{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:7XF5XFYZ5GJUKUGJSJMEC3ENPV","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":"637022546fb5a7778a80250248c0fa33f245d381e920597755c1994b9d1b2fb5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-11T04:13:38Z","title_canon_sha256":"50649835a7a70f8497217328668e4fec1a1c81432060fcee5c135b523782de17"},"schema_version":"1.0","source":{"id":"2607.10111","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.10111","created_at":"2026-07-14T01:20:25Z"},{"alias_kind":"arxiv_version","alias_value":"2607.10111v1","created_at":"2026-07-14T01:20:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.10111","created_at":"2026-07-14T01:20:25Z"},{"alias_kind":"pith_short_12","alias_value":"7XF5XFYZ5GJU","created_at":"2026-07-14T01:20:25Z"},{"alias_kind":"pith_short_16","alias_value":"7XF5XFYZ5GJUKUGJ","created_at":"2026-07-14T01:20:25Z"},{"alias_kind":"pith_short_8","alias_value":"7XF5XFYZ","created_at":"2026-07-14T01:20:25Z"}],"graph_snapshots":[{"event_id":"sha256:b55ed8817ab9ea7501236f7c194b32c9c417bd6a0b6974c7b3996bef513b1ee1","target":"graph","created_at":"2026-07-14T01:20:25Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.10111/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For integers \\(k\\le s<t\\), let \\(f^{(k)}_{s,t}(n)\\) denote the largest integer \\(m\\) such that every \\(n\\)-vertex \\(K_t^{(k)}\\)-free \\(k\\)-graph contains a set of \\(m\\) vertices spanning no copy of \\(K_s^{(k)}\\). We give an affirmative answer to a problem of Conlon, Fox and Sudakov by proving that, for every fixed \\(s\\ge4\\), \\[\n  f^{(4)}_{s,s+1}(n)=(\\log n)^{o(1)} . \\] The key input is a new \\(3\\)-uniform estimate: for every fixed \\(s\\ge3\\), \\(f^{(3)}_{s,s+1}(n)=O(\\frac{\\log n}{\\log\\log n})\\). This improves the logarithmic upper bound of Dudek and Mubayi. The proof combines hypergraph containe","authors_text":"Lin Niu, Qizhong Lin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-11T04:13:38Z","title":"Hypergraph Erd\\H{o}s--Rogers functions with consecutive clique sizes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10111","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":"sha256:280b1ba7b9c60581f61d4027e300ab9a3b115f527b5abf2c1e3dad64e61b1020","target":"record","created_at":"2026-07-14T01:20:25Z","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":"637022546fb5a7778a80250248c0fa33f245d381e920597755c1994b9d1b2fb5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-11T04:13:38Z","title_canon_sha256":"50649835a7a70f8497217328668e4fec1a1c81432060fcee5c135b523782de17"},"schema_version":"1.0","source":{"id":"2607.10111","kind":"arxiv","version":1}},"canonical_sha256":"fdcbdb9719e9934550c99258416c8d7d5b05f167feccb40f2ed9fe32cd1fb0e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fdcbdb9719e9934550c99258416c8d7d5b05f167feccb40f2ed9fe32cd1fb0e5","first_computed_at":"2026-07-14T01:20:25.778483Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-14T01:20:25.778483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nrnGaEGwCpC2mOu+ucHMzv/hgJLkcJZswYkDcr3fgaKwLYMsRY7uzjpyvKMPHxq5cI4yVuLPmHcS3/CcO9RICw==","signature_status":"signed_v1","signed_at":"2026-07-14T01:20:25.779598Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.10111","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:280b1ba7b9c60581f61d4027e300ab9a3b115f527b5abf2c1e3dad64e61b1020","sha256:b55ed8817ab9ea7501236f7c194b32c9c417bd6a0b6974c7b3996bef513b1ee1"],"state_sha256":"cd900fb35a085f34c7704c2a30b6b8b2ab0cc5e4ab95c414888991a2e1113ae1"}