{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:QSARUC4JWVDI7JVYGZBGHPXQTC","short_pith_number":"pith:QSARUC4J","canonical_record":{"source":{"id":"1409.2102","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-07T10:01:23Z","cross_cats_sorted":[],"title_canon_sha256":"c8dc3df91b0132774002c7dd35ecdc0da734934855c8067e6df7b293c351c8a2","abstract_canon_sha256":"fbc7fa0dc84f7e8d7b937f74924ef18c8d8cf2db9c92c8b256c871397a320e60"},"schema_version":"1.0"},"canonical_sha256":"84811a0b89b5468fa6b8364263bef098b896c13b78263f4ed4d760419d4f68bf","source":{"kind":"arxiv","id":"1409.2102","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.2102","created_at":"2026-05-18T02:43:17Z"},{"alias_kind":"arxiv_version","alias_value":"1409.2102v1","created_at":"2026-05-18T02:43:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2102","created_at":"2026-05-18T02:43:17Z"},{"alias_kind":"pith_short_12","alias_value":"QSARUC4JWVDI","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QSARUC4JWVDI7JVY","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QSARUC4J","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:QSARUC4JWVDI7JVYGZBGHPXQTC","target":"record","payload":{"canonical_record":{"source":{"id":"1409.2102","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-07T10:01:23Z","cross_cats_sorted":[],"title_canon_sha256":"c8dc3df91b0132774002c7dd35ecdc0da734934855c8067e6df7b293c351c8a2","abstract_canon_sha256":"fbc7fa0dc84f7e8d7b937f74924ef18c8d8cf2db9c92c8b256c871397a320e60"},"schema_version":"1.0"},"canonical_sha256":"84811a0b89b5468fa6b8364263bef098b896c13b78263f4ed4d760419d4f68bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:17.860559Z","signature_b64":"QMKHpIw8Q5FzpQgqEQqacEsdzZGnvQrqiw+l/S7aFfRs3H2GurSPKQdb40yUksGY85wDaSgIv5Nfu0ipyplJBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84811a0b89b5468fa6b8364263bef098b896c13b78263f4ed4d760419d4f68bf","last_reissued_at":"2026-05-18T02:43:17.859933Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:17.859933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.2102","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":"2026-05-18T02:43:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JVXgU4k1hXZ0Y5H7EZonRxd962Nee52OGfMz6q/IsFq6csIu37tesKr3KmZB+hUFQlku2NAZuk89PAPA4aMzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T16:43:02.388606Z"},"content_sha256":"5e8436dd43dafb91a9fe12b11b2e9dd5e9e73fba2e570302772b19b7efdef4a8","schema_version":"1.0","event_id":"sha256:5e8436dd43dafb91a9fe12b11b2e9dd5e9e73fba2e570302772b19b7efdef4a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:QSARUC4JWVDI7JVYGZBGHPXQTC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A regularizing property of the $2D$-eikonal equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Camillo De Lellis, Radu Ignat","submitted_at":"2014-09-07T10:01:23Z","abstract_excerpt":"We prove that any $2$-dimensional solution $\\psi\\in W_{loc}^{1+\\frac 1 3, 3}$ of the eikonal equation has locally Lipschitz gradient $\\nabla \\psi$ except at a locally finite number of vortices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2102","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":""},"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":"2026-05-18T02:43:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kq0bqpvzrPzzPaaXo1xSKJ0eMqpDeG5VDi5kW3MwBdNw74Z94YMcogs5mOTAQXAPDg/L4/LXlgxapN/uCBK0Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T16:43:02.388938Z"},"content_sha256":"c51606a9284a61898e14b23e7c5aaf2ab1eddd16a7556a8c072ce248d852f1e9","schema_version":"1.0","event_id":"sha256:c51606a9284a61898e14b23e7c5aaf2ab1eddd16a7556a8c072ce248d852f1e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QSARUC4JWVDI7JVYGZBGHPXQTC/bundle.json","state_url":"https://pith.science/pith/QSARUC4JWVDI7JVYGZBGHPXQTC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QSARUC4JWVDI7JVYGZBGHPXQTC/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":"2026-06-09T16:43:02Z","links":{"resolver":"https://pith.science/pith/QSARUC4JWVDI7JVYGZBGHPXQTC","bundle":"https://pith.science/pith/QSARUC4JWVDI7JVYGZBGHPXQTC/bundle.json","state":"https://pith.science/pith/QSARUC4JWVDI7JVYGZBGHPXQTC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QSARUC4JWVDI7JVYGZBGHPXQTC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QSARUC4JWVDI7JVYGZBGHPXQTC","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":"fbc7fa0dc84f7e8d7b937f74924ef18c8d8cf2db9c92c8b256c871397a320e60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-07T10:01:23Z","title_canon_sha256":"c8dc3df91b0132774002c7dd35ecdc0da734934855c8067e6df7b293c351c8a2"},"schema_version":"1.0","source":{"id":"1409.2102","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.2102","created_at":"2026-05-18T02:43:17Z"},{"alias_kind":"arxiv_version","alias_value":"1409.2102v1","created_at":"2026-05-18T02:43:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2102","created_at":"2026-05-18T02:43:17Z"},{"alias_kind":"pith_short_12","alias_value":"QSARUC4JWVDI","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QSARUC4JWVDI7JVY","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QSARUC4J","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:c51606a9284a61898e14b23e7c5aaf2ab1eddd16a7556a8c072ce248d852f1e9","target":"graph","created_at":"2026-05-18T02:43:17Z","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 prove that any $2$-dimensional solution $\\psi\\in W_{loc}^{1+\\frac 1 3, 3}$ of the eikonal equation has locally Lipschitz gradient $\\nabla \\psi$ except at a locally finite number of vortices.","authors_text":"Camillo De Lellis, Radu Ignat","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-07T10:01:23Z","title":"A regularizing property of the $2D$-eikonal equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2102","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":"sha256:5e8436dd43dafb91a9fe12b11b2e9dd5e9e73fba2e570302772b19b7efdef4a8","target":"record","created_at":"2026-05-18T02:43:17Z","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":"fbc7fa0dc84f7e8d7b937f74924ef18c8d8cf2db9c92c8b256c871397a320e60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-07T10:01:23Z","title_canon_sha256":"c8dc3df91b0132774002c7dd35ecdc0da734934855c8067e6df7b293c351c8a2"},"schema_version":"1.0","source":{"id":"1409.2102","kind":"arxiv","version":1}},"canonical_sha256":"84811a0b89b5468fa6b8364263bef098b896c13b78263f4ed4d760419d4f68bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84811a0b89b5468fa6b8364263bef098b896c13b78263f4ed4d760419d4f68bf","first_computed_at":"2026-05-18T02:43:17.859933Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:17.859933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QMKHpIw8Q5FzpQgqEQqacEsdzZGnvQrqiw+l/S7aFfRs3H2GurSPKQdb40yUksGY85wDaSgIv5Nfu0ipyplJBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:17.860559Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.2102","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e8436dd43dafb91a9fe12b11b2e9dd5e9e73fba2e570302772b19b7efdef4a8","sha256:c51606a9284a61898e14b23e7c5aaf2ab1eddd16a7556a8c072ce248d852f1e9"],"state_sha256":"3186674dc3622c4ea184e362910bda45279cf7be3466141f3708b8e14695fd3c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mnlei3ZljY2MF1QpklAdORBliZ4IXFhONbQDtOBqgG41i/a8448qouiZxdnRf3rxr7INPscuEzkWGbhFer6pDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T16:43:02.390736Z","bundle_sha256":"a0dd1678e4c151e0b8c556a85f297942ab282b0a6d3429193f092eb9226b97df"}}