dfc5a83884ab34cb2c60101132c7e55be841c89937ebe7459a407ed16d6eb78"},"schema_version":"1.0","source":{"id":"1601.02568","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02568","created_at":"2026-05-18T01:23:04Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02568v1","created_at":"2026-05-18T01:23:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02568","created_at":"2026-05-18T01:23:04Z"},{"alias_kind":"pith_short_12","alias_value":"VDFC3OIMHBZQ","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"VDFC3OIMHBZQ6RRR","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"VDFC3OIM","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:bf01b1b6ccf520d70b870f3dc20af7c719da9d8b94546f95f32e32b3cd22b403","target":"graph","created_at":"2026-05-18T01:23:04Z","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 consider differential equations of the form y'(t)=f(t,y(t)) on a (possibly infinite-dimensional) Lie group G, for f : [0,1] x G -> TG a time-dependent left invariant vector field with measurable (but not necessarily continuous) dependence on t. If a solution Evol(c):=y on [0,1] starting at the neutral element e of G exists for each f corresponding to an L^1-curve c : [0,1] -> g in the Lie algebra g of G, and Evol is smooth as a map from L^1([0,1],g) to C([0,1],G), then G is called L^1-regular. We show that all Banach-Lie groups are L^1-regular, as well as all direct limits of finite-dimensi","authors_text":"Helge Glockner","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-12-23T15:43:40Z","title":"Measurable regularity properties of infinite-dimensional Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02568","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:c959a87844cab5ed49298a7f4c2a1eaa578d04e8e0572bb5202dd650624fa615","target":"record","created_at":"2026-05-18T01:23:04Z","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":"e78d184fcf4a7d991f388c1f6c1f2656b92e70b4e8c46ad0812093ad347ce155","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-12-23T15:43:40Z","title_canon_sha256":"5dfc5a83884ab34cb2c60101132c7e55be841c89937ebe7459a407ed16d6eb78"},"schema_version":"1.0","source":{"id":"1601.02568","kind":"arxiv","version":1}},"canonical_sha256":"a8ca2db90c38730f46312be52b54adf88a7d11e51a86f92e2d1d48ece00d2872","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8ca2db90c38730f46312be52b54adf88a7d11e51a86f92e2d1d48ece00d2872","first_computed_at":"2026-05-18T01:23:04.787526Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:04.787526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4rNExfkPqZ4QpObghGb3RI7w7boyx/HRfYDQwlMckXD4ol9gsRxFOzrdeahmqTFIm3w0LeN3vhyrk7LQEOVJBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:04.787944Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.02568","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c959a87844cab5ed49298a7f4c2a1eaa578d04e8e0572bb5202dd650624fa615","sha256:bf01b1b6ccf520d70b870f3dc20af7c719da9d8b94546f95f32e32b3cd22b403"],"state_sha256":"3368793293ac0bcb4d7d76b02167614e59883acf34ee8f09a95cdb458cbe60ac"}