{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JY3BULFMDIW55P6DBDHMLJN7KX","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":"e63d2cd654c8a5f570a35f0023f98300f0cc61f992f8bccd2b8d663c9ac8d824","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-26T22:17:08Z","title_canon_sha256":"b81027a7967d42ac9e938085e44da5f903895e58c03ec182c7bd13a04e71f13c"},"schema_version":"1.0","source":{"id":"1802.09630","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.09630","created_at":"2026-05-18T00:07:55Z"},{"alias_kind":"arxiv_version","alias_value":"1802.09630v2","created_at":"2026-05-18T00:07:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.09630","created_at":"2026-05-18T00:07:55Z"},{"alias_kind":"pith_short_12","alias_value":"JY3BULFMDIW5","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"JY3BULFMDIW55P6D","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"JY3BULFM","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:d26cfa8028b160c2757a45860623a54bcd70e1d1ba80103e963da229e3547484","target":"graph","created_at":"2026-05-18T00:07:55Z","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":"Convexity plays a prominent role in a number of problems, but practical considerations frequently give rise to non-convex functions. We suggest a method for determining convex regions, and also for assessing the lack of convexity in the other regions. The method relies on a specially constructed decomposition of symmetric matrices, such as the Hessian. We illustrate theoretical results using several examples, one of which analyses a problem arising in risk measurement and management in insurance and finance.","authors_text":"Elina Moldavskaya, Ri\\v{c}ardas Zitikis, Youri Davydov","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-26T22:17:08Z","title":"Searching for, and quantifying, non-convexity of functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09630","kind":"arxiv","version":2},"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":"sha256:710aca089bc4f51f83d53db907b0bc20d6ea79e7d1070d62a1e55748dc07e7df","target":"record","created_at":"2026-05-18T00:07:55Z","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":"e63d2cd654c8a5f570a35f0023f98300f0cc61f992f8bccd2b8d663c9ac8d824","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-26T22:17:08Z","title_canon_sha256":"b81027a7967d42ac9e938085e44da5f903895e58c03ec182c7bd13a04e71f13c"},"schema_version":"1.0","source":{"id":"1802.09630","kind":"arxiv","version":2}},"canonical_sha256":"4e361a2cac1a2ddebfc308cec5a5bf55fc3aa9bb00abaf933ca1c3acf489de4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e361a2cac1a2ddebfc308cec5a5bf55fc3aa9bb00abaf933ca1c3acf489de4e","first_computed_at":"2026-05-18T00:07:55.364406Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:55.364406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ocvoz9pCGVJg8YOhK3hBllrukvRQ6YV5gXwdBZiAouF06PJtnh49lHumWEg+WK+8mX+/MRD2nMFRQ1GNIgucDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:55.365046Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.09630","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:710aca089bc4f51f83d53db907b0bc20d6ea79e7d1070d62a1e55748dc07e7df","sha256:d26cfa8028b160c2757a45860623a54bcd70e1d1ba80103e963da229e3547484"],"state_sha256":"a679cc23ae253e1bd7d0e93ddd1e4b59787e96c3e69fd83309566b9d6df85878"}