{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:WQN3QU7QABJSYH5EXZM5ZG72LZ","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":"180488820858c420b7a6c2cc72a23518bfbfec7ed35d636ec8323c6ec15395fe","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2023-11-02T02:33:35Z","title_canon_sha256":"16877763d7e9ecdc319c66b48d60419d9019eaac607f663c4a6a290dad501934"},"schema_version":"1.0","source":{"id":"2311.00950","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.00950","created_at":"2026-07-05T07:08:18Z"},{"alias_kind":"arxiv_version","alias_value":"2311.00950v1","created_at":"2026-07-05T07:08:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.00950","created_at":"2026-07-05T07:08:18Z"},{"alias_kind":"pith_short_12","alias_value":"WQN3QU7QABJS","created_at":"2026-07-05T07:08:18Z"},{"alias_kind":"pith_short_16","alias_value":"WQN3QU7QABJSYH5E","created_at":"2026-07-05T07:08:18Z"},{"alias_kind":"pith_short_8","alias_value":"WQN3QU7Q","created_at":"2026-07-05T07:08:18Z"}],"graph_snapshots":[{"event_id":"sha256:b6f3319020e70ecf3f4e159f4bd49369371e4241cf99c1bc3f983b946638924a","target":"graph","created_at":"2026-07-05T07:08:18Z","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/2311.00950/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this note we show the following strengthening of a multipartite version of the Hajnal--Szemer\\'edi theorem. For an integer $r \\ge 3$ and $\\gamma > 0$, there exists a constant $C$ such that if $p\\ge Cn^{-2/r}(\\log n)^{1/{r \\choose 2}}$ and $G$ is a balanced $r$-partite graph with each vertex class of size $n$ and $\\delta^\\ast(G)\\ge (1-1/r+\\gamma)n$, then with high probability the random subgraph $G(p)$ of $G$ contains a $K_r$-factor. We also use it to derive corresponding transversal versions.","authors_text":"Donglei Yang, Jie Han, Jie Hu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2023-11-02T02:33:35Z","title":"A robust version of the multipartite Hajnal--Szemer\\'edi theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.00950","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":"sha256:5a9805ffb0b43f603a8b7c4cb11f646c3ee12b8639adf5ebbeecfe3474172892","target":"record","created_at":"2026-07-05T07:08:18Z","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":"180488820858c420b7a6c2cc72a23518bfbfec7ed35d636ec8323c6ec15395fe","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2023-11-02T02:33:35Z","title_canon_sha256":"16877763d7e9ecdc319c66b48d60419d9019eaac607f663c4a6a290dad501934"},"schema_version":"1.0","source":{"id":"2311.00950","kind":"arxiv","version":1}},"canonical_sha256":"b41bb853f000532c1fa4be59dc9bfa5e7591b0addc249d630fefb400b6bd21f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b41bb853f000532c1fa4be59dc9bfa5e7591b0addc249d630fefb400b6bd21f0","first_computed_at":"2026-07-05T07:08:18.147349Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:08:18.147349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v4YkEThEjgBCcyWX3WSMiNQUjniLw1Om8Q2/ySM+jhN9EVY1b/jW7Tp+PTirJRmFvIqVw/fznh7lt22Rp0uIBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:08:18.149012Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.00950","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a9805ffb0b43f603a8b7c4cb11f646c3ee12b8639adf5ebbeecfe3474172892","sha256:b6f3319020e70ecf3f4e159f4bd49369371e4241cf99c1bc3f983b946638924a"],"state_sha256":"ca7a0256a0281da8956eba14a5155bd718f5e672971b60f0733f8df9901556d7"}