{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3VG4GQZ2I7F4KRJ545AUKEDW6Z","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":"3adc5618f306f87a7392bb9644a7ebbb792138c79a87c41205cc896ed8f60a86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2025-04-24T21:22:17Z","title_canon_sha256":"cb0db65a85a963f2c30c1d7f9b897e488ad5312bd9aab0acfcbcd110db2da824"},"schema_version":"1.0","source":{"id":"2504.17947","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.17947","created_at":"2026-07-05T10:53:59Z"},{"alias_kind":"arxiv_version","alias_value":"2504.17947v1","created_at":"2026-07-05T10:53:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.17947","created_at":"2026-07-05T10:53:59Z"},{"alias_kind":"pith_short_12","alias_value":"3VG4GQZ2I7F4","created_at":"2026-07-05T10:53:59Z"},{"alias_kind":"pith_short_16","alias_value":"3VG4GQZ2I7F4KRJ5","created_at":"2026-07-05T10:53:59Z"},{"alias_kind":"pith_short_8","alias_value":"3VG4GQZ2","created_at":"2026-07-05T10:53:59Z"}],"graph_snapshots":[{"event_id":"sha256:5ad89585d711b07d8635f596b4045eb11c455a4077d6bcd912cd2f5430c1619e","target":"graph","created_at":"2026-07-05T10:53:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2504.17947/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a basic computational task of finding $s$ planted rank-1 $m \\times n$ matrices in a linear subspace $\\mathcal{U} \\subseteq \\mathbb{R}^{m \\times n}$ where $\\dim(\\mathcal{U}) = R \\ge s$. The work of Johnston-Lovitz-Vijayaraghavan (FOCS 2023) gave a polynomial-time algorithm for this task and proved that it succeeds when ${R \\le (1-o(1))mn/4}$, under minimal genericity assumptions on the input. Aiming to precisely characterize the performance of this algorithm, we improve the bound to ${R \\le (1-o(1))mn/2}$ and also prove that the algorithm fails when ${R \\ge (1+o(1))mn/\\sqrt{2}}$. Nu","authors_text":"Alexander S. Wein, Jeshu Dastidar, Tait Weicht","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2025-04-24T21:22:17Z","title":"Improving the Threshold for Finding Rank-1 Matrices in a Subspace"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.17947","kind":"arxiv","version":1},"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:d9c3c8705ca691a12b3c6e7c3351c5bbc603d755b39ab8bae769bf26d1cace64","target":"record","created_at":"2026-07-05T10:53:59Z","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":"3adc5618f306f87a7392bb9644a7ebbb792138c79a87c41205cc896ed8f60a86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2025-04-24T21:22:17Z","title_canon_sha256":"cb0db65a85a963f2c30c1d7f9b897e488ad5312bd9aab0acfcbcd110db2da824"},"schema_version":"1.0","source":{"id":"2504.17947","kind":"arxiv","version":1}},"canonical_sha256":"dd4dc3433a47cbc5453de741451076f65513a9846d204a497897974c0f568c86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd4dc3433a47cbc5453de741451076f65513a9846d204a497897974c0f568c86","first_computed_at":"2026-07-05T10:53:59.172207Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:53:59.172207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8mSdd8Vf1tWulIGOCC6ZBuFUiU4nVDeJYcRosmq3QugxwpZBcTNimTfLeXmvlvBUMyY2ODjAS5yB9Ead8x6NDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:53:59.172674Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.17947","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9c3c8705ca691a12b3c6e7c3351c5bbc603d755b39ab8bae769bf26d1cace64","sha256:5ad89585d711b07d8635f596b4045eb11c455a4077d6bcd912cd2f5430c1619e"],"state_sha256":"499ffe6db333e1d3b20f7bab20cb085a96b4ac4caa3ff4f40b3e0b7e78721cc8"}