{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HMLPMKJBVIPOYKYLUIL24CRCN5","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":"7036c41bea3148c39da95a9384606ac235458f6608e0377b659a4cc69f42b655","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-24T11:48:01Z","title_canon_sha256":"1d5cf2f3016f3efdfa86e7ab7dd769c14428c1e15ee6d2a2f125887c2df9a1f8"},"schema_version":"1.0","source":{"id":"1202.5426","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.5426","created_at":"2026-05-18T01:24:37Z"},{"alias_kind":"arxiv_version","alias_value":"1202.5426v2","created_at":"2026-05-18T01:24:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5426","created_at":"2026-05-18T01:24:37Z"},{"alias_kind":"pith_short_12","alias_value":"HMLPMKJBVIPO","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HMLPMKJBVIPOYKYL","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HMLPMKJB","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:8029ed4cd6b255e2fd96d97ac1c027741b8da4dfbb39ec151d8cc2541b4f09ab","target":"graph","created_at":"2026-05-18T01:24:37Z","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 prove that if a curve parametrized by arc length is a stationary point of the Moebius energy introduced by Jun O'Hara, then it is smooth whenever the Moebius energy is finite. Our methods, interestingly, only rely on purely analytical arguments, entirely without using Moebius invariance. Furthermore, the techniques involved are not fundamentally restricted to one-dimensional domains, but are generalizable to arbitrary dimensions.","authors_text":"Armin Schikorra, Philipp Reiter, Simon Blatt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-24T11:48:01Z","title":"Hard analysis meets critical knots (Stationary points of the Moebius energy are smooth)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5426","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":"sha256:543fc3fff3fac1ab5f216b3db0f17bec89a994a2788b6289b9574e78990f5e8f","target":"record","created_at":"2026-05-18T01:24:37Z","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":"7036c41bea3148c39da95a9384606ac235458f6608e0377b659a4cc69f42b655","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-24T11:48:01Z","title_canon_sha256":"1d5cf2f3016f3efdfa86e7ab7dd769c14428c1e15ee6d2a2f125887c2df9a1f8"},"schema_version":"1.0","source":{"id":"1202.5426","kind":"arxiv","version":2}},"canonical_sha256":"3b16f62921aa1eec2b0ba217ae0a226f4bbf10942b03cf196494a6c27421a44e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b16f62921aa1eec2b0ba217ae0a226f4bbf10942b03cf196494a6c27421a44e","first_computed_at":"2026-05-18T01:24:37.176147Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:37.176147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ueBtBe0DRcvGdqF8oVkHzydXinp9S9qG2SScp+vSSy9yYNE+/L6JITi/iSXne7QDxAYML57cu/17Bdm/OyT4CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:37.176627Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.5426","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:543fc3fff3fac1ab5f216b3db0f17bec89a994a2788b6289b9574e78990f5e8f","sha256:8029ed4cd6b255e2fd96d97ac1c027741b8da4dfbb39ec151d8cc2541b4f09ab"],"state_sha256":"18fea739a4d2073753f370135449e6d95a0b4bec3a4626e4449c723976241c80"}