{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:SGMWPY7Z6VGVAU7JINHI66FSUL","short_pith_number":"pith:SGMWPY7Z","canonical_record":{"source":{"id":"2608.08901","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-09T20:23:41Z","cross_cats_sorted":[],"title_canon_sha256":"cf64c8f7e1faa14bd850c79880600228fcb363489ea7aad50841e5d53aaedf03","abstract_canon_sha256":"bd20343ab66b0375820b8e4dcfa26b8d74554ebd6fe1d23364be25bda58a362e"},"schema_version":"1.0"},"canonical_sha256":"919967e3f9f54d5053e9434e8f78b2a2d9958a85aa3969143e7b82114bdcd350","source":{"kind":"arxiv","id":"2608.08901","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.08901","created_at":"2026-08-11T01:25:40Z"},{"alias_kind":"arxiv_version","alias_value":"2608.08901v1","created_at":"2026-08-11T01:25:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.08901","created_at":"2026-08-11T01:25:40Z"},{"alias_kind":"pith_short_12","alias_value":"SGMWPY7Z6VGV","created_at":"2026-08-11T01:25:40Z"},{"alias_kind":"pith_short_16","alias_value":"SGMWPY7Z6VGVAU7J","created_at":"2026-08-11T01:25:40Z"},{"alias_kind":"pith_short_8","alias_value":"SGMWPY7Z","created_at":"2026-08-11T01:25:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:SGMWPY7Z6VGVAU7JINHI66FSUL","target":"record","payload":{"canonical_record":{"source":{"id":"2608.08901","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-09T20:23:41Z","cross_cats_sorted":[],"title_canon_sha256":"cf64c8f7e1faa14bd850c79880600228fcb363489ea7aad50841e5d53aaedf03","abstract_canon_sha256":"bd20343ab66b0375820b8e4dcfa26b8d74554ebd6fe1d23364be25bda58a362e"},"schema_version":"1.0"},"canonical_sha256":"919967e3f9f54d5053e9434e8f78b2a2d9958a85aa3969143e7b82114bdcd350","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-11T01:25:40.494822Z","signature_b64":"EDV9uFFCuowsO1VDHz40q6Qzq8RV/DOBuwIdLgKMt/mztj2JcGy+mbQbwK2Ap1hkrU3dhDcaV2h+/FxWTjBiBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"919967e3f9f54d5053e9434e8f78b2a2d9958a85aa3969143e7b82114bdcd350","last_reissued_at":"2026-08-11T01:25:40.492488Z","signature_status":"signed_v1","first_computed_at":"2026-08-11T01:25:40.492488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.08901","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-11T01:25:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9c8pum+LZL5UlFSLrOeccs/Ed8VAAJyCHlV39o5/d9Rb+sW3MiqavRRL4xFgdTBgFK1wwiUPgTN2tXD8FgaOAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T17:26:39.666988Z"},"content_sha256":"3a9019a7e9723d33298a564d9bd17d843e84ba7da6efb732c832aa77401d6bd3","schema_version":"1.0","event_id":"sha256:3a9019a7e9723d33298a564d9bd17d843e84ba7da6efb732c832aa77401d6bd3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:SGMWPY7Z6VGVAU7JINHI66FSUL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Well-posedness for the mean curvature flow on the half-space and on bounded domains","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ke Chen, Quoc-Hung Nguyen, Ruilin Hu","submitted_at":"2026-08-09T20:23:41Z","abstract_excerpt":"We study graphical mean curvature flow in arbitrary codimension over the half-space and over smooth bounded domains, subject to homogeneous Dirichlet boundary conditions. At the scaling-critical Lipschitz regularity, we prove local well-posedness for initial graphs that can be approximated in $W^{1,\\infty}$ by smooth profiles compatible with the boundary condition. Within this class, if the initial Lipschitz seminorm is sufficiently small, the corresponding solution is global; on a bounded domain, it also converges exponentially to the flat graph. Positive-time regularization is quantified by "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.08901","kind":"arxiv","version":1},"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/2608.08901/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":"2026-08-11T01:25:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DTAKXOS0ffFAU2+t6dx7an8ZQCHFvJflvRKmiSv4GVnLOw1MKfinI5G1YUKWieVsBFaj7CDmlH+LQfk7tZnMAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T17:26:39.667686Z"},"content_sha256":"6ff62793d2adc317f95aa5cf5c57915f6ac909d81cd7befae3058320d54a9021","schema_version":"1.0","event_id":"sha256:6ff62793d2adc317f95aa5cf5c57915f6ac909d81cd7befae3058320d54a9021"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SGMWPY7Z6VGVAU7JINHI66FSUL/bundle.json","state_url":"https://pith.science/pith/SGMWPY7Z6VGVAU7JINHI66FSUL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SGMWPY7Z6VGVAU7JINHI66FSUL/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":"2026-08-14T17:26:39Z","links":{"resolver":"https://pith.science/pith/SGMWPY7Z6VGVAU7JINHI66FSUL","bundle":"https://pith.science/pith/SGMWPY7Z6VGVAU7JINHI66FSUL/bundle.json","state":"https://pith.science/pith/SGMWPY7Z6VGVAU7JINHI66FSUL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SGMWPY7Z6VGVAU7JINHI66FSUL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SGMWPY7Z6VGVAU7JINHI66FSUL","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":"bd20343ab66b0375820b8e4dcfa26b8d74554ebd6fe1d23364be25bda58a362e","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-09T20:23:41Z","title_canon_sha256":"cf64c8f7e1faa14bd850c79880600228fcb363489ea7aad50841e5d53aaedf03"},"schema_version":"1.0","source":{"id":"2608.08901","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.08901","created_at":"2026-08-11T01:25:40Z"},{"alias_kind":"arxiv_version","alias_value":"2608.08901v1","created_at":"2026-08-11T01:25:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.08901","created_at":"2026-08-11T01:25:40Z"},{"alias_kind":"pith_short_12","alias_value":"SGMWPY7Z6VGV","created_at":"2026-08-11T01:25:40Z"},{"alias_kind":"pith_short_16","alias_value":"SGMWPY7Z6VGVAU7J","created_at":"2026-08-11T01:25:40Z"},{"alias_kind":"pith_short_8","alias_value":"SGMWPY7Z","created_at":"2026-08-11T01:25:40Z"}],"graph_snapshots":[{"event_id":"sha256:6ff62793d2adc317f95aa5cf5c57915f6ac909d81cd7befae3058320d54a9021","target":"graph","created_at":"2026-08-11T01:25:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.08901/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study graphical mean curvature flow in arbitrary codimension over the half-space and over smooth bounded domains, subject to homogeneous Dirichlet boundary conditions. At the scaling-critical Lipschitz regularity, we prove local well-posedness for initial graphs that can be approximated in $W^{1,\\infty}$ by smooth profiles compatible with the boundary condition. Within this class, if the initial Lipschitz seminorm is sufficiently small, the corresponding solution is global; on a bounded domain, it also converges exponentially to the flat graph. Positive-time regularization is quantified by ","authors_text":"Ke Chen, Quoc-Hung Nguyen, Ruilin Hu","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-09T20:23:41Z","title":"Well-posedness for the mean curvature flow on the half-space and on bounded domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.08901","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":"sha256:3a9019a7e9723d33298a564d9bd17d843e84ba7da6efb732c832aa77401d6bd3","target":"record","created_at":"2026-08-11T01:25:40Z","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":"bd20343ab66b0375820b8e4dcfa26b8d74554ebd6fe1d23364be25bda58a362e","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-09T20:23:41Z","title_canon_sha256":"cf64c8f7e1faa14bd850c79880600228fcb363489ea7aad50841e5d53aaedf03"},"schema_version":"1.0","source":{"id":"2608.08901","kind":"arxiv","version":1}},"canonical_sha256":"919967e3f9f54d5053e9434e8f78b2a2d9958a85aa3969143e7b82114bdcd350","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"919967e3f9f54d5053e9434e8f78b2a2d9958a85aa3969143e7b82114bdcd350","first_computed_at":"2026-08-11T01:25:40.492488Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-11T01:25:40.492488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EDV9uFFCuowsO1VDHz40q6Qzq8RV/DOBuwIdLgKMt/mztj2JcGy+mbQbwK2Ap1hkrU3dhDcaV2h+/FxWTjBiBA==","signature_status":"signed_v1","signed_at":"2026-08-11T01:25:40.494822Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.08901","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a9019a7e9723d33298a564d9bd17d843e84ba7da6efb732c832aa77401d6bd3","sha256:6ff62793d2adc317f95aa5cf5c57915f6ac909d81cd7befae3058320d54a9021"],"state_sha256":"9f822ade25db72f57c3e22e5b09d08631f51cc790bfcfccca8fdc7eff36f3b04"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/EgeJ3gmoEOWcTysZqSPuuXXQ3cOSbm/m2FRx/cwufGJNHdN7p/uLHRR+qzkOx/GAYXNkoi1Fcsj5k7qiasuBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T17:26:39.672988Z","bundle_sha256":"b715c9a8b773b7137f70a7e0ddc689043ea228e04f3a6b000478f65365628985"}}