{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:FMSRJQXGHNPHSP33TDYBEI6IPM","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":"2a1810caa77a1c0224e73f47634a13fcd4a0bd02b9e619d77532b5f08ef40a98","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-07T23:25:19Z","title_canon_sha256":"3f38ca49a60f4f9c447ca2d152729acfd0f40c3f94ec95427b04f5afa65b004b"},"schema_version":"1.0","source":{"id":"1908.02871","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.02871","created_at":"2026-07-04T23:52:24Z"},{"alias_kind":"arxiv_version","alias_value":"1908.02871v1","created_at":"2026-07-04T23:52:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.02871","created_at":"2026-07-04T23:52:24Z"},{"alias_kind":"pith_short_12","alias_value":"FMSRJQXGHNPH","created_at":"2026-07-04T23:52:24Z"},{"alias_kind":"pith_short_16","alias_value":"FMSRJQXGHNPHSP33","created_at":"2026-07-04T23:52:24Z"},{"alias_kind":"pith_short_8","alias_value":"FMSRJQXG","created_at":"2026-07-04T23:52:24Z"}],"graph_snapshots":[{"event_id":"sha256:4831cbf3004fb94d6680e63d52379e8a837f27d16efa6252d8b7c9c551d2c9a2","target":"graph","created_at":"2026-07-04T23:52:24Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.02871/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study mean curvature flow of smooth, axially symmetric surfaces in $\\mathbb{R}^3$ with Neumann boundary data. We show that all singularities at the first singular time must be of type I.","authors_text":"John Head, Sevvandi Kandanaarachchi","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-07T23:25:19Z","title":"Singularity formation in axially symmetric mean curvature flow with Neumann boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02871","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:ae9ca80a9e4fc11117dd150fe2c3d84fd50fa4eba62a13ca588276a1c213f7f4","target":"record","created_at":"2026-07-04T23:52:24Z","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":"2a1810caa77a1c0224e73f47634a13fcd4a0bd02b9e619d77532b5f08ef40a98","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-07T23:25:19Z","title_canon_sha256":"3f38ca49a60f4f9c447ca2d152729acfd0f40c3f94ec95427b04f5afa65b004b"},"schema_version":"1.0","source":{"id":"1908.02871","kind":"arxiv","version":1}},"canonical_sha256":"2b2514c2e63b5e793f7b98f01223c87b0300b550c9150da1ac3d709e8806c8c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b2514c2e63b5e793f7b98f01223c87b0300b550c9150da1ac3d709e8806c8c7","first_computed_at":"2026-07-04T23:52:24.277204Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:52:24.277204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xi0lJ7IS++3/wJuLdKp+2BYPiC0bO5To/SfXHEiYaBAvz7c6MjaBDM8wW8Qmls2a72NePEbTs5OBEysPoBpjBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T23:52:24.277547Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.02871","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae9ca80a9e4fc11117dd150fe2c3d84fd50fa4eba62a13ca588276a1c213f7f4","sha256:4831cbf3004fb94d6680e63d52379e8a837f27d16efa6252d8b7c9c551d2c9a2"],"state_sha256":"cdfc6ef85d2e5bf4da7c08628dd80643bbf0e440a858d8c443a217d310bafbf9"}