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Let $\\hbox{bs}(k)$ denote the smallest integer $m \\ge 2$ such that any collection of $m$ $k$-uniform hypergraphs on $n$ vertices with moderate densities contains a pair $G,H$ for which $\\hbox{disc}(G,H) = \\Omega(n^{(k+1)/2})$.\n  In this paper, we answer several questions raised by Bollob\\'as and Scott, prov"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2506.23264","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-29T14:38:04Z","cross_cats_sorted":[],"title_canon_sha256":"4a09ad0a971a1316548bb2f5ea7c1f1b0a0683f9cb489b4dea53050dcd3cdc68","abstract_canon_sha256":"b4f53714d79f397e8bc9100a090471f07da88f8170893d7b1a2d646c4e6c9a69"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:29:18.823282Z","signature_b64":"lSJe5USZLkQGd5Sjur0VaNHNseddIzVyaqyRXPcB3HR/AdrdD8kkYEmbOLMEca6xMWEmPH+1Q0hu3y3cRnFYBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d7ee89ebe0a4fac44a15daff030df700c7a04629ba823cae175f68d7764f557","last_reissued_at":"2026-07-05T11:29:18.822708Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:29:18.822708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Relative discrepancy of hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Diep Luong-Le, Dilong Yang, Tuan Tran","submitted_at":"2025-06-29T14:38:04Z","abstract_excerpt":"Given $k$-uniform hypergraphs $G$ and $H$ on $n$ vertices with densities $p$ and $q$, their relative discrepancy is defined as $\\hbox{disc}(G,H)=\\max\\big||E(G')\\cap E(H')|-pq\\binom{n}{k}\\big|$, where the maximum ranges over all pairs $G',H'$ with $G'\\cong G$, $H'\\cong H$, and $V(G')=V(H')$. Let $\\hbox{bs}(k)$ denote the smallest integer $m \\ge 2$ such that any collection of $m$ $k$-uniform hypergraphs on $n$ vertices with moderate densities contains a pair $G,H$ for which $\\hbox{disc}(G,H) = \\Omega(n^{(k+1)/2})$.\n  In this paper, we answer several questions raised by Bollob\\'as and Scott, prov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.23264","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.23264/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2506.23264","created_at":"2026-07-05T11:29:18.822793+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.23264v1","created_at":"2026-07-05T11:29:18.822793+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.23264","created_at":"2026-07-05T11:29:18.822793+00:00"},{"alias_kind":"pith_short_12","alias_value":"DV7ORHV6BJH2","created_at":"2026-07-05T11:29:18.822793+00:00"},{"alias_kind":"pith_short_16","alias_value":"DV7ORHV6BJH2YRFB","created_at":"2026-07-05T11:29:18.822793+00:00"},{"alias_kind":"pith_short_8","alias_value":"DV7ORHV6","created_at":"2026-07-05T11:29:18.822793+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DV7ORHV6BJH2YRFBLWX7AMG7OA","json":"https://pith.science/pith/DV7ORHV6BJH2YRFBLWX7AMG7OA.json","graph_json":"https://pith.science/api/pith-number/DV7ORHV6BJH2YRFBLWX7AMG7OA/graph.json","events_json":"https://pith.science/api/pith-number/DV7ORHV6BJH2YRFBLWX7AMG7OA/events.json","paper":"https://pith.science/paper/DV7ORHV6"},"agent_actions":{"view_html":"https://pith.science/pith/DV7ORHV6BJH2YRFBLWX7AMG7OA","download_json":"https://pith.science/pith/DV7ORHV6BJH2YRFBLWX7AMG7OA.json","view_paper":"https://pith.science/paper/DV7ORHV6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.23264&json=true","fetch_graph":"https://pith.science/api/pith-number/DV7ORHV6BJH2YRFBLWX7AMG7OA/graph.json","fetch_events":"https://pith.science/api/pith-number/DV7ORHV6BJH2YRFBLWX7AMG7OA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DV7ORHV6BJH2YRFBLWX7AMG7OA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DV7ORHV6BJH2YRFBLWX7AMG7OA/action/storage_attestation","attest_author":"https://pith.science/pith/DV7ORHV6BJH2YRFBLWX7AMG7OA/action/author_attestation","sign_citation":"https://pith.science/pith/DV7ORHV6BJH2YRFBLWX7AMG7OA/action/citation_signature","submit_replication":"https://pith.science/pith/DV7ORHV6BJH2YRFBLWX7AMG7OA/action/replication_record"}},"created_at":"2026-07-05T11:29:18.822793+00:00","updated_at":"2026-07-05T11:29:18.822793+00:00"}