{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:JQPJZ2Z4T7ZAAGWL4EQJMF75WW","short_pith_number":"pith:JQPJZ2Z4","canonical_record":{"source":{"id":"2505.03609","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-05-06T15:08:54Z","cross_cats_sorted":[],"title_canon_sha256":"ac65e85be5e97e1bb48a0db2d2b348fff173bdcc9f3ad8f3a5cdb7af0c6ae359","abstract_canon_sha256":"6674e67e443cdb245714794e4a9e27d4a06816431147a5bca309dce92b79b62f"},"schema_version":"1.0"},"canonical_sha256":"4c1e9ceb3c9ff2001acbe1209617fdb59178d3803e2db610abff958d8ae470ae","source":{"kind":"arxiv","id":"2505.03609","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.03609","created_at":"2026-07-05T11:49:09Z"},{"alias_kind":"arxiv_version","alias_value":"2505.03609v2","created_at":"2026-07-05T11:49:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.03609","created_at":"2026-07-05T11:49:09Z"},{"alias_kind":"pith_short_12","alias_value":"JQPJZ2Z4T7ZA","created_at":"2026-07-05T11:49:09Z"},{"alias_kind":"pith_short_16","alias_value":"JQPJZ2Z4T7ZAAGWL","created_at":"2026-07-05T11:49:09Z"},{"alias_kind":"pith_short_8","alias_value":"JQPJZ2Z4","created_at":"2026-07-05T11:49:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:JQPJZ2Z4T7ZAAGWL4EQJMF75WW","target":"record","payload":{"canonical_record":{"source":{"id":"2505.03609","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-05-06T15:08:54Z","cross_cats_sorted":[],"title_canon_sha256":"ac65e85be5e97e1bb48a0db2d2b348fff173bdcc9f3ad8f3a5cdb7af0c6ae359","abstract_canon_sha256":"6674e67e443cdb245714794e4a9e27d4a06816431147a5bca309dce92b79b62f"},"schema_version":"1.0"},"canonical_sha256":"4c1e9ceb3c9ff2001acbe1209617fdb59178d3803e2db610abff958d8ae470ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:49:09.853465Z","signature_b64":"dgwrtrg/yOP5INAuIq2YB5gsfSZ3BTfIqNZcb57omppd5k5jbYpMpQJBCLDKMMJ1zlhavbyKVRiBmUq1Z93zBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c1e9ceb3c9ff2001acbe1209617fdb59178d3803e2db610abff958d8ae470ae","last_reissued_at":"2026-07-05T11:49:09.852945Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:49:09.852945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.03609","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:49:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y/5zW4VoyExf6U0Oxxp3kvaF7wpZ0Yw/dup8TQ/BbZPb16HqNhi1GSrCarfrguvbViiFuBEFaGHbcOpDYwjNAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T10:48:13.075104Z"},"content_sha256":"e51b9ae6f2e9d9940d043dc0ba3b18658f4e7303b5feba80959e7131f53e8d41","schema_version":"1.0","event_id":"sha256:e51b9ae6f2e9d9940d043dc0ba3b18658f4e7303b5feba80959e7131f53e8d41"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:JQPJZ2Z4T7ZAAGWL4EQJMF75WW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global well-posedness in the critical Besov space of the skew mean curvature flow in $\\mathbb{R}^d: d\\ge 5$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jie Shao, Ning-An Lai, Yi Zhou","submitted_at":"2025-05-06T15:08:54Z","abstract_excerpt":"In this paper, we are devoted to studying the global regularity for the skew mean curvature flow with small initial data in $\\mathbb{R}^d\\, (d\\ge 5)$. By using a new div-curl lemma which was first introduced by the third author to establish a bilinear estimate, and also the interaction Morawetz estimate, the global well-posedness for the skew mean curvature flow in the critical Besov space is established, and hence the corresponding result obtained by Huang, Li and Tataru (Int. Math. Res. Not. 2024, no. 5, 3748-3798) in $\\mathbb{R}^d\\, (d\\ge 5)$ is substantially improved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.03609","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.03609/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:49:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Faav8V8J8/+Sj/qXOM8oSNpZF+wQbudj7aJrKhyUFACecrD8Ky4dKckoOEZhzPOHCx9nLNLzK6OHhE2mnN29AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T10:48:13.075738Z"},"content_sha256":"3e0fd1779f8d01d9c745c6e300f5a84d3f4c50753719d069a2e43842335df983","schema_version":"1.0","event_id":"sha256:3e0fd1779f8d01d9c745c6e300f5a84d3f4c50753719d069a2e43842335df983"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JQPJZ2Z4T7ZAAGWL4EQJMF75WW/bundle.json","state_url":"https://pith.science/pith/JQPJZ2Z4T7ZAAGWL4EQJMF75WW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JQPJZ2Z4T7ZAAGWL4EQJMF75WW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-11T10:48:13Z","links":{"resolver":"https://pith.science/pith/JQPJZ2Z4T7ZAAGWL4EQJMF75WW","bundle":"https://pith.science/pith/JQPJZ2Z4T7ZAAGWL4EQJMF75WW/bundle.json","state":"https://pith.science/pith/JQPJZ2Z4T7ZAAGWL4EQJMF75WW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JQPJZ2Z4T7ZAAGWL4EQJMF75WW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:JQPJZ2Z4T7ZAAGWL4EQJMF75WW","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":"6674e67e443cdb245714794e4a9e27d4a06816431147a5bca309dce92b79b62f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-05-06T15:08:54Z","title_canon_sha256":"ac65e85be5e97e1bb48a0db2d2b348fff173bdcc9f3ad8f3a5cdb7af0c6ae359"},"schema_version":"1.0","source":{"id":"2505.03609","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.03609","created_at":"2026-07-05T11:49:09Z"},{"alias_kind":"arxiv_version","alias_value":"2505.03609v2","created_at":"2026-07-05T11:49:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.03609","created_at":"2026-07-05T11:49:09Z"},{"alias_kind":"pith_short_12","alias_value":"JQPJZ2Z4T7ZA","created_at":"2026-07-05T11:49:09Z"},{"alias_kind":"pith_short_16","alias_value":"JQPJZ2Z4T7ZAAGWL","created_at":"2026-07-05T11:49:09Z"},{"alias_kind":"pith_short_8","alias_value":"JQPJZ2Z4","created_at":"2026-07-05T11:49:09Z"}],"graph_snapshots":[{"event_id":"sha256:3e0fd1779f8d01d9c745c6e300f5a84d3f4c50753719d069a2e43842335df983","target":"graph","created_at":"2026-07-05T11:49:09Z","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/2505.03609/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we are devoted to studying the global regularity for the skew mean curvature flow with small initial data in $\\mathbb{R}^d\\, (d\\ge 5)$. By using a new div-curl lemma which was first introduced by the third author to establish a bilinear estimate, and also the interaction Morawetz estimate, the global well-posedness for the skew mean curvature flow in the critical Besov space is established, and hence the corresponding result obtained by Huang, Li and Tataru (Int. Math. Res. Not. 2024, no. 5, 3748-3798) in $\\mathbb{R}^d\\, (d\\ge 5)$ is substantially improved.","authors_text":"Jie Shao, Ning-An Lai, Yi Zhou","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-05-06T15:08:54Z","title":"Global well-posedness in the critical Besov space of the skew mean curvature flow in $\\mathbb{R}^d: d\\ge 5$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.03609","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:e51b9ae6f2e9d9940d043dc0ba3b18658f4e7303b5feba80959e7131f53e8d41","target":"record","created_at":"2026-07-05T11:49:09Z","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":"6674e67e443cdb245714794e4a9e27d4a06816431147a5bca309dce92b79b62f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-05-06T15:08:54Z","title_canon_sha256":"ac65e85be5e97e1bb48a0db2d2b348fff173bdcc9f3ad8f3a5cdb7af0c6ae359"},"schema_version":"1.0","source":{"id":"2505.03609","kind":"arxiv","version":2}},"canonical_sha256":"4c1e9ceb3c9ff2001acbe1209617fdb59178d3803e2db610abff958d8ae470ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c1e9ceb3c9ff2001acbe1209617fdb59178d3803e2db610abff958d8ae470ae","first_computed_at":"2026-07-05T11:49:09.852945Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:49:09.852945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dgwrtrg/yOP5INAuIq2YB5gsfSZ3BTfIqNZcb57omppd5k5jbYpMpQJBCLDKMMJ1zlhavbyKVRiBmUq1Z93zBA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:49:09.853465Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.03609","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e51b9ae6f2e9d9940d043dc0ba3b18658f4e7303b5feba80959e7131f53e8d41","sha256:3e0fd1779f8d01d9c745c6e300f5a84d3f4c50753719d069a2e43842335df983"],"state_sha256":"0318924f95192afa2fceac340bee7a41b155b21d5992a7d3adcb50f4d5bd042f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yBJJmf5MkVxrOkTRO502Lt/zbIoyBMidKSM6kFgBTonTEDqTEhVPMen297GxosWofHk4rAZJeyV9SzvZ5kSIAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T10:48:13.079106Z","bundle_sha256":"2142bbf6d098e9b6a8cd390e47f18cbba609fdaf9a718728075bd2056c026e63"}}