{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:PTWLRZXAFUCXBIIS3ARMIG7TSA","short_pith_number":"pith:PTWLRZXA","canonical_record":{"source":{"id":"1404.5148","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-21T09:29:14Z","cross_cats_sorted":[],"title_canon_sha256":"6cef2bad2f99842962245a2f661f8ce7a047395c25f55ee32ccc8411f90d6096","abstract_canon_sha256":"db35c554a6e9191f6f8172d7971a1dd0f7ef4bcd7a79da40c48c11b63c133518"},"schema_version":"1.0"},"canonical_sha256":"7cecb8e6e02d0570a112d822c41bf390227224e111cf627062639a0407a7dd9a","source":{"kind":"arxiv","id":"1404.5148","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5148","created_at":"2026-05-18T02:53:42Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5148v1","created_at":"2026-05-18T02:53:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5148","created_at":"2026-05-18T02:53:42Z"},{"alias_kind":"pith_short_12","alias_value":"PTWLRZXAFUCX","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PTWLRZXAFUCXBIIS","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PTWLRZXA","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:PTWLRZXAFUCXBIIS3ARMIG7TSA","target":"record","payload":{"canonical_record":{"source":{"id":"1404.5148","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-21T09:29:14Z","cross_cats_sorted":[],"title_canon_sha256":"6cef2bad2f99842962245a2f661f8ce7a047395c25f55ee32ccc8411f90d6096","abstract_canon_sha256":"db35c554a6e9191f6f8172d7971a1dd0f7ef4bcd7a79da40c48c11b63c133518"},"schema_version":"1.0"},"canonical_sha256":"7cecb8e6e02d0570a112d822c41bf390227224e111cf627062639a0407a7dd9a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:42.623002Z","signature_b64":"odJmc0PRp6eUj9vQ9vwvNfk+9ZKfcuZf21WdPOfQdrOpPz5ZgHy5Dl9ybqCBAuyDHb2Q2EOh5neKlIGrP5q4CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7cecb8e6e02d0570a112d822c41bf390227224e111cf627062639a0407a7dd9a","last_reissued_at":"2026-05-18T02:53:42.622126Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:42.622126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.5148","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":"kQkzeh+DzKfpb4zCVQPjmXnFIgyPLM1Djpyi9c+QJ0ZXrXrajjdGHz8FG9W3TLwBZcqB9SLh1+FHWRijZhYpDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:53:23.194289Z"},"content_sha256":"38255ca3020674fa6589d87d6abc6fca8f8823f41549abb2ea8b24307186215f","schema_version":"1.0","event_id":"sha256:38255ca3020674fa6589d87d6abc6fca8f8823f41549abb2ea8b24307186215f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:PTWLRZXAFUCXBIIS3ARMIG7TSA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solvability of nonlocal elliptic problems in Sobolev spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Pavel Gurevich","submitted_at":"2014-04-21T09:29:14Z","abstract_excerpt":"We study elliptic equations of order $2m$ with nonlocal boundary-value conditions in plane angles and in bounded domains, dealing with the case where the support of nonlocal terms intersects the boundary. We establish necessary and sufficient conditions under which nonlocal problems are Fredholm in Sobolev spaces and, respectively, in weighted spaces with small weight exponents. We also obtain an asymptotics of solutions to nonlocal problems near the conjugation points on the boundary, where solutions may have power singularities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5148","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":"Bq/Ougq3xffjo6td8paU77K0pNg31K4fKBux1oJ01MsPp3htqfAFk4oVEl/thsNSpD0qaoYiTueBjhquvwGvBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:53:23.194722Z"},"content_sha256":"96d94a86e6a819881d1c41e2a82adf62e357dc013049f35629700733bc076079","schema_version":"1.0","event_id":"sha256:96d94a86e6a819881d1c41e2a82adf62e357dc013049f35629700733bc076079"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PTWLRZXAFUCXBIIS3ARMIG7TSA/bundle.json","state_url":"https://pith.science/pith/PTWLRZXAFUCXBIIS3ARMIG7TSA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PTWLRZXAFUCXBIIS3ARMIG7TSA/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":"2026-06-06T18:53:23Z","links":{"resolver":"https://pith.science/pith/PTWLRZXAFUCXBIIS3ARMIG7TSA","bundle":"https://pith.science/pith/PTWLRZXAFUCXBIIS3ARMIG7TSA/bundle.json","state":"https://pith.science/pith/PTWLRZXAFUCXBIIS3ARMIG7TSA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PTWLRZXAFUCXBIIS3ARMIG7TSA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PTWLRZXAFUCXBIIS3ARMIG7TSA","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":"db35c554a6e9191f6f8172d7971a1dd0f7ef4bcd7a79da40c48c11b63c133518","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-21T09:29:14Z","title_canon_sha256":"6cef2bad2f99842962245a2f661f8ce7a047395c25f55ee32ccc8411f90d6096"},"schema_version":"1.0","source":{"id":"1404.5148","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5148","created_at":"2026-05-18T02:53:42Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5148v1","created_at":"2026-05-18T02:53:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5148","created_at":"2026-05-18T02:53:42Z"},{"alias_kind":"pith_short_12","alias_value":"PTWLRZXAFUCX","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PTWLRZXAFUCXBIIS","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PTWLRZXA","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:96d94a86e6a819881d1c41e2a82adf62e357dc013049f35629700733bc076079","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 elliptic equations of order $2m$ with nonlocal boundary-value conditions in plane angles and in bounded domains, dealing with the case where the support of nonlocal terms intersects the boundary. We establish necessary and sufficient conditions under which nonlocal problems are Fredholm in Sobolev spaces and, respectively, in weighted spaces with small weight exponents. We also obtain an asymptotics of solutions to nonlocal problems near the conjugation points on the boundary, where solutions may have power singularities.","authors_text":"Pavel Gurevich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-21T09:29:14Z","title":"Solvability of nonlocal elliptic problems in Sobolev spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5148","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":"sha256:38255ca3020674fa6589d87d6abc6fca8f8823f41549abb2ea8b24307186215f","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":"db35c554a6e9191f6f8172d7971a1dd0f7ef4bcd7a79da40c48c11b63c133518","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-21T09:29:14Z","title_canon_sha256":"6cef2bad2f99842962245a2f661f8ce7a047395c25f55ee32ccc8411f90d6096"},"schema_version":"1.0","source":{"id":"1404.5148","kind":"arxiv","version":1}},"canonical_sha256":"7cecb8e6e02d0570a112d822c41bf390227224e111cf627062639a0407a7dd9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7cecb8e6e02d0570a112d822c41bf390227224e111cf627062639a0407a7dd9a","first_computed_at":"2026-05-18T02:53:42.622126Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:42.622126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"odJmc0PRp6eUj9vQ9vwvNfk+9ZKfcuZf21WdPOfQdrOpPz5ZgHy5Dl9ybqCBAuyDHb2Q2EOh5neKlIGrP5q4CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:42.623002Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.5148","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38255ca3020674fa6589d87d6abc6fca8f8823f41549abb2ea8b24307186215f","sha256:96d94a86e6a819881d1c41e2a82adf62e357dc013049f35629700733bc076079"],"state_sha256":"75a23eb757957ee6f0b45fe6207c07b2c3d91b78c5363e28d36ba8a8663ea97b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XRSw+GdbYiE4sSVwEqgYChcjm21C2y58fAorPZpXS6SAn3tspOCJjLR8YyY3q7i3GkTa635oy1ZjQHx/GJ5yCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T18:53:23.198210Z","bundle_sha256":"28f82e55fabe0b10068dfcef90453b334bf1d8a8b392c084c9cc33d24edc4a18"}}