{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:6RNH3ZY26AEYHPKCGN2525RL6J","short_pith_number":"pith:6RNH3ZY2","schema_version":"1.0","canonical_sha256":"f45a7de71af00983bd423375dd762bf27247f1fa95bbf0225ac38a98850942f5","source":{"kind":"arxiv","id":"2605.18620","version":1},"attestation_state":"computed","paper":{"title":"Singleton Optimality in Standard Quadratic Programs with the GOE","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Xin Chen","submitted_at":"2026-05-18T16:29:32Z","abstract_excerpt":"We study the standard quadratic optimization problem over the simplex when the objective matrix is drawn from the Gaussian Orthogonal Ensemble (GOE). Let \\(\\kappa_n\\) denote the support size of the almost surely unique global optimizer. We prove \\[ \\Prob(\\kappa_n>1)\\sim 2\\sqrt{2\\pi}\\,\\frac{\\sqrt{\\log n}}{n}. \\] The proof combines an exact two-coordinate condition for edge improvement with a product formula obtained by conditioning on the diagonal order statistics. Boundary-layer estimates identify the leading contribution and show that supports of size at least three are negligible. Consequent"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.18620","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-05-18T16:29:32Z","cross_cats_sorted":[],"title_canon_sha256":"69700cbacfe97ddc12d6f4a3d0abc74ab2317236fa5eef45a7275e67b15bb63e","abstract_canon_sha256":"c065c81bc8d52bff60d5961b995c9903ad04dedc204087efc3cd296b41338b41"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:06:11.179774Z","signature_b64":"d33Op5COIHll1yEr5ERMilczdpUZJ1t4P1xmw9KcgOyFdCh3H9y48DzePOIyvVJFIE1EKUoQSw743ZRcz8/ZCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f45a7de71af00983bd423375dd762bf27247f1fa95bbf0225ac38a98850942f5","last_reissued_at":"2026-05-20T00:06:11.179027Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:06:11.179027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Singleton Optimality in Standard Quadratic Programs with the GOE","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Xin Chen","submitted_at":"2026-05-18T16:29:32Z","abstract_excerpt":"We study the standard quadratic optimization problem over the simplex when the objective matrix is drawn from the Gaussian Orthogonal Ensemble (GOE). Let \\(\\kappa_n\\) denote the support size of the almost surely unique global optimizer. We prove \\[ \\Prob(\\kappa_n>1)\\sim 2\\sqrt{2\\pi}\\,\\frac{\\sqrt{\\log n}}{n}. \\] The proof combines an exact two-coordinate condition for edge improvement with a product formula obtained by conditioning on the diagonal order statistics. Boundary-layer estimates identify the leading contribution and show that supports of size at least three are negligible. Consequent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18620","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.18620/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T00:01:59.222559Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"04320d06a20cf5265df331d11a30ecfd6abc33e097257408ce4cf85a0371f942"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2605.18620","created_at":"2026-05-20T00:06:11.179138+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.18620v1","created_at":"2026-05-20T00:06:11.179138+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.18620","created_at":"2026-05-20T00:06:11.179138+00:00"},{"alias_kind":"pith_short_12","alias_value":"6RNH3ZY26AEY","created_at":"2026-05-20T00:06:11.179138+00:00"},{"alias_kind":"pith_short_16","alias_value":"6RNH3ZY26AEYHPKC","created_at":"2026-05-20T00:06:11.179138+00:00"},{"alias_kind":"pith_short_8","alias_value":"6RNH3ZY2","created_at":"2026-05-20T00:06:11.179138+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6RNH3ZY26AEYHPKCGN2525RL6J","json":"https://pith.science/pith/6RNH3ZY26AEYHPKCGN2525RL6J.json","graph_json":"https://pith.science/api/pith-number/6RNH3ZY26AEYHPKCGN2525RL6J/graph.json","events_json":"https://pith.science/api/pith-number/6RNH3ZY26AEYHPKCGN2525RL6J/events.json","paper":"https://pith.science/paper/6RNH3ZY2"},"agent_actions":{"view_html":"https://pith.science/pith/6RNH3ZY26AEYHPKCGN2525RL6J","download_json":"https://pith.science/pith/6RNH3ZY26AEYHPKCGN2525RL6J.json","view_paper":"https://pith.science/paper/6RNH3ZY2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.18620&json=true","fetch_graph":"https://pith.science/api/pith-number/6RNH3ZY26AEYHPKCGN2525RL6J/graph.json","fetch_events":"https://pith.science/api/pith-number/6RNH3ZY26AEYHPKCGN2525RL6J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6RNH3ZY26AEYHPKCGN2525RL6J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6RNH3ZY26AEYHPKCGN2525RL6J/action/storage_attestation","attest_author":"https://pith.science/pith/6RNH3ZY26AEYHPKCGN2525RL6J/action/author_attestation","sign_citation":"https://pith.science/pith/6RNH3ZY26AEYHPKCGN2525RL6J/action/citation_signature","submit_replication":"https://pith.science/pith/6RNH3ZY26AEYHPKCGN2525RL6J/action/replication_record"}},"created_at":"2026-05-20T00:06:11.179138+00:00","updated_at":"2026-05-20T00:06:11.179138+00:00"}