{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KYKYD5F2X47AEAKJ2GSE77GMSM","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":"08ab466bbee48b6356fd0f09324a3b4aad280a687c8c858edd2e7a1463abc5c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-09-24T04:09:18Z","title_canon_sha256":"5f3d835e4ac56043e25750f86f97236b863905429c0d75f93002ea4f19190975"},"schema_version":"1.0","source":{"id":"1209.5146","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.5146","created_at":"2026-05-18T03:44:59Z"},{"alias_kind":"arxiv_version","alias_value":"1209.5146v1","created_at":"2026-05-18T03:44:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.5146","created_at":"2026-05-18T03:44:59Z"},{"alias_kind":"pith_short_12","alias_value":"KYKYD5F2X47A","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KYKYD5F2X47AEAKJ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KYKYD5F2","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:444d3cc750fbcfcdbbb4a9bc6961f19b1c7255d5ede21a3d67fe3404f5d1c581","target":"graph","created_at":"2026-05-18T03:44:59Z","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":"In this paper, we use the distance comparison principle, first been developed by G. Huisken, to study the spatial curve shortening flow. We have got the result that if the initial curve is the helix, then the local minimum of the ratio of the extrinsic and intrinsic distance is non-decreasing. And we have proved a Grayson type theorem for a variety of spatial curves.","authors_text":"Siming He","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-09-24T04:09:18Z","title":"Distance comparison principle and Grayson type theorem in the three dimensional curve shortening flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5146","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":"sha256:05eeb79d662790deeafd86f9b304ec3ae97a738460eeaf64715166931b7ab97e","target":"record","created_at":"2026-05-18T03:44:59Z","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":"08ab466bbee48b6356fd0f09324a3b4aad280a687c8c858edd2e7a1463abc5c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-09-24T04:09:18Z","title_canon_sha256":"5f3d835e4ac56043e25750f86f97236b863905429c0d75f93002ea4f19190975"},"schema_version":"1.0","source":{"id":"1209.5146","kind":"arxiv","version":1}},"canonical_sha256":"561581f4babf3e020149d1a44ffccc933a60ddfd87bfa4ee73922d4afe437165","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"561581f4babf3e020149d1a44ffccc933a60ddfd87bfa4ee73922d4afe437165","first_computed_at":"2026-05-18T03:44:59.075627Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:59.075627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9yMoVZhcETUCVusG/wLU8QddEC1ET/K4B0QW+UcWQeNObe4MNgPrd1Txq5s2E5Pu6PSISQreK6MXIP7XnuZTBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:59.076644Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.5146","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05eeb79d662790deeafd86f9b304ec3ae97a738460eeaf64715166931b7ab97e","sha256:444d3cc750fbcfcdbbb4a9bc6961f19b1c7255d5ede21a3d67fe3404f5d1c581"],"state_sha256":"ffba8c994efaa5e6f0cb41b450bb0ff9bc0877eee907b5858b4a1a8731db1a58"}