{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LPGH44JM4SS5BBMZNVHMXDD5GL","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":"2a3fc0af4c79de63ad1201771db94d3ebe1f09381998718d6d9ae5af17e5b027","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-17T23:04:15Z","title_canon_sha256":"3c472c2323dc915885e25736a01399716f4fb3309a1323f1df981701dfc661fc"},"schema_version":"1.0","source":{"id":"1312.4995","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4995","created_at":"2026-05-18T02:41:08Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4995v2","created_at":"2026-05-18T02:41:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4995","created_at":"2026-05-18T02:41:08Z"},{"alias_kind":"pith_short_12","alias_value":"LPGH44JM4SS5","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LPGH44JM4SS5BBMZ","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LPGH44JM","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:e3093b7ddf220332c82ec50dc5670ce1318f2b87e2286c7d5beb480cb591ea60","target":"graph","created_at":"2026-05-18T02:41:08Z","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":"We study properties of Sobolev-type metrics on the space of immersed plane curves. We show that the geodesic equation for Sobolev-type metrics with constant coefficients of order 2 and higher is globally well-posed for smooth initial data as well as initial data in certain Sobolev spaces. Thus the space of closed plane curves equipped with such a metric is geodesically complete. We find lower bounds for the geodesic distance in terms of curvature and its derivatives.","authors_text":"David Mumford, Martins Bruveris, Peter W. Michor","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-17T23:04:15Z","title":"Geodesic Completeness for Sobolev Metrics on the Space of Immersed Plane Curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4995","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":"sha256:18be01d6e5293e2b197d23d9200b783a9a07b61e3c88a44a249966d60e57871a","target":"record","created_at":"2026-05-18T02:41:08Z","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":"2a3fc0af4c79de63ad1201771db94d3ebe1f09381998718d6d9ae5af17e5b027","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-17T23:04:15Z","title_canon_sha256":"3c472c2323dc915885e25736a01399716f4fb3309a1323f1df981701dfc661fc"},"schema_version":"1.0","source":{"id":"1312.4995","kind":"arxiv","version":2}},"canonical_sha256":"5bcc7e712ce4a5d085996d4ecb8c7d32e8691c5bf22db4e692718c490d82b12c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5bcc7e712ce4a5d085996d4ecb8c7d32e8691c5bf22db4e692718c490d82b12c","first_computed_at":"2026-05-18T02:41:08.769672Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:08.769672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7PFA0FWCTbmZW1y8Jon8LbC5qaZr02limwhBZhMbaP2niegVCLgEQeGHlz57BfjJ1cVkGxd3y3OaMFkGC4P1DA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:08.770125Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.4995","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18be01d6e5293e2b197d23d9200b783a9a07b61e3c88a44a249966d60e57871a","sha256:e3093b7ddf220332c82ec50dc5670ce1318f2b87e2286c7d5beb480cb591ea60"],"state_sha256":"5a8bc9fd2c71b8bd39fa77e7f24297404625dc734f999dda074d5770601903a4"}