{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WXXCUODSFDQIIK6QZ3MVFTS7KD","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":"5407dbcf657bd6886e469472867404648a738f3e11b54931dedff69fd68f17df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-05T02:32:54Z","title_canon_sha256":"5a4c8068e412da82080ddb813300fb3ec667be340d1128a532939b79029713b9"},"schema_version":"1.0","source":{"id":"1609.01019","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01019","created_at":"2026-05-18T00:45:58Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01019v2","created_at":"2026-05-18T00:45:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01019","created_at":"2026-05-18T00:45:58Z"},{"alias_kind":"pith_short_12","alias_value":"WXXCUODSFDQI","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"WXXCUODSFDQIIK6Q","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"WXXCUODS","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:d681de74f4c44c1356d62a1a47141846047ba39191db15b90462b6d728652dfa","target":"graph","created_at":"2026-05-18T00:45:58Z","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":"In this paper, we present a branch and bound algorithm for extracting approximate solutions to Global Polynomial Optimization (GPO) problems with bounded feasible sets.\n  The algorithm is based on a combination of SOS/Moment relaxations and successively bisecting a hyper-rectangle containing the feasible set of the GPO problem. At each iteration, the algorithm makes a comparison between the volume of the hyper-rectangles and their associated lower bounds to the GPO problem obtained by SOS/Moment relaxations to choose and subdivide an existing hyper-rectangle. For any desired accuracy, if we us","authors_text":"Hesameddin Mohammadi, Matthew M. Peet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-05T02:32:54Z","title":"Combining SOS and Moment Relaxations with Branch and Bound to Extract Solutions to Global Polynomial Optimization Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01019","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":"sha256:0a99630eb4db94375cf2a7688fa882e07ade91dc3798ed9f9c293bbda5bd61c9","target":"record","created_at":"2026-05-18T00:45:58Z","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":"5407dbcf657bd6886e469472867404648a738f3e11b54931dedff69fd68f17df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-05T02:32:54Z","title_canon_sha256":"5a4c8068e412da82080ddb813300fb3ec667be340d1128a532939b79029713b9"},"schema_version":"1.0","source":{"id":"1609.01019","kind":"arxiv","version":2}},"canonical_sha256":"b5ee2a387228e0842bd0ced952ce5f50e0740cc8a71f7f898343155e595c4c9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5ee2a387228e0842bd0ced952ce5f50e0740cc8a71f7f898343155e595c4c9d","first_computed_at":"2026-05-18T00:45:58.645829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:58.645829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LT8HnD6QGIZpaALtE6efSQZZpuVJ4KkR0IhRopehBOS6NGWE8LWBtSjT0UDx7BmX2LlYkYWyoxmoi8kluK1yCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:58.646291Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.01019","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a99630eb4db94375cf2a7688fa882e07ade91dc3798ed9f9c293bbda5bd61c9","sha256:d681de74f4c44c1356d62a1a47141846047ba39191db15b90462b6d728652dfa"],"state_sha256":"b736171469793382de34424b8282bf3d568d2f52a19aad1fcaac9fb7f6ef1824"}