{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:NIGNK52E3X43LXOMFR3N6WDBHS","short_pith_number":"pith:NIGNK52E","schema_version":"1.0","canonical_sha256":"6a0cd57744ddf9b5ddcc2c76df58613cb3ae76eed42a57373cca1b9c71a165a3","source":{"kind":"arxiv","id":"2412.03153","version":2},"attestation_state":"computed","paper":{"title":"A seamless local-nonlocal coupling diffusion model with $H^1$ vanishing nonlocality convergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yanzun Meng, Zuoqiang Shi","submitted_at":"2024-12-04T09:22:02Z","abstract_excerpt":"Based on the development in dealing with nonlocal boundary conditions, we propose a seamless local-nonlocal coupling diffusion model in this paper. In our model, a finite constant interaction horizon is equipped in the nonlocal part and transmission conditions are imposed on a co-dimension one interface. To achieve a seamless coupling, we introduce an auxiliary function to merge the nonlocal model with the local part and design a proper coupling transmission condition to ensure the stability and convergence. In addition, by introducing bilinear form, well-posedness of the proposed model can be"},"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":"2412.03153","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-12-04T09:22:02Z","cross_cats_sorted":[],"title_canon_sha256":"1a76f7660cb875f539c4abf36af6e230abc429da555a60d48b3f82325fd48d48","abstract_canon_sha256":"77f89484cbd0925581ea05410abd91a210e468a02879699a4589a0b1c9ca0b46"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:25:06.121910Z","signature_b64":"tHjBrqqEAXS/8ZG9Xtyk0WOKLwkLaW4ryRX8vR+XePTVSKRmNb8+Bb4i4mnu5Ycgq7MPzgI7v/4+7rK9iM1QCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a0cd57744ddf9b5ddcc2c76df58613cb3ae76eed42a57373cca1b9c71a165a3","last_reissued_at":"2026-07-05T11:25:06.121426Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:25:06.121426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A seamless local-nonlocal coupling diffusion model with $H^1$ vanishing nonlocality convergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yanzun Meng, Zuoqiang Shi","submitted_at":"2024-12-04T09:22:02Z","abstract_excerpt":"Based on the development in dealing with nonlocal boundary conditions, we propose a seamless local-nonlocal coupling diffusion model in this paper. In our model, a finite constant interaction horizon is equipped in the nonlocal part and transmission conditions are imposed on a co-dimension one interface. To achieve a seamless coupling, we introduce an auxiliary function to merge the nonlocal model with the local part and design a proper coupling transmission condition to ensure the stability and convergence. In addition, by introducing bilinear form, well-posedness of the proposed model can be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.03153","kind":"arxiv","version":2},"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/2412.03153/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":"2412.03153","created_at":"2026-07-05T11:25:06.121484+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.03153v2","created_at":"2026-07-05T11:25:06.121484+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.03153","created_at":"2026-07-05T11:25:06.121484+00:00"},{"alias_kind":"pith_short_12","alias_value":"NIGNK52E3X43","created_at":"2026-07-05T11:25:06.121484+00:00"},{"alias_kind":"pith_short_16","alias_value":"NIGNK52E3X43LXOM","created_at":"2026-07-05T11:25:06.121484+00:00"},{"alias_kind":"pith_short_8","alias_value":"NIGNK52E","created_at":"2026-07-05T11:25:06.121484+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/NIGNK52E3X43LXOMFR3N6WDBHS","json":"https://pith.science/pith/NIGNK52E3X43LXOMFR3N6WDBHS.json","graph_json":"https://pith.science/api/pith-number/NIGNK52E3X43LXOMFR3N6WDBHS/graph.json","events_json":"https://pith.science/api/pith-number/NIGNK52E3X43LXOMFR3N6WDBHS/events.json","paper":"https://pith.science/paper/NIGNK52E"},"agent_actions":{"view_html":"https://pith.science/pith/NIGNK52E3X43LXOMFR3N6WDBHS","download_json":"https://pith.science/pith/NIGNK52E3X43LXOMFR3N6WDBHS.json","view_paper":"https://pith.science/paper/NIGNK52E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.03153&json=true","fetch_graph":"https://pith.science/api/pith-number/NIGNK52E3X43LXOMFR3N6WDBHS/graph.json","fetch_events":"https://pith.science/api/pith-number/NIGNK52E3X43LXOMFR3N6WDBHS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NIGNK52E3X43LXOMFR3N6WDBHS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NIGNK52E3X43LXOMFR3N6WDBHS/action/storage_attestation","attest_author":"https://pith.science/pith/NIGNK52E3X43LXOMFR3N6WDBHS/action/author_attestation","sign_citation":"https://pith.science/pith/NIGNK52E3X43LXOMFR3N6WDBHS/action/citation_signature","submit_replication":"https://pith.science/pith/NIGNK52E3X43LXOMFR3N6WDBHS/action/replication_record"}},"created_at":"2026-07-05T11:25:06.121484+00:00","updated_at":"2026-07-05T11:25:06.121484+00:00"}