{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UM5B37ITLLZ77DR22POO3ICO52","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":"77975518a13e5bb9fe09b270ab4cd598ebfc03ab093865c6649993f4e442a308","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-05T02:33:25Z","title_canon_sha256":"039d5c93be09945a0097d1bec63a7987746c9ca5694df3fddf683e85a87db2c0"},"schema_version":"1.0","source":{"id":"1811.01491","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.01491","created_at":"2026-05-18T00:01:34Z"},{"alias_kind":"arxiv_version","alias_value":"1811.01491v1","created_at":"2026-05-18T00:01:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.01491","created_at":"2026-05-18T00:01:34Z"},{"alias_kind":"pith_short_12","alias_value":"UM5B37ITLLZ7","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UM5B37ITLLZ77DR2","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UM5B37IT","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:b44e9ff4fa4beafd1aabde7538a9acd3cecd7d041317cd8d3ad4198d545e1bbc","target":"graph","created_at":"2026-05-18T00:01:34Z","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 study hypergraph discrepancy in two closely related random models of hypergraphs on $n$ vertices and $m$ hyperedges. The first model, $\\mathcal{H}_1$, is when every vertex is present in exactly $t$ randomly chosen hyperedges. The premise of this is closely tied to, and motivated by the Beck-Fiala conjecture. The second, perhaps more natural model, $\\mathcal{H}_2$, is when the entries of the $m \\times n$ incidence matrix is sampled in an i.i.d. fashion, each with probability $p$. We prove the following:\n  1. In $\\mathcal{H}_1$, when $\\log^{10}n \\ll t \\ll \\sqrt{n}$, and $m = n$, we show that ","authors_text":"Aditya Potukuchi","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-05T02:33:25Z","title":"Discrepancy in random hypergraph models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01491","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":"sha256:4c99578122c7da2ebcd4c86d9e81cc04c1c9069b02569bda375f7a1c05d78104","target":"record","created_at":"2026-05-18T00:01:34Z","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":"77975518a13e5bb9fe09b270ab4cd598ebfc03ab093865c6649993f4e442a308","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-05T02:33:25Z","title_canon_sha256":"039d5c93be09945a0097d1bec63a7987746c9ca5694df3fddf683e85a87db2c0"},"schema_version":"1.0","source":{"id":"1811.01491","kind":"arxiv","version":1}},"canonical_sha256":"a33a1dfd135af3ff8e3ad3dceda04eee8185ab22e64917a5daa292deeae3ef38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a33a1dfd135af3ff8e3ad3dceda04eee8185ab22e64917a5daa292deeae3ef38","first_computed_at":"2026-05-18T00:01:34.158666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:34.158666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nTa3S+LKooz+p0P7qYxSDCpNc4THOj5SBU421/eyyB556XLR+FwyrNo3OgCf/GKmXePRFNTx/r+M35faBBbwDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:34.159373Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.01491","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c99578122c7da2ebcd4c86d9e81cc04c1c9069b02569bda375f7a1c05d78104","sha256:b44e9ff4fa4beafd1aabde7538a9acd3cecd7d041317cd8d3ad4198d545e1bbc"],"state_sha256":"2c6e09af5410f78578714a1e8bf3615946af1f85443260f613e5fbbf8b519207"}