{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PK5FKQDBF7ACPLLEJZUZ4E6TUS","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":"925ba13c776b6148ed80346bc1cbd9453aa9a2f287e24211bf9c5ab20650e39c","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-25T12:15:02Z","title_canon_sha256":"161e4ebc3089890f46f033b32aad3fe76204d2b2a8b49da2a725e358dfbaa654"},"schema_version":"1.0","source":{"id":"2605.25761","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.25761","created_at":"2026-05-26T02:04:53Z"},{"alias_kind":"arxiv_version","alias_value":"2605.25761v1","created_at":"2026-05-26T02:04:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25761","created_at":"2026-05-26T02:04:53Z"},{"alias_kind":"pith_short_12","alias_value":"PK5FKQDBF7AC","created_at":"2026-05-26T02:04:53Z"},{"alias_kind":"pith_short_16","alias_value":"PK5FKQDBF7ACPLLE","created_at":"2026-05-26T02:04:53Z"},{"alias_kind":"pith_short_8","alias_value":"PK5FKQDB","created_at":"2026-05-26T02:04:53Z"}],"graph_snapshots":[{"event_id":"sha256:81e11157b0479f4885c76ee55130526d181d943393c5a513a39365265eac0983","target":"graph","created_at":"2026-05-26T02:04:53Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.25761/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the Laplace equation posed in the unbounded rectangular domain $\\Pi = I \\times (0,\\infty)$ with $I= (0,2\\pi)$, and subject to nonlocal boundary conditions on $\\partial \\Pi$ in the trace sense. The analysis is carried out in the Bochner-Sobolev space $W^2_{p,1}(\\Pi;X)$, associated with the Bochner space $L^{p,1}(\\Pi;X)$, with $ p \\in (1,\\infty)$ and $X$ is a suitable Banach space. To solve the problem, we employ a generalized spectral method. In particular, we introduce the notion of $\\otimes$-basis generated by tensor products and extend the classical scheme known from the scalar case","authors_text":"Bilal Bilalov, Lubomira Softova, Pia Salerno, Sabina Sadigova","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-25T12:15:02Z","title":"Nonlocal problem for Laplace equation in Bochner spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25761","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":"sha256:69072237ffd49967c6f67738d203094476f1355a3d4b9f45a171b23210099680","target":"record","created_at":"2026-05-26T02:04:53Z","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":"925ba13c776b6148ed80346bc1cbd9453aa9a2f287e24211bf9c5ab20650e39c","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-25T12:15:02Z","title_canon_sha256":"161e4ebc3089890f46f033b32aad3fe76204d2b2a8b49da2a725e358dfbaa654"},"schema_version":"1.0","source":{"id":"2605.25761","kind":"arxiv","version":1}},"canonical_sha256":"7aba5540612fc027ad644e699e13d3a493f683cdc9f88d5387422deb7acf4ef7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7aba5540612fc027ad644e699e13d3a493f683cdc9f88d5387422deb7acf4ef7","first_computed_at":"2026-05-26T02:04:53.610528Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T02:04:53.610528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XmPdyOhyxJxhq7y/RkokeC7d1q95hcsSNOocn+Kog/niP7ARTyq02kTPvEuGtWAU3KIUBLxRN2Cu56LLfOVNCQ==","signature_status":"signed_v1","signed_at":"2026-05-26T02:04:53.611231Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.25761","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69072237ffd49967c6f67738d203094476f1355a3d4b9f45a171b23210099680","sha256:81e11157b0479f4885c76ee55130526d181d943393c5a513a39365265eac0983"],"state_sha256":"fb96f45a20100f3aee3201d780b736f1f73497ce923919e457247ef95427c140"}