{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:7ZIH2Z6RIMLNOL7SW7CBUV3KPI","short_pith_number":"pith:7ZIH2Z6R","canonical_record":{"source":{"id":"1301.2382","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-11T02:51:13Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"0a25a64ab4b843723afd5114e9570e2db64a4fc97a09f61e35131f19481c7b2a","abstract_canon_sha256":"a2b929b7c8e9e77518018f8cd09791dfbddd38aecf87a9f051bd0ce090225a34"},"schema_version":"1.0"},"canonical_sha256":"fe507d67d14316d72ff2b7c41a576a7a265f373f2da812ee374e413119c713cc","source":{"kind":"arxiv","id":"1301.2382","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2382","created_at":"2026-05-18T03:17:01Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2382v2","created_at":"2026-05-18T03:17:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2382","created_at":"2026-05-18T03:17:01Z"},{"alias_kind":"pith_short_12","alias_value":"7ZIH2Z6RIMLN","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"7ZIH2Z6RIMLNOL7S","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"7ZIH2Z6R","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:7ZIH2Z6RIMLNOL7SW7CBUV3KPI","target":"record","payload":{"canonical_record":{"source":{"id":"1301.2382","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-11T02:51:13Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"0a25a64ab4b843723afd5114e9570e2db64a4fc97a09f61e35131f19481c7b2a","abstract_canon_sha256":"a2b929b7c8e9e77518018f8cd09791dfbddd38aecf87a9f051bd0ce090225a34"},"schema_version":"1.0"},"canonical_sha256":"fe507d67d14316d72ff2b7c41a576a7a265f373f2da812ee374e413119c713cc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:01.016294Z","signature_b64":"7SUZa3GBuCYF/2b5/YpW/Tuhyz89QWlxPgDRaiRytCU8UCkbAQj95PN4vSuO4uII+qeuJqrR0tCOI8LAJ7YOAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe507d67d14316d72ff2b7c41a576a7a265f373f2da812ee374e413119c713cc","last_reissued_at":"2026-05-18T03:17:01.015598Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:01.015598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.2382","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:17:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TZMKag4DAFFbr0F+C+Pa89YwIQOZ4jJQrArpc1LvRzsJMrZM6/7t9ZPnPlagZ9rw4UyjqtnPcNcl1hDeO4vJCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:33:07.390751Z"},"content_sha256":"aa32a8d8b94709144e00f541fa02c9a143baf54f9de47e5194ecae1da6fd3eec","schema_version":"1.0","event_id":"sha256:aa32a8d8b94709144e00f541fa02c9a143baf54f9de47e5194ecae1da6fd3eec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:7ZIH2Z6RIMLNOL7SW7CBUV3KPI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Recent developments in non-asymptotic theory of random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Mark Rudelson","submitted_at":"2013-01-11T02:51:13Z","abstract_excerpt":"Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications in high-dimensional convexity, analysis of convergence of algorithms, as well as in random matrix theory itself. In these notes we survey some recent results in this area and describe the techniques aimed for obtaining explicit probability bounds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2382","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:17:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XxNufGibOH8j9t3OzFZLzfNWHV253MjbuvUFzZWkxzfM25Gswk+jJkzWVKawAh/vMpzbcdt+rR8AXkJAYemJBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:33:07.391098Z"},"content_sha256":"7a91f4e2552246697fcc00cc466767ab20bd2f07b35e6988b6f65b152ca0f5ad","schema_version":"1.0","event_id":"sha256:7a91f4e2552246697fcc00cc466767ab20bd2f07b35e6988b6f65b152ca0f5ad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7ZIH2Z6RIMLNOL7SW7CBUV3KPI/bundle.json","state_url":"https://pith.science/pith/7ZIH2Z6RIMLNOL7SW7CBUV3KPI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7ZIH2Z6RIMLNOL7SW7CBUV3KPI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T03:33:07Z","links":{"resolver":"https://pith.science/pith/7ZIH2Z6RIMLNOL7SW7CBUV3KPI","bundle":"https://pith.science/pith/7ZIH2Z6RIMLNOL7SW7CBUV3KPI/bundle.json","state":"https://pith.science/pith/7ZIH2Z6RIMLNOL7SW7CBUV3KPI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7ZIH2Z6RIMLNOL7SW7CBUV3KPI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7ZIH2Z6RIMLNOL7SW7CBUV3KPI","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":"a2b929b7c8e9e77518018f8cd09791dfbddd38aecf87a9f051bd0ce090225a34","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-11T02:51:13Z","title_canon_sha256":"0a25a64ab4b843723afd5114e9570e2db64a4fc97a09f61e35131f19481c7b2a"},"schema_version":"1.0","source":{"id":"1301.2382","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2382","created_at":"2026-05-18T03:17:01Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2382v2","created_at":"2026-05-18T03:17:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2382","created_at":"2026-05-18T03:17:01Z"},{"alias_kind":"pith_short_12","alias_value":"7ZIH2Z6RIMLN","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"7ZIH2Z6RIMLNOL7S","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"7ZIH2Z6R","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:7a91f4e2552246697fcc00cc466767ab20bd2f07b35e6988b6f65b152ca0f5ad","target":"graph","created_at":"2026-05-18T03:17:01Z","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":"Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications in high-dimensional convexity, analysis of convergence of algorithms, as well as in random matrix theory itself. In these notes we survey some recent results in this area and describe the techniques aimed for obtaining explicit probability bounds.","authors_text":"Mark Rudelson","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-11T02:51:13Z","title":"Recent developments in non-asymptotic theory of random matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2382","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:aa32a8d8b94709144e00f541fa02c9a143baf54f9de47e5194ecae1da6fd3eec","target":"record","created_at":"2026-05-18T03:17:01Z","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":"a2b929b7c8e9e77518018f8cd09791dfbddd38aecf87a9f051bd0ce090225a34","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-11T02:51:13Z","title_canon_sha256":"0a25a64ab4b843723afd5114e9570e2db64a4fc97a09f61e35131f19481c7b2a"},"schema_version":"1.0","source":{"id":"1301.2382","kind":"arxiv","version":2}},"canonical_sha256":"fe507d67d14316d72ff2b7c41a576a7a265f373f2da812ee374e413119c713cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe507d67d14316d72ff2b7c41a576a7a265f373f2da812ee374e413119c713cc","first_computed_at":"2026-05-18T03:17:01.015598Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:01.015598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7SUZa3GBuCYF/2b5/YpW/Tuhyz89QWlxPgDRaiRytCU8UCkbAQj95PN4vSuO4uII+qeuJqrR0tCOI8LAJ7YOAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:01.016294Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.2382","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa32a8d8b94709144e00f541fa02c9a143baf54f9de47e5194ecae1da6fd3eec","sha256:7a91f4e2552246697fcc00cc466767ab20bd2f07b35e6988b6f65b152ca0f5ad"],"state_sha256":"675c8a31fdfea979aa30d6e241f556413fbbed54ff3acd3525d9fc6b98560741"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K7NvZYJkqHHUJSFGwRQIshDancE3XzxscyZtVZqHsxvNvPSNWavqg/m6T0kVlYce4SLYY73+0L58tVpxMdZqDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T03:33:07.393107Z","bundle_sha256":"d89fb2640724adecae3ceee9db27ea25ef33e842a7c37b7eef9076eacc92a0cb"}}