{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:QU7PIMHQ4RCRANXGA4BSD3MPX2","short_pith_number":"pith:QU7PIMHQ","schema_version":"1.0","canonical_sha256":"853ef430f0e4451036e6070321ed8fbe9a4ece3eadd67e3d6fe0016515ad8a56","source":{"kind":"arxiv","id":"2607.22672","version":1},"attestation_state":"computed","paper":{"title":"Coupling of Local and Nonlocal Problems Using Local Boundary Conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Burak Aksoylu, Fatih Celiker, Patrick Diehl","submitted_at":"2026-07-06T17:48:59Z","abstract_excerpt":"We present a novel coupling method for local and nonlocal diffusion problems in 1D. Unlike other methods, our coupling method exclusively uses local boundary conditions. This is possible because our nonlocal operators enforce them by construction. Leveraging this advantageous property, we construct a seamless coupling that is remarkably natural. The utilization of local boundary conditions allows for the transfer of well-established numerical methods from local problems to nonlocal ones. Our local-to-nonlocal coupling method is inspired by the domain decomposition method, which we would like t"},"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":"2607.22672","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-06T17:48:59Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"f863522d09042e677fdc1af338e3428fbf769ffbbbdfd7bd854366a3d4b91e31","abstract_canon_sha256":"9e9ce3aa39aa8d0ec6135e55a6a6d3c30091da615becd5dbfac48b982cdb3f2c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-28T00:21:48.365688Z","signature_b64":"9HsnUCbCSNJBKFHLW/ySxTFIUGeonub6Gs3VV6zHH1wTl4U0X0Q3Ppu7V5tUQT83LLdy6Zai4RdRLcPgYnKYCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"853ef430f0e4451036e6070321ed8fbe9a4ece3eadd67e3d6fe0016515ad8a56","last_reissued_at":"2026-07-28T00:21:48.364831Z","signature_status":"signed_v1","first_computed_at":"2026-07-28T00:21:48.364831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coupling of Local and Nonlocal Problems Using Local Boundary Conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Burak Aksoylu, Fatih Celiker, Patrick Diehl","submitted_at":"2026-07-06T17:48:59Z","abstract_excerpt":"We present a novel coupling method for local and nonlocal diffusion problems in 1D. Unlike other methods, our coupling method exclusively uses local boundary conditions. This is possible because our nonlocal operators enforce them by construction. Leveraging this advantageous property, we construct a seamless coupling that is remarkably natural. The utilization of local boundary conditions allows for the transfer of well-established numerical methods from local problems to nonlocal ones. Our local-to-nonlocal coupling method is inspired by the domain decomposition method, which we would like t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.22672","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.22672/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2607.22672","created_at":"2026-07-28T00:21:48.365261+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.22672v1","created_at":"2026-07-28T00:21:48.365261+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.22672","created_at":"2026-07-28T00:21:48.365261+00:00"},{"alias_kind":"pith_short_12","alias_value":"QU7PIMHQ4RCR","created_at":"2026-07-28T00:21:48.365261+00:00"},{"alias_kind":"pith_short_16","alias_value":"QU7PIMHQ4RCRANXG","created_at":"2026-07-28T00:21:48.365261+00:00"},{"alias_kind":"pith_short_8","alias_value":"QU7PIMHQ","created_at":"2026-07-28T00:21:48.365261+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/QU7PIMHQ4RCRANXGA4BSD3MPX2","json":"https://pith.science/pith/QU7PIMHQ4RCRANXGA4BSD3MPX2.json","graph_json":"https://pith.science/api/pith-number/QU7PIMHQ4RCRANXGA4BSD3MPX2/graph.json","events_json":"https://pith.science/api/pith-number/QU7PIMHQ4RCRANXGA4BSD3MPX2/events.json","paper":"https://pith.science/paper/QU7PIMHQ"},"agent_actions":{"view_html":"https://pith.science/pith/QU7PIMHQ4RCRANXGA4BSD3MPX2","download_json":"https://pith.science/pith/QU7PIMHQ4RCRANXGA4BSD3MPX2.json","view_paper":"https://pith.science/paper/QU7PIMHQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.22672&json=true","fetch_graph":"https://pith.science/api/pith-number/QU7PIMHQ4RCRANXGA4BSD3MPX2/graph.json","fetch_events":"https://pith.science/api/pith-number/QU7PIMHQ4RCRANXGA4BSD3MPX2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QU7PIMHQ4RCRANXGA4BSD3MPX2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QU7PIMHQ4RCRANXGA4BSD3MPX2/action/storage_attestation","attest_author":"https://pith.science/pith/QU7PIMHQ4RCRANXGA4BSD3MPX2/action/author_attestation","sign_citation":"https://pith.science/pith/QU7PIMHQ4RCRANXGA4BSD3MPX2/action/citation_signature","submit_replication":"https://pith.science/pith/QU7PIMHQ4RCRANXGA4BSD3MPX2/action/replication_record"}},"created_at":"2026-07-28T00:21:48.365261+00:00","updated_at":"2026-07-28T00:21:48.365261+00:00"}