{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6PV5KLOMLAXKDXSYWJTOO6RDDB","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":"ab8a53447cdaf4712b95c65db1ffd4aba94a0e902ffe50f990d474e8a2c6b78f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-15T14:39:12Z","title_canon_sha256":"0cce8e4fbc857331f505d067630967a9d28bec564e8d6e9c2faa147bc58be3da"},"schema_version":"1.0","source":{"id":"1609.04675","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04675","created_at":"2026-05-18T00:21:35Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04675v8","created_at":"2026-05-18T00:21:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04675","created_at":"2026-05-18T00:21:35Z"},{"alias_kind":"pith_short_12","alias_value":"6PV5KLOMLAXK","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6PV5KLOMLAXKDXSY","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6PV5KLOM","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:c2f3839bf99e15e3915a30d0f85c740b35f7ac8c14c707aa92bbaffa15119799","target":"graph","created_at":"2026-05-18T00:21:35Z","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":"This paper presents a new methodology and algorithm for solving post buckling problems of a large deformed elastic beam. The total potential energy of this beam is a nonconvex functional, which can be used to model both pre- and post-buckling phenomena. By using a canonical dual finite element method, a new primal-dual semi-definite programming (PD-SDP) algorithm is presented, which can be used to obtain all possible post-buckled solutions. Applications are illustrated by several numerical examples with different boundary conditions. We find that the global minimum solution of the nonconvex po","authors_text":"David Y. Gao, Elaf J. Ali","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-15T14:39:12Z","title":"On SDP Method for Solving Canonical Dual Problem in Post Buckling of Large Deformed Elastic Beam"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04675","kind":"arxiv","version":8},"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":"sha256:487587ae11e989275c4b09d03e1eed494c297ba7601ae99e3214221b5e6ddf6d","target":"record","created_at":"2026-05-18T00:21:35Z","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":"ab8a53447cdaf4712b95c65db1ffd4aba94a0e902ffe50f990d474e8a2c6b78f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-15T14:39:12Z","title_canon_sha256":"0cce8e4fbc857331f505d067630967a9d28bec564e8d6e9c2faa147bc58be3da"},"schema_version":"1.0","source":{"id":"1609.04675","kind":"arxiv","version":8}},"canonical_sha256":"f3ebd52dcc582ea1de58b266e77a23185c4468772e522b625c218b8c300e4c23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3ebd52dcc582ea1de58b266e77a23185c4468772e522b625c218b8c300e4c23","first_computed_at":"2026-05-18T00:21:35.571165Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:35.571165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PVgfxmVbrYSNKsodfuDk9CO7VhAzPYejfHJ3fslLMcU7Z1OvG7m7rZlqYaRcVq+tgisMeac1m4Tz+no7ia60BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:35.571892Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.04675","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:487587ae11e989275c4b09d03e1eed494c297ba7601ae99e3214221b5e6ddf6d","sha256:c2f3839bf99e15e3915a30d0f85c740b35f7ac8c14c707aa92bbaffa15119799"],"state_sha256":"21e5d17e3533076ad451311d58191edfa4f51c5a8a8ccff92f6d9805c5298ab9"}