{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:JFBGW7MVSBALUBSOKW6WEYUCQW","short_pith_number":"pith:JFBGW7MV","schema_version":"1.0","canonical_sha256":"49426b7d959040ba064e55bd62628285b8eba4a91a25bf2151a89067f585cb4b","source":{"kind":"arxiv","id":"1112.0746","version":1},"attestation_state":"computed","paper":{"title":"Atomistic-to-Continuum Coupling Approximation of a One-Dimensional Toy Model for Density Functional Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"B. Langwallner, C. Ortner, E. S\\\"uli","submitted_at":"2011-12-04T11:27:33Z","abstract_excerpt":"We consider an atomistic model defined through an interaction field satisfying a variational principle, and can therefore be considered a toy model of (orbital free) density functional theory. We investigate atomistic-to-continuum coupling mechanisms for this atomistic model, paying special attention to the dependence of the atomistic subproblem on the atomistic region boundary and the boundary conditions. We rigorously prove first-order error estimates for two related coupling mechanisms."},"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":"1112.0746","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-12-04T11:27:33Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"da688843af2a8075d0c321720c6bbef8acc5500f7b3cd9ec0261aaa25f6e42c2","abstract_canon_sha256":"b2bf0b699cf66303d3d3d686b8c6995ee70273cfa46485898952e2f6207e020e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:05.742032Z","signature_b64":"3DiULrN9b+uab5PVpC1p2X35IKvPqXsACQ+tM/y/0Bhr+AahTRGwp86Es9ea6jTR77NKo/0njmnFRtjax2kpCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49426b7d959040ba064e55bd62628285b8eba4a91a25bf2151a89067f585cb4b","last_reissued_at":"2026-05-18T04:07:05.741360Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:05.741360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Atomistic-to-Continuum Coupling Approximation of a One-Dimensional Toy Model for Density Functional Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"B. Langwallner, C. Ortner, E. S\\\"uli","submitted_at":"2011-12-04T11:27:33Z","abstract_excerpt":"We consider an atomistic model defined through an interaction field satisfying a variational principle, and can therefore be considered a toy model of (orbital free) density functional theory. We investigate atomistic-to-continuum coupling mechanisms for this atomistic model, paying special attention to the dependence of the atomistic subproblem on the atomistic region boundary and the boundary conditions. We rigorously prove first-order error estimates for two related coupling mechanisms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0746","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1112.0746","created_at":"2026-05-18T04:07:05.741469+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.0746v1","created_at":"2026-05-18T04:07:05.741469+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0746","created_at":"2026-05-18T04:07:05.741469+00:00"},{"alias_kind":"pith_short_12","alias_value":"JFBGW7MVSBAL","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"JFBGW7MVSBALUBSO","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"JFBGW7MV","created_at":"2026-05-18T12:26:32.869790+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/JFBGW7MVSBALUBSOKW6WEYUCQW","json":"https://pith.science/pith/JFBGW7MVSBALUBSOKW6WEYUCQW.json","graph_json":"https://pith.science/api/pith-number/JFBGW7MVSBALUBSOKW6WEYUCQW/graph.json","events_json":"https://pith.science/api/pith-number/JFBGW7MVSBALUBSOKW6WEYUCQW/events.json","paper":"https://pith.science/paper/JFBGW7MV"},"agent_actions":{"view_html":"https://pith.science/pith/JFBGW7MVSBALUBSOKW6WEYUCQW","download_json":"https://pith.science/pith/JFBGW7MVSBALUBSOKW6WEYUCQW.json","view_paper":"https://pith.science/paper/JFBGW7MV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.0746&json=true","fetch_graph":"https://pith.science/api/pith-number/JFBGW7MVSBALUBSOKW6WEYUCQW/graph.json","fetch_events":"https://pith.science/api/pith-number/JFBGW7MVSBALUBSOKW6WEYUCQW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JFBGW7MVSBALUBSOKW6WEYUCQW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JFBGW7MVSBALUBSOKW6WEYUCQW/action/storage_attestation","attest_author":"https://pith.science/pith/JFBGW7MVSBALUBSOKW6WEYUCQW/action/author_attestation","sign_citation":"https://pith.science/pith/JFBGW7MVSBALUBSOKW6WEYUCQW/action/citation_signature","submit_replication":"https://pith.science/pith/JFBGW7MVSBALUBSOKW6WEYUCQW/action/replication_record"}},"created_at":"2026-05-18T04:07:05.741469+00:00","updated_at":"2026-05-18T04:07:05.741469+00:00"}