{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:K6BAIFWUP6U76NQ7WCF4MWRPXL","short_pith_number":"pith:K6BAIFWU","schema_version":"1.0","canonical_sha256":"57820416d47fa9ff361fb08bc65a2fbad2bec108a32d85ebf2d8aa7406f5b97c","source":{"kind":"arxiv","id":"2607.00732","version":1},"attestation_state":"computed","paper":{"title":"Generalized Erd\\H{o}s--Rogers problems for $r$-uniform hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lulu Dai, Qizhong Lin","submitted_at":"2026-07-01T10:17:22Z","abstract_excerpt":"Let \\(F\\) and \\(G\\) be \\(r\\)-uniform hypergraphs, and let \\(f_{F,G}(n)\\) be the largest integer \\(m\\) such that every \\(n\\)-vertex \\(G\\)-free \\(r\\)-graph contains an induced \\(F\\)-free subgraph on \\(m\\) vertices. We prove that, if \\(r\\ge3\\), \\(F\\) is nonempty, \\(G\\) is \\(2\\)-tightly connected, and there is no homomorphism from \\(G\\) to \\(F\\), then \\[\n  f_{F,G}(n)\\le C(\\log n)^{\\beta_F},\n  \\qquad\n  \\beta_F=\n  \\max_{\\substack{\\emptyset\\ne P\\subseteq\\partial_2F}}\n  \\frac{e(P)}{v(P)-1}. \\] For \\(r=3\\), this confirms a conjecture of He and Nie for tightly connected \\(3\\)-graphs, sharpening their ea"},"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":"2607.00732","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-01T10:17:22Z","cross_cats_sorted":[],"title_canon_sha256":"9489672a0c5da4030a333b63f1f36599e1235b60d72f3399e010190be119376b","abstract_canon_sha256":"e96f2247b3611a943dd1212db886cb270acd7ac0715b67622f6ad54bc6bf9801"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T01:17:52.870484Z","signature_b64":"ewBm9tq9bo2XMLx/PsAbBcy9FCdNOsabY/Y/EuxQPLBmxQh0nKBIi++A3AkeAuklOlq0+mGpOZwU18VRYY8nBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57820416d47fa9ff361fb08bc65a2fbad2bec108a32d85ebf2d8aa7406f5b97c","last_reissued_at":"2026-07-02T01:17:52.870075Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T01:17:52.870075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized Erd\\H{o}s--Rogers problems for $r$-uniform hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lulu Dai, Qizhong Lin","submitted_at":"2026-07-01T10:17:22Z","abstract_excerpt":"Let \\(F\\) and \\(G\\) be \\(r\\)-uniform hypergraphs, and let \\(f_{F,G}(n)\\) be the largest integer \\(m\\) such that every \\(n\\)-vertex \\(G\\)-free \\(r\\)-graph contains an induced \\(F\\)-free subgraph on \\(m\\) vertices. We prove that, if \\(r\\ge3\\), \\(F\\) is nonempty, \\(G\\) is \\(2\\)-tightly connected, and there is no homomorphism from \\(G\\) to \\(F\\), then \\[\n  f_{F,G}(n)\\le C(\\log n)^{\\beta_F},\n  \\qquad\n  \\beta_F=\n  \\max_{\\substack{\\emptyset\\ne P\\subseteq\\partial_2F}}\n  \\frac{e(P)}{v(P)-1}. \\] For \\(r=3\\), this confirms a conjecture of He and Nie for tightly connected \\(3\\)-graphs, sharpening their ea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00732","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/2607.00732/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":"2607.00732","created_at":"2026-07-02T01:17:52.870133+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.00732v1","created_at":"2026-07-02T01:17:52.870133+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.00732","created_at":"2026-07-02T01:17:52.870133+00:00"},{"alias_kind":"pith_short_12","alias_value":"K6BAIFWUP6U7","created_at":"2026-07-02T01:17:52.870133+00:00"},{"alias_kind":"pith_short_16","alias_value":"K6BAIFWUP6U76NQ7","created_at":"2026-07-02T01:17:52.870133+00:00"},{"alias_kind":"pith_short_8","alias_value":"K6BAIFWU","created_at":"2026-07-02T01:17:52.870133+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/K6BAIFWUP6U76NQ7WCF4MWRPXL","json":"https://pith.science/pith/K6BAIFWUP6U76NQ7WCF4MWRPXL.json","graph_json":"https://pith.science/api/pith-number/K6BAIFWUP6U76NQ7WCF4MWRPXL/graph.json","events_json":"https://pith.science/api/pith-number/K6BAIFWUP6U76NQ7WCF4MWRPXL/events.json","paper":"https://pith.science/paper/K6BAIFWU"},"agent_actions":{"view_html":"https://pith.science/pith/K6BAIFWUP6U76NQ7WCF4MWRPXL","download_json":"https://pith.science/pith/K6BAIFWUP6U76NQ7WCF4MWRPXL.json","view_paper":"https://pith.science/paper/K6BAIFWU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.00732&json=true","fetch_graph":"https://pith.science/api/pith-number/K6BAIFWUP6U76NQ7WCF4MWRPXL/graph.json","fetch_events":"https://pith.science/api/pith-number/K6BAIFWUP6U76NQ7WCF4MWRPXL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K6BAIFWUP6U76NQ7WCF4MWRPXL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K6BAIFWUP6U76NQ7WCF4MWRPXL/action/storage_attestation","attest_author":"https://pith.science/pith/K6BAIFWUP6U76NQ7WCF4MWRPXL/action/author_attestation","sign_citation":"https://pith.science/pith/K6BAIFWUP6U76NQ7WCF4MWRPXL/action/citation_signature","submit_replication":"https://pith.science/pith/K6BAIFWUP6U76NQ7WCF4MWRPXL/action/replication_record"}},"created_at":"2026-07-02T01:17:52.870133+00:00","updated_at":"2026-07-02T01:17:52.870133+00:00"}