{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:5FXESDOY5BTD5BD6P2IJXF5IGK","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":"c7715e6651c885d97232101c8bbfb419f5bcf45c1b3e899ec48404d1c2c2822b","cross_cats_sorted":["cs.CC","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-02-19T22:18:46Z","title_canon_sha256":"7345224c094d7e295977f305678313a9c4e4cfe367a44097cc3cf522f7248609"},"schema_version":"1.0","source":{"id":"1902.07324","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.07324","created_at":"2026-05-17T23:49:14Z"},{"alias_kind":"arxiv_version","alias_value":"1902.07324v2","created_at":"2026-05-17T23:49:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.07324","created_at":"2026-05-17T23:49:14Z"},{"alias_kind":"pith_short_12","alias_value":"5FXESDOY5BTD","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"5FXESDOY5BTD5BD6","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"5FXESDOY","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:6918395079574d36c07a787183685ed6d4a67fcf63e8db2cfae7f4471e5e1d8f","target":"graph","created_at":"2026-05-17T23:49:14Z","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":"Given a random $n \\times n$ symmetric matrix $\\boldsymbol W$ drawn from the Gaussian orthogonal ensemble (GOE), we consider the problem of certifying an upper bound on the maximum value of the quadratic form $\\boldsymbol x^\\top \\boldsymbol W \\boldsymbol x$ over all vectors $\\boldsymbol x$ in a constraint set $\\mathcal{S} \\subset \\mathbb{R}^n$. For a certain class of normalized constraint sets $\\mathcal{S}$ we show that, conditional on certain complexity-theoretic assumptions, there is no polynomial-time algorithm certifying a better upper bound than the largest eigenvalue of $\\boldsymbol W$. A","authors_text":"Afonso S. Bandeira, Alexander S. Wein, Dmitriy Kunisky","cross_cats":["cs.CC","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-02-19T22:18:46Z","title":"Computational Hardness of Certifying Bounds on Constrained PCA Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.07324","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:c69a8b7dd6beacfe5f668d3eb0bbaaee3db7aa985b2e20e241879a71feb6c26a","target":"record","created_at":"2026-05-17T23:49:14Z","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":"c7715e6651c885d97232101c8bbfb419f5bcf45c1b3e899ec48404d1c2c2822b","cross_cats_sorted":["cs.CC","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-02-19T22:18:46Z","title_canon_sha256":"7345224c094d7e295977f305678313a9c4e4cfe367a44097cc3cf522f7248609"},"schema_version":"1.0","source":{"id":"1902.07324","kind":"arxiv","version":2}},"canonical_sha256":"e96e490dd8e8663e847e7e909b97a8328fd51cd0179d6015aac76b98188d4ddc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e96e490dd8e8663e847e7e909b97a8328fd51cd0179d6015aac76b98188d4ddc","first_computed_at":"2026-05-17T23:49:14.596199Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:14.596199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zv7sx2o9ugE9xxi7qfIICpj7bDPtmnqoXI6m1xCVb1kcKqIqUvgdhcmXXteDW2OCdnm+do0wkQo6Ne9omqwLBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:14.596974Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.07324","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c69a8b7dd6beacfe5f668d3eb0bbaaee3db7aa985b2e20e241879a71feb6c26a","sha256:6918395079574d36c07a787183685ed6d4a67fcf63e8db2cfae7f4471e5e1d8f"],"state_sha256":"f5f084a43f9395f4765c119976c7d63a8cfd1c88dcd308c5b075975987d76fea"}