{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:PJU34EJMVFOM7OYTNKRKFKON3Q","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":"5086c1f677ace9e30f88eba465f2b525b6abd831cfcaaf429161d916f2b96fc5","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-06-18T11:24:34Z","title_canon_sha256":"87f6997ed9f437b3704a43703ff07551dbb2e99603550327cf7ec3f9d79dcd5f"},"schema_version":"1.0","source":{"id":"2506.15360","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.15360","created_at":"2026-07-05T11:23:41Z"},{"alias_kind":"arxiv_version","alias_value":"2506.15360v1","created_at":"2026-07-05T11:23:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.15360","created_at":"2026-07-05T11:23:41Z"},{"alias_kind":"pith_short_12","alias_value":"PJU34EJMVFOM","created_at":"2026-07-05T11:23:41Z"},{"alias_kind":"pith_short_16","alias_value":"PJU34EJMVFOM7OYT","created_at":"2026-07-05T11:23:41Z"},{"alias_kind":"pith_short_8","alias_value":"PJU34EJM","created_at":"2026-07-05T11:23:41Z"}],"graph_snapshots":[{"event_id":"sha256:bd2d5db5b67b9af232f99b5362a104215bfccd879d6ba11abf8f0f863d1cf29c","target":"graph","created_at":"2026-07-05T11:23:41Z","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/2506.15360/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the problem of estimating the diagonal of an implicitly given matrix $\\Ab$. For such a matrix we have access to an oracle that allows us to evaluate the matrix quadratic form $ \\ub^\\top \\Ab \\ub$. Based on this query oracle, we propose a stochastic diagonal estimation method with random variable $\\ub$ drawn from the standard Gaussian distribution. We provide the element-wise and norm-wise sample complexities of the proposed method. Our numerical experiments on different types and dimensions matrices demonstrate the effectiveness of our method and validate the tightness of theoretical r","authors_text":"Haishan Ye, Xiangyu Chang","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-06-18T11:24:34Z","title":"Stochastic Diagonal Estimation Based on Matrix Quadratic Form Oracles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.15360","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":"sha256:685e121b7c15328ec18ee16d55a98c26bd889c967ce4527246845d2079908bc7","target":"record","created_at":"2026-07-05T11:23:41Z","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":"5086c1f677ace9e30f88eba465f2b525b6abd831cfcaaf429161d916f2b96fc5","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-06-18T11:24:34Z","title_canon_sha256":"87f6997ed9f437b3704a43703ff07551dbb2e99603550327cf7ec3f9d79dcd5f"},"schema_version":"1.0","source":{"id":"2506.15360","kind":"arxiv","version":1}},"canonical_sha256":"7a69be112ca95ccfbb136aa2a2a9cddc007096233cf9a1df8fe79ed6a2d75d2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a69be112ca95ccfbb136aa2a2a9cddc007096233cf9a1df8fe79ed6a2d75d2a","first_computed_at":"2026-07-05T11:23:41.866117Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:23:41.866117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DQY4tIBB0r3c228wUA96eZ2DnADFWB4THZlffmfARRTovgmL6DmTyg9u34B2k4usg9LxOBu050VTcZEo9HKnCg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:23:41.866642Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.15360","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:685e121b7c15328ec18ee16d55a98c26bd889c967ce4527246845d2079908bc7","sha256:bd2d5db5b67b9af232f99b5362a104215bfccd879d6ba11abf8f0f863d1cf29c"],"state_sha256":"7f7a00c073dab8bb275f0108ea216a54587506633b0cfcb73d0b650b2a91afa2"}