{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:E7IG4P6SZADHU5GQOD3RIX43PJ","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":"a7ffae89b2d4ab541da805a0ffa78c3fc768fe2464dcab22aafb8ac8a34a9da3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-04T14:00:07Z","title_canon_sha256":"3a3b1720aaccbd0e95bb1de7ac8a9645483da71f756f9ddca2ec0c4da9681d59"},"schema_version":"1.0","source":{"id":"1112.0753","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.0753","created_at":"2026-05-18T04:07:05Z"},{"alias_kind":"arxiv_version","alias_value":"1112.0753v1","created_at":"2026-05-18T04:07:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0753","created_at":"2026-05-18T04:07:05Z"},{"alias_kind":"pith_short_12","alias_value":"E7IG4P6SZADH","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"E7IG4P6SZADHU5GQ","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"E7IG4P6S","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:8cc599b362f68145d141b680c9294beaf8adf69756629c954fca1b5dcc927628","target":"graph","created_at":"2026-05-18T04:07:05Z","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":"It is shown that a random $(0,1)$ matrix whose rows are independent random vectors of exactly $n/2$ zero components is non-singular with probability $1-O(n^{-C})$ for any $C>0$. The proof uses a non-standard inverse-type Littlewood-Offord result.","authors_text":"Hoi H. Nguyen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-04T14:00:07Z","title":"On the singularity of random combinatorial matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0753","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":"sha256:805f6d7986f7e5719198c7c81c3485fe6fe2acb4c7c59cf4003b59fe18d36b37","target":"record","created_at":"2026-05-18T04:07:05Z","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":"a7ffae89b2d4ab541da805a0ffa78c3fc768fe2464dcab22aafb8ac8a34a9da3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-04T14:00:07Z","title_canon_sha256":"3a3b1720aaccbd0e95bb1de7ac8a9645483da71f756f9ddca2ec0c4da9681d59"},"schema_version":"1.0","source":{"id":"1112.0753","kind":"arxiv","version":1}},"canonical_sha256":"27d06e3fd2c8067a74d070f7145f9b7a541ab586e64022067543d8fcf2a64b92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27d06e3fd2c8067a74d070f7145f9b7a541ab586e64022067543d8fcf2a64b92","first_computed_at":"2026-05-18T04:07:05.719958Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:05.719958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qbaghqZPxJ0r4ZCik1Acca8Yz3racU5L6E78h5OGgArYJ0YIC0NRETE4p9XqS1nXEGol93LgCgBFhJasy0RTDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:05.720396Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.0753","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:805f6d7986f7e5719198c7c81c3485fe6fe2acb4c7c59cf4003b59fe18d36b37","sha256:8cc599b362f68145d141b680c9294beaf8adf69756629c954fca1b5dcc927628"],"state_sha256":"35874f6285fee8202d3b6c8cbb2d0f429ecd97eb64409efa26d6197a5974c8dc"}