{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:VAX4PCCWQC2FWGGR7YADCGHASU","short_pith_number":"pith:VAX4PCCW","schema_version":"1.0","canonical_sha256":"a82fc7885680b45b18d1fe003118e0951db1012ab5c2a3b9a1191bcc6e6c57d1","source":{"kind":"arxiv","id":"1008.3716","version":2},"attestation_state":"computed","paper":{"title":"Analysis of the quasi-nonlocal approximation of linear and circular chains in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Mitchell Luskin, Pavel Belik","submitted_at":"2010-08-22T19:05:28Z","abstract_excerpt":"We give an analysis of the stability and displacement error for linear and circular atomistic chains in the plane when the atomistic energy is approximated by the Cauchy-Born continuum energy and by the quasi-nonlocal atomistic-to-continuum coupling energy. We consider atomistic energies that include Lennard-Jones type nearest neighbor and next nearest neighbor pair-potential interactions. Previous analyses for linear chains have shown that the Cauchy-Born and quasi-nonlocal approximations reproduce (up to the order of the lattice spacing) the atomistic lattice stability for perturbations that"},"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":"1008.3716","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-08-22T19:05:28Z","cross_cats_sorted":[],"title_canon_sha256":"1fb6817e604a04c8f77af2f9725bce89bd93491ddd289d678c9b7b03b18edeaa","abstract_canon_sha256":"7c788b585bd5a53c196ca8550b31743792a0c136819df4d5af461831663027d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:29.966692Z","signature_b64":"nibmVgUc2FHz2cLR615BPRE+M3dc9H1DdVhgFLz69MAhw+LKLMkQ1q9t72L1pGiWiui9NvgCk0nrY7yuaDOEBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a82fc7885680b45b18d1fe003118e0951db1012ab5c2a3b9a1191bcc6e6c57d1","last_reissued_at":"2026-05-18T04:21:29.966347Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:29.966347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analysis of the quasi-nonlocal approximation of linear and circular chains in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Mitchell Luskin, Pavel Belik","submitted_at":"2010-08-22T19:05:28Z","abstract_excerpt":"We give an analysis of the stability and displacement error for linear and circular atomistic chains in the plane when the atomistic energy is approximated by the Cauchy-Born continuum energy and by the quasi-nonlocal atomistic-to-continuum coupling energy. We consider atomistic energies that include Lennard-Jones type nearest neighbor and next nearest neighbor pair-potential interactions. Previous analyses for linear chains have shown that the Cauchy-Born and quasi-nonlocal approximations reproduce (up to the order of the lattice spacing) the atomistic lattice stability for perturbations that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3716","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":""},"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":"1008.3716","created_at":"2026-05-18T04:21:29.966407+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.3716v2","created_at":"2026-05-18T04:21:29.966407+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3716","created_at":"2026-05-18T04:21:29.966407+00:00"},{"alias_kind":"pith_short_12","alias_value":"VAX4PCCWQC2F","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_16","alias_value":"VAX4PCCWQC2FWGGR","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_8","alias_value":"VAX4PCCW","created_at":"2026-05-18T12:26:15.391820+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/VAX4PCCWQC2FWGGR7YADCGHASU","json":"https://pith.science/pith/VAX4PCCWQC2FWGGR7YADCGHASU.json","graph_json":"https://pith.science/api/pith-number/VAX4PCCWQC2FWGGR7YADCGHASU/graph.json","events_json":"https://pith.science/api/pith-number/VAX4PCCWQC2FWGGR7YADCGHASU/events.json","paper":"https://pith.science/paper/VAX4PCCW"},"agent_actions":{"view_html":"https://pith.science/pith/VAX4PCCWQC2FWGGR7YADCGHASU","download_json":"https://pith.science/pith/VAX4PCCWQC2FWGGR7YADCGHASU.json","view_paper":"https://pith.science/paper/VAX4PCCW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.3716&json=true","fetch_graph":"https://pith.science/api/pith-number/VAX4PCCWQC2FWGGR7YADCGHASU/graph.json","fetch_events":"https://pith.science/api/pith-number/VAX4PCCWQC2FWGGR7YADCGHASU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VAX4PCCWQC2FWGGR7YADCGHASU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VAX4PCCWQC2FWGGR7YADCGHASU/action/storage_attestation","attest_author":"https://pith.science/pith/VAX4PCCWQC2FWGGR7YADCGHASU/action/author_attestation","sign_citation":"https://pith.science/pith/VAX4PCCWQC2FWGGR7YADCGHASU/action/citation_signature","submit_replication":"https://pith.science/pith/VAX4PCCWQC2FWGGR7YADCGHASU/action/replication_record"}},"created_at":"2026-05-18T04:21:29.966407+00:00","updated_at":"2026-05-18T04:21:29.966407+00:00"}