{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3DKKVBXQIAQEQIV7XRAJBZASNY","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":"966542cde223fa0925ee32a1f953aff716a60f858b68bcfd7ddc4ac6b07b34db","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-25T05:37:01Z","title_canon_sha256":"4db6980f51605cee000d203c2d83e615301924898212839427872cf985d5fc6e"},"schema_version":"1.0","source":{"id":"1705.09053","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.09053","created_at":"2026-05-18T00:19:17Z"},{"alias_kind":"arxiv_version","alias_value":"1705.09053v2","created_at":"2026-05-18T00:19:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09053","created_at":"2026-05-18T00:19:17Z"},{"alias_kind":"pith_short_12","alias_value":"3DKKVBXQIAQE","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3DKKVBXQIAQEQIV7","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3DKKVBXQ","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:8d48f8b4641af95da16fc989124f6a5660d099c291891be050f5488b0c62c846","target":"graph","created_at":"2026-05-18T00:19:17Z","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":"Let $P_n^1,\\dots, P_n^d$ be $n\\times n$ permutation matrices drawn independently and uniformly at random, and set $S_n^d:=\\sum_{\\ell=1}^d P_n^\\ell$. We show that if $\\log^{12}n/(\\log \\log n)^{4} \\le d=O(n)$, then the empirical spectral distribution of $S_n^d/\\sqrt{d}$ converges weakly to the circular law in probability as $n \\to \\infty$.","authors_text":"Anirban Basak, Nicholas Cook, Ofer Zeitouni","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-25T05:37:01Z","title":"Circular law for the sum of random permutation matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09053","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:cfb9c9cc0af6ab9fc7951bcaf11f69aacd5705cfee7dd886b232ee3058f4d71c","target":"record","created_at":"2026-05-18T00:19:17Z","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":"966542cde223fa0925ee32a1f953aff716a60f858b68bcfd7ddc4ac6b07b34db","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-25T05:37:01Z","title_canon_sha256":"4db6980f51605cee000d203c2d83e615301924898212839427872cf985d5fc6e"},"schema_version":"1.0","source":{"id":"1705.09053","kind":"arxiv","version":2}},"canonical_sha256":"d8d4aa86f040204822bfbc4090e4126e01048eee89d05a4aa33a73a1707c899a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8d4aa86f040204822bfbc4090e4126e01048eee89d05a4aa33a73a1707c899a","first_computed_at":"2026-05-18T00:19:17.205476Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:17.205476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"18hXiNhguEIocip1EXqudBuSKx+VeMhdWywC/YGYwfcMjhznv5cCmlSxCZidQaP6GBETbZzlOLISmR7Y9wSSBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:17.206089Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.09053","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfb9c9cc0af6ab9fc7951bcaf11f69aacd5705cfee7dd886b232ee3058f4d71c","sha256:8d48f8b4641af95da16fc989124f6a5660d099c291891be050f5488b0c62c846"],"state_sha256":"ab56e04363d572f47392627c5a629d66531052a4c005dd9864b316badb6a6f24"}