{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PGT3CZKYN7R5LJL2YRYYI6PQ22","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":"a69b5ad0d132adba5c031dc76f1414f9eff2d9a1bba8e401357fbcba9baf1f04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-14T21:09:19Z","title_canon_sha256":"bab8d8cc0ca5f9221c261a7966fb0e33c5a891571f940f6acb705b813161cb88"},"schema_version":"1.0","source":{"id":"1407.3817","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.3817","created_at":"2026-05-18T02:47:32Z"},{"alias_kind":"arxiv_version","alias_value":"1407.3817v1","created_at":"2026-05-18T02:47:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.3817","created_at":"2026-05-18T02:47:32Z"},{"alias_kind":"pith_short_12","alias_value":"PGT3CZKYN7R5","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PGT3CZKYN7R5LJL2","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PGT3CZKY","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:7c117b8c4b0fc3ca48c8665d7803d605fe155dfe2ee93c3162534add33f6ca0e","target":"graph","created_at":"2026-05-18T02:47:32Z","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":"Let $\\mathrm{ch}(G)$ denote the choice number of a graph $G$, and let $K_{s*k}$ be the complete $k$-partite graph with $s$ vertices in each part. Erd\\H{o}s, Rubin, and Taylor showed that $\\mathrm{ch}( K_{2*k})=k$, and suggested the problem of determining the choice number of $K_{s*k}.$ The first author established\n  $\\mathrm{ch}( K_{3*k})=\\left\\lceil \\frac{4k-1}{3}\\right\\rceil$. Here we prove $\\mathrm{ch} (K_{4*k})=\\left\\lceil \\frac{3k-1}{2}\\right\\rceil$.","authors_text":"Andrew Salmon, H. A. Kierstead, Ran Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-14T21:09:19Z","title":"On the choice number of complete multipartite graphs with part size four"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3817","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":"sha256:46e3cceef522ef38a56b4d39a7434e1738f2dccb1e3e2c2423a8f5ac7ab45597","target":"record","created_at":"2026-05-18T02:47:32Z","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":"a69b5ad0d132adba5c031dc76f1414f9eff2d9a1bba8e401357fbcba9baf1f04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-14T21:09:19Z","title_canon_sha256":"bab8d8cc0ca5f9221c261a7966fb0e33c5a891571f940f6acb705b813161cb88"},"schema_version":"1.0","source":{"id":"1407.3817","kind":"arxiv","version":1}},"canonical_sha256":"79a7b165586fe3d5a57ac4718479f0d6a556dc8493a5a86430934ae4ac85f8e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79a7b165586fe3d5a57ac4718479f0d6a556dc8493a5a86430934ae4ac85f8e9","first_computed_at":"2026-05-18T02:47:32.551736Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:32.551736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EB1bYeUwM/MyRtX5MW9Ict/ampG8hcdmYDZT7NH85xaGAyQYFcGB4PMMARj38o8EckNCbmIUSjINco0829EcBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:32.552174Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.3817","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46e3cceef522ef38a56b4d39a7434e1738f2dccb1e3e2c2423a8f5ac7ab45597","sha256:7c117b8c4b0fc3ca48c8665d7803d605fe155dfe2ee93c3162534add33f6ca0e"],"state_sha256":"454e0fc83add15a0a10f11dbda5dbdad9495df07849c5e944c6443de983a0c24"}