{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2NBJVCON6UIN5SJOV5WA7JKUTI","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":"04e0fb9c4a20bf0d51221ffe9342068a3ba791f2ebe183de44b8ed07c937c95c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-10T14:36:52Z","title_canon_sha256":"95d82c1c52cdd65d08e7108f885a1cf5a0f40963fe0d439776ee2ca57fe9bd1e"},"schema_version":"1.0","source":{"id":"1807.03676","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.03676","created_at":"2026-05-18T00:11:03Z"},{"alias_kind":"arxiv_version","alias_value":"1807.03676v1","created_at":"2026-05-18T00:11:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.03676","created_at":"2026-05-18T00:11:03Z"},{"alias_kind":"pith_short_12","alias_value":"2NBJVCON6UIN","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2NBJVCON6UIN5SJO","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2NBJVCON","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:b186e3c31e518882f85386230735d786af3254100a61b047bd414a311f1a3d1f","target":"graph","created_at":"2026-05-18T00:11:03Z","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 study translation-invariant integrodifferential operators that generate L\\'{e}vy processes. First, we investigate different notions of what a solution to a nonlocal Dirichlet problem is and we provide the classical representation formula for distributional solutions. Second, we study the question under which assumptions distributional solutions are twice differentiable in the classical sense. Sufficient conditions and counterexamples are provided.","authors_text":"{\\L}ukasz Le\\.zaj, Moritz Kassmann, Tomasz Grzywny","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-10T14:36:52Z","title":"Remarks on the nonlocal Dirichlet problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03676","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:d1555abb6f0f1122aef130edb0fc74c8c59bfa1e56816b05e1bf28178089468d","target":"record","created_at":"2026-05-18T00:11:03Z","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":"04e0fb9c4a20bf0d51221ffe9342068a3ba791f2ebe183de44b8ed07c937c95c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-10T14:36:52Z","title_canon_sha256":"95d82c1c52cdd65d08e7108f885a1cf5a0f40963fe0d439776ee2ca57fe9bd1e"},"schema_version":"1.0","source":{"id":"1807.03676","kind":"arxiv","version":1}},"canonical_sha256":"d3429a89cdf510dec92eaf6c0fa5549a14c2f23b549453bf45032a4d8486691e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3429a89cdf510dec92eaf6c0fa5549a14c2f23b549453bf45032a4d8486691e","first_computed_at":"2026-05-18T00:11:03.558713Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:03.558713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1yPCnD5m/XeDIMAIG3qqiAy4ZazqyEw5+8Tykr/oiLAj6+qCMvhxkvZQrAMu6FmlAg5anrd37QKCSjV+3zKnCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:03.559403Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.03676","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1555abb6f0f1122aef130edb0fc74c8c59bfa1e56816b05e1bf28178089468d","sha256:b186e3c31e518882f85386230735d786af3254100a61b047bd414a311f1a3d1f"],"state_sha256":"f1b342b073ada9267a585d9a4293113d2c2b67e36d16773a1866b4ed6cfa6c70"}