{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BJIBSH4IXV64ODNYBNC5QR4XKW","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":"f08ef96054abed3c3325cb6145cb84e509d4f2d1a30ed8a6f80aef005d73db99","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-26T14:38:24Z","title_canon_sha256":"fb534088cd81e3d1d0b8e0cc21ed984655bab44e62b220adafaccecd8f509c9b"},"schema_version":"1.0","source":{"id":"1308.5600","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5600","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5600v2","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5600","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"pith_short_12","alias_value":"BJIBSH4IXV64","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BJIBSH4IXV64ODNY","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BJIBSH4I","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:05941064a311f62c264e05684ca766949af104cab545d039e60bb4e5bb6118b6","target":"graph","created_at":"2026-05-18T01:28:06Z","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 noncompact surfaces evolving by mean curvature flow. Without any symmetry assumptions, we prove that any solution that is $C^3$-close at some time to a standard neck will develop a neckpinch singularity in finite time, will become asymptotically rotationally symmetric in a space-time neighborhood of its singular set, and will have a unique tangent flow.","authors_text":"Dan Knopf, Zhou Gang","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-26T14:38:24Z","title":"Universality in mean curvature flow neckpinches"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5600","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":"sha256:165851a62a65e2320ed896fabb36707df325f7067f506450472d0d27c9737e4d","target":"record","created_at":"2026-05-18T01:28:06Z","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":"f08ef96054abed3c3325cb6145cb84e509d4f2d1a30ed8a6f80aef005d73db99","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-26T14:38:24Z","title_canon_sha256":"fb534088cd81e3d1d0b8e0cc21ed984655bab44e62b220adafaccecd8f509c9b"},"schema_version":"1.0","source":{"id":"1308.5600","kind":"arxiv","version":2}},"canonical_sha256":"0a50191f88bd7dc70db80b45d8479755a782025ebf70392d1c49e735ce7acb5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a50191f88bd7dc70db80b45d8479755a782025ebf70392d1c49e735ce7acb5f","first_computed_at":"2026-05-18T01:28:06.173189Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:06.173189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xIWGQKqjJZDWfNQFJR2gbQp1cU4NR6ieF+uq7oPdtfg09xFstO6WreDSUbsaFRoi0kOC7pzNT8dgJRn9vy/JDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:06.173840Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.5600","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:165851a62a65e2320ed896fabb36707df325f7067f506450472d0d27c9737e4d","sha256:05941064a311f62c264e05684ca766949af104cab545d039e60bb4e5bb6118b6"],"state_sha256":"111c821e7ae4f2e76506edb0c397595cbcd8998e6850c63e7b9c02c8e729b8e3"}