{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:B6XC3CS23PMJ4VGF5DOPQWPBRF","short_pith_number":"pith:B6XC3CS2","canonical_record":{"source":{"id":"1404.5162","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-21T10:23:43Z","cross_cats_sorted":[],"title_canon_sha256":"fc0d115319b9828eb669fb019c8cd91be0e17ce0fa12f63d168929ac7ed42dd1","abstract_canon_sha256":"03c0cce200d599b5dd8513dbe750d16899a882cdaf1be07f62b0bda5688edff3"},"schema_version":"1.0"},"canonical_sha256":"0fae2d8a5adbd89e54c5e8dcf859e189646f5119c7371edbd7a5f9f3fe3e5964","source":{"kind":"arxiv","id":"1404.5162","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5162","created_at":"2026-05-18T02:53:42Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5162v1","created_at":"2026-05-18T02:53:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5162","created_at":"2026-05-18T02:53:42Z"},{"alias_kind":"pith_short_12","alias_value":"B6XC3CS23PMJ","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"B6XC3CS23PMJ4VGF","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"B6XC3CS2","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:B6XC3CS23PMJ4VGF5DOPQWPBRF","target":"record","payload":{"canonical_record":{"source":{"id":"1404.5162","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-21T10:23:43Z","cross_cats_sorted":[],"title_canon_sha256":"fc0d115319b9828eb669fb019c8cd91be0e17ce0fa12f63d168929ac7ed42dd1","abstract_canon_sha256":"03c0cce200d599b5dd8513dbe750d16899a882cdaf1be07f62b0bda5688edff3"},"schema_version":"1.0"},"canonical_sha256":"0fae2d8a5adbd89e54c5e8dcf859e189646f5119c7371edbd7a5f9f3fe3e5964","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:42.559408Z","signature_b64":"VMb75dYvrWPnRHf29WViPI3U1+WLnFrSmSZTkbc/OA0G+fcLkdNdaEjyT5DNUBJm1YeUjcJjTocH9fGwd05ODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0fae2d8a5adbd89e54c5e8dcf859e189646f5119c7371edbd7a5f9f3fe3e5964","last_reissued_at":"2026-05-18T02:53:42.558591Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:42.558591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.5162","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":"2026-05-18T02:53:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2oKayGJ7zwKwgbGIbQBEc6VM79rcmc45gLuZCRh/XUwO/NYemZsVCxPXITk9kX1GI4BrTDT2K13DD0cCyYmiAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:54:49.813353Z"},"content_sha256":"b9d3b7e45b3eb5139ef9d2ecdd89facccf3bcbee842cb2938d7a5ff8416346fa","schema_version":"1.0","event_id":"sha256:b9d3b7e45b3eb5139ef9d2ecdd89facccf3bcbee842cb2938d7a5ff8416346fa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:B6XC3CS23PMJ4VGF5DOPQWPBRF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The consistency conditions and the smoothness of generalized solutions of nonlocal elliptic problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Pavel Gurevich","submitted_at":"2014-04-21T10:23:43Z","abstract_excerpt":"We study smoothness of generalized solutions of nonlocal elliptic problems in plane bounded domains with piecewise smooth boundary. The case where the support of nonlocal terms can intersect the boundary is considered. We find conditions that are necessary and sufficient for any generalized solution to possess an appropriate smoothness (in terms of Sobolev spaces). Both homogeneous and nonhomogeneous nonlocal boundary-value conditions are studied."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5162","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":"2026-05-18T02:53:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hZ91rAs5fjz7ejMLAjzk0L/1xkvRawRGQrn85k4HF3voRTGTDcwLheJ/wB4VMGa3QbG+JLaDvXIQMPU+2B9MAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:54:49.814039Z"},"content_sha256":"eb6c0a4fc46e7b62b5c264d13a1c4e7ae23b428bc472463dcf69ed32214af2b4","schema_version":"1.0","event_id":"sha256:eb6c0a4fc46e7b62b5c264d13a1c4e7ae23b428bc472463dcf69ed32214af2b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B6XC3CS23PMJ4VGF5DOPQWPBRF/bundle.json","state_url":"https://pith.science/pith/B6XC3CS23PMJ4VGF5DOPQWPBRF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B6XC3CS23PMJ4VGF5DOPQWPBRF/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":"2026-06-06T19:54:49Z","links":{"resolver":"https://pith.science/pith/B6XC3CS23PMJ4VGF5DOPQWPBRF","bundle":"https://pith.science/pith/B6XC3CS23PMJ4VGF5DOPQWPBRF/bundle.json","state":"https://pith.science/pith/B6XC3CS23PMJ4VGF5DOPQWPBRF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B6XC3CS23PMJ4VGF5DOPQWPBRF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:B6XC3CS23PMJ4VGF5DOPQWPBRF","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":"03c0cce200d599b5dd8513dbe750d16899a882cdaf1be07f62b0bda5688edff3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-21T10:23:43Z","title_canon_sha256":"fc0d115319b9828eb669fb019c8cd91be0e17ce0fa12f63d168929ac7ed42dd1"},"schema_version":"1.0","source":{"id":"1404.5162","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5162","created_at":"2026-05-18T02:53:42Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5162v1","created_at":"2026-05-18T02:53:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5162","created_at":"2026-05-18T02:53:42Z"},{"alias_kind":"pith_short_12","alias_value":"B6XC3CS23PMJ","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"B6XC3CS23PMJ4VGF","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"B6XC3CS2","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:eb6c0a4fc46e7b62b5c264d13a1c4e7ae23b428bc472463dcf69ed32214af2b4","target":"graph","created_at":"2026-05-18T02:53:42Z","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 smoothness of generalized solutions of nonlocal elliptic problems in plane bounded domains with piecewise smooth boundary. The case where the support of nonlocal terms can intersect the boundary is considered. We find conditions that are necessary and sufficient for any generalized solution to possess an appropriate smoothness (in terms of Sobolev spaces). Both homogeneous and nonhomogeneous nonlocal boundary-value conditions are studied.","authors_text":"Pavel Gurevich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-21T10:23:43Z","title":"The consistency conditions and the smoothness of generalized solutions of nonlocal elliptic problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5162","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:b9d3b7e45b3eb5139ef9d2ecdd89facccf3bcbee842cb2938d7a5ff8416346fa","target":"record","created_at":"2026-05-18T02:53:42Z","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":"03c0cce200d599b5dd8513dbe750d16899a882cdaf1be07f62b0bda5688edff3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-21T10:23:43Z","title_canon_sha256":"fc0d115319b9828eb669fb019c8cd91be0e17ce0fa12f63d168929ac7ed42dd1"},"schema_version":"1.0","source":{"id":"1404.5162","kind":"arxiv","version":1}},"canonical_sha256":"0fae2d8a5adbd89e54c5e8dcf859e189646f5119c7371edbd7a5f9f3fe3e5964","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0fae2d8a5adbd89e54c5e8dcf859e189646f5119c7371edbd7a5f9f3fe3e5964","first_computed_at":"2026-05-18T02:53:42.558591Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:42.558591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VMb75dYvrWPnRHf29WViPI3U1+WLnFrSmSZTkbc/OA0G+fcLkdNdaEjyT5DNUBJm1YeUjcJjTocH9fGwd05ODw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:42.559408Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.5162","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9d3b7e45b3eb5139ef9d2ecdd89facccf3bcbee842cb2938d7a5ff8416346fa","sha256:eb6c0a4fc46e7b62b5c264d13a1c4e7ae23b428bc472463dcf69ed32214af2b4"],"state_sha256":"5cb9b9bf2f77495260dd55ef2eefcbc1c8878c3434fb32b688fcb75c690b16dc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TbyE/zDFzCn6DtoUHthdmCxf1tSanCsG5v2qmjpAbK7JQYrxpM3GtUBuJ2sHTqzHWVg2rFkHizptuF/nS3u5Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T19:54:49.817254Z","bundle_sha256":"07a755065b806e96dbdfccf15b06be4bd3f4b49f11f92c1655a17387e3493988"}}