{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:XBNR55GHLT62Z5CDVX5KMGO33G","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":"fa1206a2b26cb25895859e36acfd798ac3f76cee106a124833d73feaa7e38017","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-02-19T15:31:35Z","title_canon_sha256":"a2f53cd0731d15fc85dd2a10f7106d984522a6b66a17b0dfb57baeefe32a818f"},"schema_version":"1.0","source":{"id":"2502.13819","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.13819","created_at":"2026-07-05T10:22:13Z"},{"alias_kind":"arxiv_version","alias_value":"2502.13819v2","created_at":"2026-07-05T10:22:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.13819","created_at":"2026-07-05T10:22:13Z"},{"alias_kind":"pith_short_12","alias_value":"XBNR55GHLT62","created_at":"2026-07-05T10:22:13Z"},{"alias_kind":"pith_short_16","alias_value":"XBNR55GHLT62Z5CD","created_at":"2026-07-05T10:22:13Z"},{"alias_kind":"pith_short_8","alias_value":"XBNR55GH","created_at":"2026-07-05T10:22:13Z"}],"graph_snapshots":[{"event_id":"sha256:aaadc00cc2d990480c0bb0b6a6132fe9e7ecbb4f87240fd56ab5e9253c1f39f1","target":"graph","created_at":"2026-07-05T10:22:13Z","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/2502.13819/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $A$ be an $n\\times n$ random matrix with independent, identically distributed mean 0, variance 1 subgaussian entries. We prove that $$ \\mathbb{P}(A\\text{ has distinct singular values})\\geq 1-e^{-cn} $$ for some $c>0$, confirming a conjecture of Vu. This result is then generalized to singular values of rectangular random matrices with i.i.d. entries.\n  We also prove that for two fixed real numbers $\\lambda_1,\\lambda_2$ with a sufficient lower bound on $|\\lambda_1-\\lambda_2|$, we have a joint singular value small ball estimate for any $\\epsilon>0$ $$ \\mathbb{P}(\\sigma_{min}(A-\\lambda_1I_n)\\l","authors_text":"Yi Han","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-02-19T15:31:35Z","title":"Simplicity of singular value spectrum of random matrices and two-point quantitative invertibility"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.13819","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:acebf77609e017b6ce3ee460bc61166dc6bb843fa0ebcd8224a05e9fcb998094","target":"record","created_at":"2026-07-05T10:22:13Z","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":"fa1206a2b26cb25895859e36acfd798ac3f76cee106a124833d73feaa7e38017","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-02-19T15:31:35Z","title_canon_sha256":"a2f53cd0731d15fc85dd2a10f7106d984522a6b66a17b0dfb57baeefe32a818f"},"schema_version":"1.0","source":{"id":"2502.13819","kind":"arxiv","version":2}},"canonical_sha256":"b85b1ef4c75cfdacf443adfaa619dbd9aed729e657d333bf617e7e3c1faff2bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b85b1ef4c75cfdacf443adfaa619dbd9aed729e657d333bf617e7e3c1faff2bd","first_computed_at":"2026-07-05T10:22:13.856008Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:22:13.856008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VI79iqOAgIrbwJAu1UWjD0ECKP3Wzr4ATmzslNY5+xE7gZGA8xbwBInH+2v71Ueiu+w/BHi/MozJ/HMca8ZUBg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:22:13.856709Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.13819","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:acebf77609e017b6ce3ee460bc61166dc6bb843fa0ebcd8224a05e9fcb998094","sha256:aaadc00cc2d990480c0bb0b6a6132fe9e7ecbb4f87240fd56ab5e9253c1f39f1"],"state_sha256":"4c2b2af733fb4fe6f044901bb7f1a7d72bcb54f7d278dfa5cc9bb82ff95af2a9"}