{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:XF7G44WPIHVLVY626W7IZMWDLD","short_pith_number":"pith:XF7G44WP","schema_version":"1.0","canonical_sha256":"b97e6e72cf41eabae3daf5be8cb2c358f6a1feb6db483373853823cdd36c34c6","source":{"kind":"arxiv","id":"0910.2013","version":3},"attestation_state":"computed","paper":{"title":"Iterative Methods for the Force-based Quasicontinuum Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Christoph Ortner, Matthew Dobson, Mitchell Luskin","submitted_at":"2009-10-12T13:21:14Z","abstract_excerpt":"Force-based atomistic-continuum hybrid methods are the only known pointwise consistent methods for coupling a general atomistic model to a finite element continuum model. For this reason, and due to their algorithmic simplicity, force-based coupling methods have become a popular class of atomistic-continuum hybrid models as well as other types of multiphysics models. However, the recently discovered unusual stability properties of the linearized force-based quasicontinuum (QCF) approximation, especially its indefiniteness, present a challenge to the development of efficient and reliable iterat"},"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":"0910.2013","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-10-12T13:21:14Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"32ea682fd9d706e18ebb6130f596853ed0986dfa16a77511b410471705dd0ce5","abstract_canon_sha256":"1b7d1b634d3270bc3e91f1ef76b18cdc38d0ee44fae4f8b50d240d0f3f418ccd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T23:06:29.778857Z","signature_b64":"jKc8PByjiejMI0m0q2GfkJW257O1PuVkghz6lun2FGpIAfZ+kV1leWx1BploAOtWAu80r2AI7YOnzGLoS7SQCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b97e6e72cf41eabae3daf5be8cb2c358f6a1feb6db483373853823cdd36c34c6","last_reissued_at":"2026-06-03T23:06:29.778420Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T23:06:29.778420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Iterative Methods for the Force-based Quasicontinuum Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Christoph Ortner, Matthew Dobson, Mitchell Luskin","submitted_at":"2009-10-12T13:21:14Z","abstract_excerpt":"Force-based atomistic-continuum hybrid methods are the only known pointwise consistent methods for coupling a general atomistic model to a finite element continuum model. For this reason, and due to their algorithmic simplicity, force-based coupling methods have become a popular class of atomistic-continuum hybrid models as well as other types of multiphysics models. However, the recently discovered unusual stability properties of the linearized force-based quasicontinuum (QCF) approximation, especially its indefiniteness, present a challenge to the development of efficient and reliable iterat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2013","kind":"arxiv","version":3},"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/0910.2013/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":"0910.2013","created_at":"2026-06-03T23:06:29.778486+00:00"},{"alias_kind":"arxiv_version","alias_value":"0910.2013v3","created_at":"2026-06-03T23:06:29.778486+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.2013","created_at":"2026-06-03T23:06:29.778486+00:00"},{"alias_kind":"pith_short_12","alias_value":"XF7G44WPIHVL","created_at":"2026-06-03T23:06:29.778486+00:00"},{"alias_kind":"pith_short_16","alias_value":"XF7G44WPIHVLVY62","created_at":"2026-06-03T23:06:29.778486+00:00"},{"alias_kind":"pith_short_8","alias_value":"XF7G44WP","created_at":"2026-06-03T23:06:29.778486+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/XF7G44WPIHVLVY626W7IZMWDLD","json":"https://pith.science/pith/XF7G44WPIHVLVY626W7IZMWDLD.json","graph_json":"https://pith.science/api/pith-number/XF7G44WPIHVLVY626W7IZMWDLD/graph.json","events_json":"https://pith.science/api/pith-number/XF7G44WPIHVLVY626W7IZMWDLD/events.json","paper":"https://pith.science/paper/XF7G44WP"},"agent_actions":{"view_html":"https://pith.science/pith/XF7G44WPIHVLVY626W7IZMWDLD","download_json":"https://pith.science/pith/XF7G44WPIHVLVY626W7IZMWDLD.json","view_paper":"https://pith.science/paper/XF7G44WP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0910.2013&json=true","fetch_graph":"https://pith.science/api/pith-number/XF7G44WPIHVLVY626W7IZMWDLD/graph.json","fetch_events":"https://pith.science/api/pith-number/XF7G44WPIHVLVY626W7IZMWDLD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XF7G44WPIHVLVY626W7IZMWDLD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XF7G44WPIHVLVY626W7IZMWDLD/action/storage_attestation","attest_author":"https://pith.science/pith/XF7G44WPIHVLVY626W7IZMWDLD/action/author_attestation","sign_citation":"https://pith.science/pith/XF7G44WPIHVLVY626W7IZMWDLD/action/citation_signature","submit_replication":"https://pith.science/pith/XF7G44WPIHVLVY626W7IZMWDLD/action/replication_record"}},"created_at":"2026-06-03T23:06:29.778486+00:00","updated_at":"2026-06-03T23:06:29.778486+00:00"}