{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:V5ADDUVST5S4IDLEIZ2ZHAH6CI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ee62e5c9edc3e5a8e22648649329e3d2824a27790d03cba5d5d0a95b88fb23af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-12-12T12:33:35Z","title_canon_sha256":"da8289759bc9e331dd3c919ce7484e39d4f7d11fcd89a77bd5bfda1895f990cb"},"schema_version":"1.0","source":{"id":"1112.2528","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2528","created_at":"2026-05-18T04:06:34Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2528v1","created_at":"2026-05-18T04:06:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2528","created_at":"2026-05-18T04:06:34Z"},{"alias_kind":"pith_short_12","alias_value":"V5ADDUVST5S4","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"V5ADDUVST5S4IDLE","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"V5ADDUVS","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:34990e4873c006f90ca43a8d91b91d9309d25d5938568d5ed1e2f08b5271a5b9","target":"graph","created_at":"2026-05-18T04:06:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The development of consistent and stable quasicontinuum models for multi-dimensional crystalline solids remains a challenge. For example, proving stability of the force-based quasicontinuum (QCF) model remains an open problem. In 1D and 2D, we show that by blending atomistic and Cauchy--Born continuum forces (instead of a sharp transition as in the QCF method) one obtains positive-definite blended force-based quasicontinuum (B-QCF) models. We establish sharp conditions on the required blending width.","authors_text":"Christoph Ortner, Mitchell Luskin, Xingjie Helen Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-12-12T12:33:35Z","title":"Positive-Definiteness of the Blended Force-Based Quasicontinuum Method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2528","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:719c74ff1396aea5d1ccd8e7f3d6a460ea32b322eb287d13e29d5065d22ba14e","target":"record","created_at":"2026-05-18T04:06:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ee62e5c9edc3e5a8e22648649329e3d2824a27790d03cba5d5d0a95b88fb23af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-12-12T12:33:35Z","title_canon_sha256":"da8289759bc9e331dd3c919ce7484e39d4f7d11fcd89a77bd5bfda1895f990cb"},"schema_version":"1.0","source":{"id":"1112.2528","kind":"arxiv","version":1}},"canonical_sha256":"af4031d2b29f65c40d6446759380fe122bc9c2158cfcf91b6dda3dce2a9dee57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af4031d2b29f65c40d6446759380fe122bc9c2158cfcf91b6dda3dce2a9dee57","first_computed_at":"2026-05-18T04:06:34.089474Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:34.089474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BW3MyieICIU1NKiOMhOlqi7b/XXDD7CtTt6YDlR9CQe2ghH9p93Yd69H/SFB0ZiSTatkXst1ubDCOKEluYQ7Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:34.090150Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.2528","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:719c74ff1396aea5d1ccd8e7f3d6a460ea32b322eb287d13e29d5065d22ba14e","sha256:34990e4873c006f90ca43a8d91b91d9309d25d5938568d5ed1e2f08b5271a5b9"],"state_sha256":"e7a8e279c7ebd20a62f7f289ef0b9ab03c319965bbf1004fa329969d42da8ae1"}