{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FJHEGLIO7GEI764ME6QJ3CA7VZ","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":"59d455feb866a9518bea8dd812c9ef66d5da25915c9c7026f4e91c28e241b332","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-10-21T20:22:52Z","title_canon_sha256":"e8af32dee9c439bc8c4fd3bbe391b269e17a452b4aff1ce1fdc8a13ed19e431a"},"schema_version":"1.0","source":{"id":"1510.06421","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.06421","created_at":"2026-05-18T01:03:40Z"},{"alias_kind":"arxiv_version","alias_value":"1510.06421v2","created_at":"2026-05-18T01:03:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.06421","created_at":"2026-05-18T01:03:40Z"},{"alias_kind":"pith_short_12","alias_value":"FJHEGLIO7GEI","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FJHEGLIO7GEI764M","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FJHEGLIO","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:1d732d076b16838bc73546d0eacc107c5d02d7204cc878a5e867645a35eee169","target":"graph","created_at":"2026-05-18T01:03:40Z","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 technique of semidefinite programming (SDP) relaxation can be used to obtain a nontrivial bound on the optimal value of a nonconvex quadratically constrained quadratic program (QCQP). We explore concave quadratic inequalities that hold for any vector in the integer lattice ${\\bf Z}^n$, and show that adding these inequalities to a mixed-integer nonconvex QCQP can improve the SDP-based bound on the optimal value. This scheme is tested using several numerical problem instances of the max-cut problem and the integer least squares problem.","authors_text":"Jaehyun Park, Stephen Boyd","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-10-21T20:22:52Z","title":"Concave Quadratic Cuts for Mixed-Integer Quadratic Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06421","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":"sha256:6dc4310e6479f5ae9dd4ac98299faef138e64890fd9e760db5f2e566f8fb6ab8","target":"record","created_at":"2026-05-18T01:03:40Z","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":"59d455feb866a9518bea8dd812c9ef66d5da25915c9c7026f4e91c28e241b332","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-10-21T20:22:52Z","title_canon_sha256":"e8af32dee9c439bc8c4fd3bbe391b269e17a452b4aff1ce1fdc8a13ed19e431a"},"schema_version":"1.0","source":{"id":"1510.06421","kind":"arxiv","version":2}},"canonical_sha256":"2a4e432d0ef9888ffb8c27a09d881fae54c1b0394759c49f622499ad130d2c05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a4e432d0ef9888ffb8c27a09d881fae54c1b0394759c49f622499ad130d2c05","first_computed_at":"2026-05-18T01:03:40.899743Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:40.899743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r2aA4QCRJlFkEPcT9xiuD404d6vrDnmhWojCC2cdul5G0oKZpmsYeP/ToCoJdraeuqHDkTGIRR+pwgYF8PJyDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:40.900156Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.06421","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6dc4310e6479f5ae9dd4ac98299faef138e64890fd9e760db5f2e566f8fb6ab8","sha256:1d732d076b16838bc73546d0eacc107c5d02d7204cc878a5e867645a35eee169"],"state_sha256":"87acc6bc59380e48601bb4c26745fb23412a7a172a8e05a60e4e4a0f2572b6de"}