{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2FZMHOHCTJI3NAID6LNXYZ3WNF","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":"5874ff845ac46faf6e24be4fdbb6152e5d58f56dc6ba355df7bc0e47615f8ba5","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-16T17:19:56Z","title_canon_sha256":"d4a6b0cf31b566a28973c98835e0d7a09b86e6ef97d59efe88ab7f10d2890a27"},"schema_version":"1.0","source":{"id":"1710.05880","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.05880","created_at":"2026-05-17T23:59:23Z"},{"alias_kind":"arxiv_version","alias_value":"1710.05880v2","created_at":"2026-05-17T23:59:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05880","created_at":"2026-05-17T23:59:23Z"},{"alias_kind":"pith_short_12","alias_value":"2FZMHOHCTJI3","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2FZMHOHCTJI3NAID","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2FZMHOHC","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:171abdeb7a50bb04b174949260eeb7f00a7b8f0001fde1b78cfe859630f7a2de","target":"graph","created_at":"2026-05-17T23:59:23Z","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 an optimal extension and trace theorem for Sobolev spaces of nonlocal operators. The extension is given by a suitable Poisson integral and solves the corresponding nonlocal Dirichlet problem. We give a Douglas-type formula for the quadratic form of the Poisson extension.","authors_text":"Artur Rutkowski, Katarzyna Pietruska-Pa{\\l}uba, Krzysztof Bogdan, Tomasz Grzywny","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-16T17:19:56Z","title":"Extension and trace for nonlocal operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05880","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:a898bb8990afaa2824ed9f5dddf5acc60bcf187817f0948b849ad7e82fea727d","target":"record","created_at":"2026-05-17T23:59:23Z","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":"5874ff845ac46faf6e24be4fdbb6152e5d58f56dc6ba355df7bc0e47615f8ba5","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-16T17:19:56Z","title_canon_sha256":"d4a6b0cf31b566a28973c98835e0d7a09b86e6ef97d59efe88ab7f10d2890a27"},"schema_version":"1.0","source":{"id":"1710.05880","kind":"arxiv","version":2}},"canonical_sha256":"d172c3b8e29a51b68103f2db7c67766941aa025f9b802676292066e5b5fec6c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d172c3b8e29a51b68103f2db7c67766941aa025f9b802676292066e5b5fec6c9","first_computed_at":"2026-05-17T23:59:23.111088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:23.111088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jXwtcAhYmFiy199/cUvpMBcdwPDRiyaQk4MO2cXbhRkPbheumMQebsATd13Io1PRfafIKr3t5/Qs/QZtPX3GDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:23.111692Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.05880","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a898bb8990afaa2824ed9f5dddf5acc60bcf187817f0948b849ad7e82fea727d","sha256:171abdeb7a50bb04b174949260eeb7f00a7b8f0001fde1b78cfe859630f7a2de"],"state_sha256":"dd97ffabb6e6e5d8bf310f976715221f0a0a136973f48de033eeb17649839042"}