{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SUSVC7XQGJJTSPNIDJZ6DBNLZL","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":"205baf9c915453a0921bad1e2498c1cc56ce58bba2d954764e5590755174e0ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-05T20:25:01Z","title_canon_sha256":"16d4ef66b102fee64d92a6763e9ef19c9de8b5d46de34dc6ded99b98820fe942"},"schema_version":"1.0","source":{"id":"1811.02018","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.02018","created_at":"2026-05-18T00:01:32Z"},{"alias_kind":"arxiv_version","alias_value":"1811.02018v1","created_at":"2026-05-18T00:01:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.02018","created_at":"2026-05-18T00:01:32Z"},{"alias_kind":"pith_short_12","alias_value":"SUSVC7XQGJJT","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SUSVC7XQGJJTSPNI","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SUSVC7XQ","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:8daa7030974f498bcebe02b77b09e4160d45c1644d8412ab9b031917525cbca1","target":"graph","created_at":"2026-05-18T00:01:32Z","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":"Given a graph $G$ and $p \\in [0,1]$, let $G_p$ denote the random subgraph of $G$ obtained by keeping each edge independently with probability $p$. Alon, Krivelevich, and Sudokov proved $\\mathbb{E} [\\chi(G_p)] \\geq C_p \\frac{\\chi(G)}{\\log |V(G)|}$, and Bukh conjectured an improvement of $\\mathbb{E}[\\chi(G_p)] \\geq C_p \\frac{\\chi(G)}{\\log \\chi(G)}$. We prove a new spectral lower bound on $\\mathbb{E}[\\chi(G_p)]$, as progress towards Bukh's conjecture. We also propose the stronger conjecture that for any fixed $p \\leq 1/2$, among all graphs of fixed chromatic number, $\\mathbb{E}[\\chi(G_p)]$ is min","authors_text":"Catherine Lee, David Townley, Henry Reichard, Pat Devlin, Ross Berkowitz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-05T20:25:01Z","title":"Expected Chromatic Number of Random Subgraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.02018","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":"sha256:8fe0e289fa7c0a58d3b2eda04dbaf0c350259eb3ac87b1320108e51e5d4671dc","target":"record","created_at":"2026-05-18T00:01:32Z","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":"205baf9c915453a0921bad1e2498c1cc56ce58bba2d954764e5590755174e0ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-05T20:25:01Z","title_canon_sha256":"16d4ef66b102fee64d92a6763e9ef19c9de8b5d46de34dc6ded99b98820fe942"},"schema_version":"1.0","source":{"id":"1811.02018","kind":"arxiv","version":1}},"canonical_sha256":"9525517ef03253393da81a73e185abcad2c2490d187543ee838f0665d69bcf52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9525517ef03253393da81a73e185abcad2c2490d187543ee838f0665d69bcf52","first_computed_at":"2026-05-18T00:01:32.549926Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:32.549926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PZrlvqY1siZpUIUFdYaQXhKBXHVtL0mwQ9C6iPwpof7xO0G2h9zoShhC6Zg0b6rYy4IZUL+jSv5sTbNJZMz8Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:32.550388Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.02018","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fe0e289fa7c0a58d3b2eda04dbaf0c350259eb3ac87b1320108e51e5d4671dc","sha256:8daa7030974f498bcebe02b77b09e4160d45c1644d8412ab9b031917525cbca1"],"state_sha256":"165134dd546f4c7d3a8e2a309e18bbef910aa4ad4dac1569b89411d2b0e6e71c"}