{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Z7KRLUZOHTW62JDPVBB4Y73VHM","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":"473dce1f09325ac163f397e3605eaf3a47692b5259571c814ad4d6cc80e297ad","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-20T09:42:06Z","title_canon_sha256":"157b68e3aba8e88cdeb40a4799c828ce94378e4c669937c7c314e8bf923e267c"},"schema_version":"1.0","source":{"id":"1204.4571","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.4571","created_at":"2026-05-18T01:13:10Z"},{"alias_kind":"arxiv_version","alias_value":"1204.4571v1","created_at":"2026-05-18T01:13:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4571","created_at":"2026-05-18T01:13:10Z"},{"alias_kind":"pith_short_12","alias_value":"Z7KRLUZOHTW6","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"Z7KRLUZOHTW62JDP","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"Z7KRLUZO","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:e870c980887218fae8ac956790d5f9ecd659e9e196096d7f363a896ecfd11f9f","target":"graph","created_at":"2026-05-18T01:13:10Z","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 give a proof that Brakke's mean curvature flow under the unit density assumption is smooth almost everywhere in space-time. More generally, if the velocity is equal in a weak sense to its mean curvature plus some given \\alpha-H\\\"{o}lder continuous vector field, then we show C^{2,\\alpha} regularity almost everywhere.","authors_text":"Yoshihiro Tonegawa","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-20T09:42:06Z","title":"A second derivative H\\\"{o}lder estimate for weak mean curvature flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4571","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":"sha256:8adba6447474c7b9cdffba5cb96492b880407df2cff4e3f11cb530df57eda6ce","target":"record","created_at":"2026-05-18T01:13:10Z","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":"473dce1f09325ac163f397e3605eaf3a47692b5259571c814ad4d6cc80e297ad","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-20T09:42:06Z","title_canon_sha256":"157b68e3aba8e88cdeb40a4799c828ce94378e4c669937c7c314e8bf923e267c"},"schema_version":"1.0","source":{"id":"1204.4571","kind":"arxiv","version":1}},"canonical_sha256":"cfd515d32e3ceded246fa843cc7f753b390dee779c956a55b3bf35b213a9aa93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfd515d32e3ceded246fa843cc7f753b390dee779c956a55b3bf35b213a9aa93","first_computed_at":"2026-05-18T01:13:10.082951Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:10.082951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TwhoTGSTkIMiclNzQscSVkS2o4tkf1baI1Qll1dYczCfPMguvNhKFc4gEPCpnUY8/nR8u08UVwawu18w7+h2Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:10.083344Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.4571","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8adba6447474c7b9cdffba5cb96492b880407df2cff4e3f11cb530df57eda6ce","sha256:e870c980887218fae8ac956790d5f9ecd659e9e196096d7f363a896ecfd11f9f"],"state_sha256":"8604ece6557b8921e266d2bd69fc5f99abb91b0393e9420f1d0a9d275ccafa0b"}