{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:3UOXJQKCLGMJB25Y53OG6KMPB4","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":"9cf740fcc3bbc53f11d3ad61d49cc3849272178bffcd64f874bd952f07b0bd5a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-03-22T11:11:12Z","title_canon_sha256":"1279332d6ee3887c288b257a1a1ba34d18a3691a5c1c22407fbc0e0e547fe3e9"},"schema_version":"1.0","source":{"id":"2203.11616","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.11616","created_at":"2026-07-05T05:13:32Z"},{"alias_kind":"arxiv_version","alias_value":"2203.11616v2","created_at":"2026-07-05T05:13:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.11616","created_at":"2026-07-05T05:13:32Z"},{"alias_kind":"pith_short_12","alias_value":"3UOXJQKCLGMJ","created_at":"2026-07-05T05:13:32Z"},{"alias_kind":"pith_short_16","alias_value":"3UOXJQKCLGMJB25Y","created_at":"2026-07-05T05:13:32Z"},{"alias_kind":"pith_short_8","alias_value":"3UOXJQKC","created_at":"2026-07-05T05:13:32Z"}],"graph_snapshots":[{"event_id":"sha256:2026a0663b2bdd77c491d0adcd45f20dc776cba112d49330911850fdbf4154b9","target":"graph","created_at":"2026-07-05T05:13:32Z","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/2203.11616/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The main goal of this paper is to prove existence and non-existence results for deterministic Kardar-Parisi-Zhang type equations involving non-local \"gradient terms\". More precisely, let $\\Omega \\subset \\mathbb{R}^N$, $N \\geq 2$, be a bounded domain with boundary $\\partial \\Omega$ of class $C^2$. For $s \\in (0,1)$, we consider problems of the form \\[ \\tag{KPZ} \\left\\{ \\begin{aligned} (-\\Delta)^s u & = \\mu(x) |\\mathbb{D}(u)|^q + \\lambda f(x), \\quad && \\mbox{ in } \\Omega,\\\\ u & = 0, && \\mbox{ in } \\mathbb{R}^N \\setminus \\Omega, \\end{aligned} \\right. \\] where $q > 1$ and $\\lambda > 0$ are real pa","authors_text":"Abdelbadie Younes, Antonio J. Fern\\'andez, Boumediene Abdellaoui, Tommaso Leonori","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-03-22T11:11:12Z","title":"Deterministic KPZ-type equations with nonlocal \"gradient terms\""},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.11616","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":"sha256:65d872b1f3fb8d8cb9b13930fde8074a8e47e9f50a40fb18c1192414b645b2cb","target":"record","created_at":"2026-07-05T05:13:32Z","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":"9cf740fcc3bbc53f11d3ad61d49cc3849272178bffcd64f874bd952f07b0bd5a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-03-22T11:11:12Z","title_canon_sha256":"1279332d6ee3887c288b257a1a1ba34d18a3691a5c1c22407fbc0e0e547fe3e9"},"schema_version":"1.0","source":{"id":"2203.11616","kind":"arxiv","version":2}},"canonical_sha256":"dd1d74c142599890ebb8eedc6f298f0f0f0b1c4fc0d9fb19d98c760438becd7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd1d74c142599890ebb8eedc6f298f0f0f0b1c4fc0d9fb19d98c760438becd7d","first_computed_at":"2026-07-05T05:13:32.867795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:13:32.867795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gPjM2LurbumYIMSSkoVkFjdQXHVQe8h95lu28NoxNXp4UF0NPPxT5Z2+qaMnFbl6v3GeU7QXi4sE4EsoFucjAw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:13:32.868234Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.11616","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65d872b1f3fb8d8cb9b13930fde8074a8e47e9f50a40fb18c1192414b645b2cb","sha256:2026a0663b2bdd77c491d0adcd45f20dc776cba112d49330911850fdbf4154b9"],"state_sha256":"8557b30bd8ec179757afffa335ed9c12cf3dddba98fc98ab3ed7af0f9c73912e"}