{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:GVH43T2F3K5NID6HIL4SHX2VSO","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":"5e51b832426ed7276377f71b5980359e90ec30e2186b1beac598787ced29c572","cross_cats_sorted":["cs.DS","cs.NA","math.NA","math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-06-04T17:20:42Z","title_canon_sha256":"ae44ec04607a78b8dd2e07d9ad01ed116c967668834d3b6f2851b3ea70d2dac2"},"schema_version":"1.0","source":{"id":"2406.02502","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.02502","created_at":"2026-07-05T08:27:20Z"},{"alias_kind":"arxiv_version","alias_value":"2406.02502v1","created_at":"2026-07-05T08:27:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.02502","created_at":"2026-07-05T08:27:20Z"},{"alias_kind":"pith_short_12","alias_value":"GVH43T2F3K5N","created_at":"2026-07-05T08:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"GVH43T2F3K5NID6H","created_at":"2026-07-05T08:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"GVH43T2F","created_at":"2026-07-05T08:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:0f0c4ef9baec2c6ad9c6ded83733ef7c03f058806e73434e58e76e2ae3c732d1","target":"graph","created_at":"2026-07-05T08:27:20Z","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/2406.02502/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a matrix $A \\in \\mathbb{R}^{m\\times d}$ with singular values $\\sigma_1\\geq \\cdots \\geq \\sigma_d$, and a random matrix $G \\in \\mathbb{R}^{m\\times d}$ with iid $N(0,T)$ entries for some $T>0$, we derive new bounds on the Frobenius distance between subspaces spanned by the top-$k$ (right) singular vectors of $A$ and $A+G$. This problem arises in numerous applications in statistics where a data matrix may be corrupted by Gaussian noise, and in the analysis of the Gaussian mechanism in differential privacy, where Gaussian noise is added to data to preserve private information. We show that, f","authors_text":"Oren Mangoubi, Peiyao Lai","cross_cats":["cs.DS","cs.NA","math.NA","math.PR","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-06-04T17:20:42Z","title":"Singular Subspace Perturbation Bounds via Rectangular Random Matrix Diffusions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.02502","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:f54293c47eadfeca4efc738d4065e194ef79feddae65a64e4d6f1219b150e09f","target":"record","created_at":"2026-07-05T08:27:20Z","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":"5e51b832426ed7276377f71b5980359e90ec30e2186b1beac598787ced29c572","cross_cats_sorted":["cs.DS","cs.NA","math.NA","math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-06-04T17:20:42Z","title_canon_sha256":"ae44ec04607a78b8dd2e07d9ad01ed116c967668834d3b6f2851b3ea70d2dac2"},"schema_version":"1.0","source":{"id":"2406.02502","kind":"arxiv","version":1}},"canonical_sha256":"354fcdcf45dabad40fc742f923df5593aa3da192390939ca532896cf67d2ea0c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"354fcdcf45dabad40fc742f923df5593aa3da192390939ca532896cf67d2ea0c","first_computed_at":"2026-07-05T08:27:20.672801Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:27:20.672801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DN0azFvIFuYEVHXqfXyinRSgoQVUKSTBx/lxeJxrk1qaifmWGSH82WbblB1chJp9h8K8eGJ+MHwrtmLCkOF4Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:27:20.673349Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.02502","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f54293c47eadfeca4efc738d4065e194ef79feddae65a64e4d6f1219b150e09f","sha256:0f0c4ef9baec2c6ad9c6ded83733ef7c03f058806e73434e58e76e2ae3c732d1"],"state_sha256":"b73378cce28636eb1d341c3714cfdfa858620afdb9f72092da1b774efe482041"}