{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:JPUPE7R2DMKZJZW5RCJOOQS3KM","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":"4892446a519380f5480d44499da334aaa63a23ab23d3cfabbeec3df3db4a5b1b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-02-17T21:31:23Z","title_canon_sha256":"f0be33c181401b7a5bf3ef3d037726a06e999a08a2c6c3cb7ad94b9064aaf706"},"schema_version":"1.0","source":{"id":"1902.06329","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.06329","created_at":"2026-05-17T23:53:45Z"},{"alias_kind":"arxiv_version","alias_value":"1902.06329v1","created_at":"2026-05-17T23:53:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.06329","created_at":"2026-05-17T23:53:45Z"},{"alias_kind":"pith_short_12","alias_value":"JPUPE7R2DMKZ","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"JPUPE7R2DMKZJZW5","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"JPUPE7R2","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:64bb8b423eb41e5ea2a58500dba7c74a568cfe6e605b3b2e31405f75ee22a92f","target":"graph","created_at":"2026-05-17T23:53:45Z","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 G be a regular Lie group which is a directed union of regular Lie groups G_i (all modelled on possibly infinite-dimensional, locally convex spaces). We show that G is the direct limit of the G_i as a regular Lie group whenever G admits a so-called direct limit chart. Notably, this allows the regular Lie group Diff_c(M) of compactly supported smooth diffeomorphisms to be interpreted as a direct limit of the regular Lie groups Diff_K(M) of smooth diffeomorphisms supported in compact subsets K of M, even if the finite-dimensional smooth manifold M is merely paracompact (but not necessarily si","authors_text":"Helge Glockner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-02-17T21:31:23Z","title":"Direct limits of regular Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.06329","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":"sha256:9f3c614907600be78346f77febda9ff9a9356b2ac77cc475272de3233235c9ea","target":"record","created_at":"2026-05-17T23:53:45Z","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":"4892446a519380f5480d44499da334aaa63a23ab23d3cfabbeec3df3db4a5b1b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-02-17T21:31:23Z","title_canon_sha256":"f0be33c181401b7a5bf3ef3d037726a06e999a08a2c6c3cb7ad94b9064aaf706"},"schema_version":"1.0","source":{"id":"1902.06329","kind":"arxiv","version":1}},"canonical_sha256":"4be8f27e3a1b1594e6dd8892e7425b5318f0afb3cb10e5f28e046ecf04ae3500","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4be8f27e3a1b1594e6dd8892e7425b5318f0afb3cb10e5f28e046ecf04ae3500","first_computed_at":"2026-05-17T23:53:45.844886Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:45.844886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gsqA6OYNXaMn8YnpPhgbCyYHbmw+H9GNowvFCg8eju7HgwC1YZe01H3c/S20SFkN6eVvaNOVdQE5R36HGx1wBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:45.845549Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.06329","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f3c614907600be78346f77febda9ff9a9356b2ac77cc475272de3233235c9ea","sha256:64bb8b423eb41e5ea2a58500dba7c74a568cfe6e605b3b2e31405f75ee22a92f"],"state_sha256":"49561be7fa2bdc4e814dd450569dc8843a3720881c4fdedc0583b1ea3da9c7c5"}