{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:PJ7NNIHKPMJKFOJTIINHWEDXVF","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":"70f94d940b96a305714798f2e89310ed6291c4474898df07e12e184b9001e714","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-05-12T17:06:02Z","title_canon_sha256":"ddd3a69f07e3f098b8c5001f7f3ae44c99d1cca31a5fd20aedf3fd1f46765b2b"},"schema_version":"1.0","source":{"id":"0905.1909","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.1909","created_at":"2026-05-18T01:36:52Z"},{"alias_kind":"arxiv_version","alias_value":"0905.1909v1","created_at":"2026-05-18T01:36:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.1909","created_at":"2026-05-18T01:36:52Z"},{"alias_kind":"pith_short_12","alias_value":"PJ7NNIHKPMJK","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"PJ7NNIHKPMJKFOJT","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"PJ7NNIHK","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:55c314510c39d8f4e46c9495c5adb16a8fdd338d6699d4c8633a066627e4c3c3","target":"graph","created_at":"2026-05-18T01:36:52Z","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":"We show that the absolute value of the determinant of a matrix with random independent (but not necessarily iid) entries is strongly concentrated around its mean. As an application, we show that the Godsil-Gutman and Barvinok estimators for the permanent of a strictly positive matrix give sub-exponential approximation ratios with high probability.","authors_text":"Kevin P. Costello, Van Vu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-05-12T17:06:02Z","title":"Concentration of random determinants and permanent estimators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.1909","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":"sha256:4500f4f856c19edbe6c7adc4214fb7dd7f300523f2535f2c750dd7e4788cc15f","target":"record","created_at":"2026-05-18T01:36:52Z","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":"70f94d940b96a305714798f2e89310ed6291c4474898df07e12e184b9001e714","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-05-12T17:06:02Z","title_canon_sha256":"ddd3a69f07e3f098b8c5001f7f3ae44c99d1cca31a5fd20aedf3fd1f46765b2b"},"schema_version":"1.0","source":{"id":"0905.1909","kind":"arxiv","version":1}},"canonical_sha256":"7a7ed6a0ea7b12a2b933421a7b1077a9682477b19154dfba318c08ebc21eb529","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a7ed6a0ea7b12a2b933421a7b1077a9682477b19154dfba318c08ebc21eb529","first_computed_at":"2026-05-18T01:36:52.056906Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:52.056906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f1sHqdA8J1GnI7ziml52cJGMcuPdNP2SEJ89RL7ZGje2zx0YdB36bu3n0xqeRLsWNofnoOpBfePhqW8zfnnIDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:52.057644Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.1909","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4500f4f856c19edbe6c7adc4214fb7dd7f300523f2535f2c750dd7e4788cc15f","sha256:55c314510c39d8f4e46c9495c5adb16a8fdd338d6699d4c8633a066627e4c3c3"],"state_sha256":"8dd671b1b2bcf5ad7f995c24f0357a6ed5fe29e0fd8a5a5b538fcd8716f8beec"}