{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:4ZN4GEDST45OGV2XBPC477B43R","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":"8ad76939c0d5b353420e2e32e26a9e62fe994aebe93767b82d7151883e7cfef6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-11-25T15:13:02Z","title_canon_sha256":"3ddd5c9a8f073ade05a2d31aaa4d86b227535f33d6759f13905542565d30c9f2"},"schema_version":"1.0","source":{"id":"2411.16465","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.16465","created_at":"2026-07-05T09:40:09Z"},{"alias_kind":"arxiv_version","alias_value":"2411.16465v1","created_at":"2026-07-05T09:40:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.16465","created_at":"2026-07-05T09:40:09Z"},{"alias_kind":"pith_short_12","alias_value":"4ZN4GEDST45O","created_at":"2026-07-05T09:40:09Z"},{"alias_kind":"pith_short_16","alias_value":"4ZN4GEDST45OGV2X","created_at":"2026-07-05T09:40:09Z"},{"alias_kind":"pith_short_8","alias_value":"4ZN4GEDS","created_at":"2026-07-05T09:40:09Z"}],"graph_snapshots":[{"event_id":"sha256:6a9ad7edfec845b19f33f955e709e4c338541b19b24c57ee0a648850948688b3","target":"graph","created_at":"2026-07-05T09:40:09Z","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/2411.16465/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a graph $G$, its Hall ratio $\\rho(G)=\\max_{H\\subseteq G}\\frac{|V(H)|}{\\alpha(H)}$ forms a natural lower bound on its fractional chromatic number $\\chi_f(G)$. A recent line of research studied the fundamental question of whether $\\chi_f(G)$ can be bounded in terms of a (linear) function of $\\rho(G)$. In a breakthrough-result, Dvo\\v{r}\\'{a}k, Ossona de Mendez and Wu gave a strong negative answer by proving the existence of graphs with bounded Hall ratio and arbitrarily large fractional chromatic number. In this paper, we solve two natural follow-up problems that were raised by Dvo\\v{r}\\'{a","authors_text":"Raphael Steiner","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-11-25T15:13:02Z","title":"Fractional chromatic number vs. Hall ratio"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.16465","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:a02117711e61bc44b3ea898a86e3f4d8e3c890d71c58d4d2ed30161e7f0de093","target":"record","created_at":"2026-07-05T09:40:09Z","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":"8ad76939c0d5b353420e2e32e26a9e62fe994aebe93767b82d7151883e7cfef6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-11-25T15:13:02Z","title_canon_sha256":"3ddd5c9a8f073ade05a2d31aaa4d86b227535f33d6759f13905542565d30c9f2"},"schema_version":"1.0","source":{"id":"2411.16465","kind":"arxiv","version":1}},"canonical_sha256":"e65bc310729f3ae357570bc5cffc3cdc4d77c7ddbcfd9a4c3ec49f6846470ce0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e65bc310729f3ae357570bc5cffc3cdc4d77c7ddbcfd9a4c3ec49f6846470ce0","first_computed_at":"2026-07-05T09:40:09.705231Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:40:09.705231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y5oNzsMOONeKQWSF8NbCmk//yn55PnkgZ0IHNfbajRq+5cKhJBgqr3zEooxTLk/4Ubgp5WZTjVs5A1FoP+IeDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:40:09.705698Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.16465","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a02117711e61bc44b3ea898a86e3f4d8e3c890d71c58d4d2ed30161e7f0de093","sha256:6a9ad7edfec845b19f33f955e709e4c338541b19b24c57ee0a648850948688b3"],"state_sha256":"efe8b8651e628c0a172c7c0572b324d15abe82ad5d15ca1c4dbbf5d9583825ec"}