{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:2NBJVCON6UIN5SJOV5WA7JKUTI","short_pith_number":"pith:2NBJVCON","schema_version":"1.0","canonical_sha256":"d3429a89cdf510dec92eaf6c0fa5549a14c2f23b549453bf45032a4d8486691e","source":{"kind":"arxiv","id":"1807.03676","version":1},"attestation_state":"computed","paper":{"title":"Remarks on the nonlocal Dirichlet problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"{\\L}ukasz Le\\.zaj, Moritz Kassmann, Tomasz Grzywny","submitted_at":"2018-07-10T14:36:52Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1807.03676","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-10T14:36:52Z","cross_cats_sorted":[],"title_canon_sha256":"95d82c1c52cdd65d08e7108f885a1cf5a0f40963fe0d439776ee2ca57fe9bd1e","abstract_canon_sha256":"04e0fb9c4a20bf0d51221ffe9342068a3ba791f2ebe183de44b8ed07c937c95c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:03.559403Z","signature_b64":"1yPCnD5m/XeDIMAIG3qqiAy4ZazqyEw5+8Tykr/oiLAj6+qCMvhxkvZQrAMu6FmlAg5anrd37QKCSjV+3zKnCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3429a89cdf510dec92eaf6c0fa5549a14c2f23b549453bf45032a4d8486691e","last_reissued_at":"2026-05-18T00:11:03.558713Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:03.558713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Remarks on the nonlocal Dirichlet problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"{\\L}ukasz Le\\.zaj, Moritz Kassmann, Tomasz Grzywny","submitted_at":"2018-07-10T14:36:52Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03676","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1807.03676","created_at":"2026-05-18T00:11:03.558816+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.03676v1","created_at":"2026-05-18T00:11:03.558816+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.03676","created_at":"2026-05-18T00:11:03.558816+00:00"},{"alias_kind":"pith_short_12","alias_value":"2NBJVCON6UIN","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"2NBJVCON6UIN5SJO","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"2NBJVCON","created_at":"2026-05-18T12:32:02.567920+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2NBJVCON6UIN5SJOV5WA7JKUTI","json":"https://pith.science/pith/2NBJVCON6UIN5SJOV5WA7JKUTI.json","graph_json":"https://pith.science/api/pith-number/2NBJVCON6UIN5SJOV5WA7JKUTI/graph.json","events_json":"https://pith.science/api/pith-number/2NBJVCON6UIN5SJOV5WA7JKUTI/events.json","paper":"https://pith.science/paper/2NBJVCON"},"agent_actions":{"view_html":"https://pith.science/pith/2NBJVCON6UIN5SJOV5WA7JKUTI","download_json":"https://pith.science/pith/2NBJVCON6UIN5SJOV5WA7JKUTI.json","view_paper":"https://pith.science/paper/2NBJVCON","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.03676&json=true","fetch_graph":"https://pith.science/api/pith-number/2NBJVCON6UIN5SJOV5WA7JKUTI/graph.json","fetch_events":"https://pith.science/api/pith-number/2NBJVCON6UIN5SJOV5WA7JKUTI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2NBJVCON6UIN5SJOV5WA7JKUTI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2NBJVCON6UIN5SJOV5WA7JKUTI/action/storage_attestation","attest_author":"https://pith.science/pith/2NBJVCON6UIN5SJOV5WA7JKUTI/action/author_attestation","sign_citation":"https://pith.science/pith/2NBJVCON6UIN5SJOV5WA7JKUTI/action/citation_signature","submit_replication":"https://pith.science/pith/2NBJVCON6UIN5SJOV5WA7JKUTI/action/replication_record"}},"created_at":"2026-05-18T00:11:03.558816+00:00","updated_at":"2026-05-18T00:11:03.558816+00:00"}