{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TVJA5VQUIE64GPM46YIFFXJ5MJ","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":"2414533f0f2243e725375a9f8cf630223a208e13e9078775c6323aba0f855932","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-12T13:06:02Z","title_canon_sha256":"e431c046bbe59f08e1383bc8d9d1f433481750b7a98d500502585591a4663fca"},"schema_version":"1.0","source":{"id":"1601.02840","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02840","created_at":"2026-05-18T01:22:59Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02840v1","created_at":"2026-05-18T01:22:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02840","created_at":"2026-05-18T01:22:59Z"},{"alias_kind":"pith_short_12","alias_value":"TVJA5VQUIE64","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TVJA5VQUIE64GPM4","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TVJA5VQU","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:f7cccd8bd5096351a2fa891f0ed768b53a4a4de60610a5669c3ea67cd27e7312","target":"graph","created_at":"2026-05-18T01:22:59Z","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":"Jun O'Hara invented a family of knot energies $E^{j,p}$, $j,p \\in (0, \\infty)$. We study the negative gradient flow of the sum of one of the energies $E^\\alpha = E^{\\alpha,1}$, $\\alpha \\in (2,3)$, and a positive multiple of the length.\n  Showing that the gradients of these knot energies can be written as the normal part of a quasilinear operator, we derive short time existence results for these flows. We then prove long time existence and convergence to critical points.","authors_text":"Simon Blatt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-12T13:06:02Z","title":"The Gradient Flow of O'Hara's Knot Energies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02840","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:fcc144d8bf6d9a5b3f9fbf321452df5260f05f629dd508f6a23a75a705b23ed2","target":"record","created_at":"2026-05-18T01:22:59Z","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":"2414533f0f2243e725375a9f8cf630223a208e13e9078775c6323aba0f855932","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-12T13:06:02Z","title_canon_sha256":"e431c046bbe59f08e1383bc8d9d1f433481750b7a98d500502585591a4663fca"},"schema_version":"1.0","source":{"id":"1601.02840","kind":"arxiv","version":1}},"canonical_sha256":"9d520ed614413dc33d9cf61052dd3d627152e5817d06a1c3ed3e4d76603198eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d520ed614413dc33d9cf61052dd3d627152e5817d06a1c3ed3e4d76603198eb","first_computed_at":"2026-05-18T01:22:59.492007Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:59.492007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h1/31vNjGpGo4U0lQhLVDZ95S4/usxKTKhS2OCPnHJblyqSVBhyqj0wxc+iXPOzSVJSCg6APJUw6XtCTTAXNDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:59.492450Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.02840","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fcc144d8bf6d9a5b3f9fbf321452df5260f05f629dd508f6a23a75a705b23ed2","sha256:f7cccd8bd5096351a2fa891f0ed768b53a4a4de60610a5669c3ea67cd27e7312"],"state_sha256":"bfbf41834071b031c6c86f5740a07dfbf08b214a3f0a22becbfb82acd2e6705b"}