{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:OK4RYQL43QPGU6HTAD4G633KZ5","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":"45d6ce6e342f4d7e53f5441c367c4ed0943f4fe801da3b6aa1e33631a8c723c4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-22T00:27:37Z","title_canon_sha256":"6b37c44e950cac94554c23e607a621459f0fb0133b0fc89c05fad67ad88b3226"},"schema_version":"1.0","source":{"id":"1901.07128","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.07128","created_at":"2026-05-17T23:55:48Z"},{"alias_kind":"arxiv_version","alias_value":"1901.07128v1","created_at":"2026-05-17T23:55:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.07128","created_at":"2026-05-17T23:55:48Z"},{"alias_kind":"pith_short_12","alias_value":"OK4RYQL43QPG","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"OK4RYQL43QPGU6HT","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"OK4RYQL4","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:e022a6ece51760e63cef13e3d8af1262dcf5478e297b26441f616aa01e330b08","target":"graph","created_at":"2026-05-17T23:55:48Z","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 show that any initial closed curve suitably close to a circle flows under length-constrained curve diffusion to a round circle in infinite time with exponential convergence. We provide an estimate on the total length of time for which such curves are not strictly convex. We further show that there are no closed translating solutions to the flow and that the only closed rotators are circles.","authors_text":"Glen Wheeler, James McCoy, Yuhan Wu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-22T00:27:37Z","title":"Length-constrained curve diffusion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07128","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:cdbb5df856e52e9e56e586b95e9b01f5445ae0ac79a853fea7621c13e675da44","target":"record","created_at":"2026-05-17T23:55:48Z","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":"45d6ce6e342f4d7e53f5441c367c4ed0943f4fe801da3b6aa1e33631a8c723c4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-22T00:27:37Z","title_canon_sha256":"6b37c44e950cac94554c23e607a621459f0fb0133b0fc89c05fad67ad88b3226"},"schema_version":"1.0","source":{"id":"1901.07128","kind":"arxiv","version":1}},"canonical_sha256":"72b91c417cdc1e6a78f300f86f6f6acf738e4897bf39b49840d0c9339a84c663","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72b91c417cdc1e6a78f300f86f6f6acf738e4897bf39b49840d0c9339a84c663","first_computed_at":"2026-05-17T23:55:48.074105Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:48.074105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qe82Z4D3Ck1/bGOH+XE53itmkAjMomxF2QuraPkjc91tdvFJagNKUFo6Ul39W8wCDweQ9kec/nHyA/D/tODQDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:48.074690Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.07128","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cdbb5df856e52e9e56e586b95e9b01f5445ae0ac79a853fea7621c13e675da44","sha256:e022a6ece51760e63cef13e3d8af1262dcf5478e297b26441f616aa01e330b08"],"state_sha256":"b4f7cd8e890db29a97aecdf94eb582264f2caa05057a2af82efb3773fd574208"}