{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:Q4CU2QTIIL3JX5CLFC3AWYRM3U","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":"493cc0722acfdbd01b43c47038ac898a33c63e754c3956d26c345b0662fc21b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-08T02:25:35Z","title_canon_sha256":"f6e0e9426363014f625563f917f3e07790f6184e0cec8cb498add264720486d1"},"schema_version":"1.0","source":{"id":"1602.02451","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.02451","created_at":"2026-05-18T00:50:40Z"},{"alias_kind":"arxiv_version","alias_value":"1602.02451v2","created_at":"2026-05-18T00:50:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02451","created_at":"2026-05-18T00:50:40Z"},{"alias_kind":"pith_short_12","alias_value":"Q4CU2QTIIL3J","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q4CU2QTIIL3JX5CL","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q4CU2QTI","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:834027bb34b84d286d9ce52d030da505f68d0a1545657a4733bfba974c86afa3","target":"graph","created_at":"2026-05-18T00:50:40Z","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 introduce a nonlocal evolution equation inspired by the C\\'ordoba-C\\'ordoba-Fontelos nonlocal transport equation. The C\\'ordoba-C\\'ordoba-Fontelos equation can be regarded as a model for the 2D surface quasigeostrophic equation or the Birkhoff-Rott equation. We prove blowup in finite time, and more importantly, investigate conditions under which the solution forms a cusp in finite time.","authors_text":"Maria Radosz, Vu Hoang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-08T02:25:35Z","title":"Cusp formation for a nonlocal evolution equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02451","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":"sha256:202df12fd946f55ce3a5465ccc5f201e06c7d8373348f316af0361b2358b349e","target":"record","created_at":"2026-05-18T00:50:40Z","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":"493cc0722acfdbd01b43c47038ac898a33c63e754c3956d26c345b0662fc21b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-08T02:25:35Z","title_canon_sha256":"f6e0e9426363014f625563f917f3e07790f6184e0cec8cb498add264720486d1"},"schema_version":"1.0","source":{"id":"1602.02451","kind":"arxiv","version":2}},"canonical_sha256":"87054d426842f69bf44b28b60b622cdd2fd28920e5e112e429468176fb4e6fc9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87054d426842f69bf44b28b60b622cdd2fd28920e5e112e429468176fb4e6fc9","first_computed_at":"2026-05-18T00:50:40.418297Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:40.418297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VyunwV3/hjFRyQXtHgv8YUBt44NmWEopYc/rCg5t7IoEM95fBBiD192lhVzQ30ArocrrDkuiuLQpZvLJw6+LCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:40.419011Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.02451","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:202df12fd946f55ce3a5465ccc5f201e06c7d8373348f316af0361b2358b349e","sha256:834027bb34b84d286d9ce52d030da505f68d0a1545657a4733bfba974c86afa3"],"state_sha256":"596c4424884e35373cdcc8af495f6db1f27a2f68d5ed214d63701d2e8859486f"}