{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:V33Z2K32CAENFUJJJIGAWBIRMA","short_pith_number":"pith:V33Z2K32","schema_version":"1.0","canonical_sha256":"aef79d2b7a1008d2d1294a0c0b0511603894ba169795fde61f5c3c61779534f8","source":{"kind":"arxiv","id":"1203.5854","version":1},"attestation_state":"computed","paper":{"title":"Symmetries of 2-lattices and second order accuracy of the Cauchy--Born Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci"],"primary_cat":"math.NA","authors_text":"Brian Van Koten, Christoph Ortner","submitted_at":"2012-03-27T01:41:37Z","abstract_excerpt":"We show that the Cauchy--Born model of a single-species 2-lattice is second order if the atomistic and continuum kinematics are connected in a novel way. Our proof uses a generalization to 2-lattices of the point symmetry of Bravais lattices. Moreover, by identifying similar symmetries in multi-species pair interaction models, we construct a new stored energy density, using shift-gradients but not strain gradients, that is also second order accurate. These results can be used to develop highly accurate continuum models and atomistic/continuum coupling methods for materials such as graphene, hc"},"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":"1203.5854","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-03-27T01:41:37Z","cross_cats_sorted":["cond-mat.mtrl-sci"],"title_canon_sha256":"2711a924b4b4398ca74e3f8b405ebd08c36438c5103f9a4a53f526bf8230d762","abstract_canon_sha256":"4208ac67b14deea8e782a285fc737618c75a831e2a86e00fdb3fef7cbae97191"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:13.265156Z","signature_b64":"5MZ89Hr3Wz8gxqZhEna0rRPAW1LefeAr49SElXo919TYXvOzdcMMjgluu39uU8k8YI8NouVHr8HRja5ZJyxsCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aef79d2b7a1008d2d1294a0c0b0511603894ba169795fde61f5c3c61779534f8","last_reissued_at":"2026-05-18T03:59:13.264387Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:13.264387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symmetries of 2-lattices and second order accuracy of the Cauchy--Born Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci"],"primary_cat":"math.NA","authors_text":"Brian Van Koten, Christoph Ortner","submitted_at":"2012-03-27T01:41:37Z","abstract_excerpt":"We show that the Cauchy--Born model of a single-species 2-lattice is second order if the atomistic and continuum kinematics are connected in a novel way. Our proof uses a generalization to 2-lattices of the point symmetry of Bravais lattices. Moreover, by identifying similar symmetries in multi-species pair interaction models, we construct a new stored energy density, using shift-gradients but not strain gradients, that is also second order accurate. These results can be used to develop highly accurate continuum models and atomistic/continuum coupling methods for materials such as graphene, hc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5854","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":"1203.5854","created_at":"2026-05-18T03:59:13.264502+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.5854v1","created_at":"2026-05-18T03:59:13.264502+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.5854","created_at":"2026-05-18T03:59:13.264502+00:00"},{"alias_kind":"pith_short_12","alias_value":"V33Z2K32CAEN","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_16","alias_value":"V33Z2K32CAENFUJJ","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_8","alias_value":"V33Z2K32","created_at":"2026-05-18T12:27:25.539911+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/V33Z2K32CAENFUJJJIGAWBIRMA","json":"https://pith.science/pith/V33Z2K32CAENFUJJJIGAWBIRMA.json","graph_json":"https://pith.science/api/pith-number/V33Z2K32CAENFUJJJIGAWBIRMA/graph.json","events_json":"https://pith.science/api/pith-number/V33Z2K32CAENFUJJJIGAWBIRMA/events.json","paper":"https://pith.science/paper/V33Z2K32"},"agent_actions":{"view_html":"https://pith.science/pith/V33Z2K32CAENFUJJJIGAWBIRMA","download_json":"https://pith.science/pith/V33Z2K32CAENFUJJJIGAWBIRMA.json","view_paper":"https://pith.science/paper/V33Z2K32","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.5854&json=true","fetch_graph":"https://pith.science/api/pith-number/V33Z2K32CAENFUJJJIGAWBIRMA/graph.json","fetch_events":"https://pith.science/api/pith-number/V33Z2K32CAENFUJJJIGAWBIRMA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V33Z2K32CAENFUJJJIGAWBIRMA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V33Z2K32CAENFUJJJIGAWBIRMA/action/storage_attestation","attest_author":"https://pith.science/pith/V33Z2K32CAENFUJJJIGAWBIRMA/action/author_attestation","sign_citation":"https://pith.science/pith/V33Z2K32CAENFUJJJIGAWBIRMA/action/citation_signature","submit_replication":"https://pith.science/pith/V33Z2K32CAENFUJJJIGAWBIRMA/action/replication_record"}},"created_at":"2026-05-18T03:59:13.264502+00:00","updated_at":"2026-05-18T03:59:13.264502+00:00"}