{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7XFMZP7P4S7CEQ265M4LIT4SCF","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":"b34edd186937c428ad7199aa148cf2d1620292f784e41579233705e3125198f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-30T02:10:16Z","title_canon_sha256":"e7eff18c1fea96fea056a2923ad9905653a57f501b7d8a99dbd5297920926486"},"schema_version":"1.0","source":{"id":"1309.7705","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7705","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7705v2","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7705","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"pith_short_12","alias_value":"7XFMZP7P4S7C","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"7XFMZP7P4S7CEQ26","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"7XFMZP7P","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:42f5e44548c12faa538de06fafef837ab88dfccb0deb3b134f19207e1f26c284","target":"graph","created_at":"2026-05-18T02:42:39Z","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":"Recently, Kim and Park have found an infinite family of graphs whose squares are not chromatic-choosable. Xuding Zhu asked whether there is some $k$ such that all $k$th power graphs are chromatic-choosable. We answer this question in the negative: we show that there is a positive constant $c$ such that for any $k$ there is a family of graphs $G$ with $\\chi(G^k)$ unbounded and $\\chi_{\\ell}(G^k)\\geq c \\chi(G^k) \\log \\chi(G^k)$. We also provide an upper bound, $\\chi_{\\ell}(G^k)<\\chi(G^k)^3$ for $k>1$.","authors_text":"Benjamin Reiniger, Elyse Yeager, Nicholas Kosar, Sarka Petrickova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-30T02:10:16Z","title":"A note on list-coloring powers of graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7705","kind":"arxiv","version":2},"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":"sha256:7bf3865e21ca5b3fd071441d8faa47f135e2d860266c437a26c1b0dba4afaf99","target":"record","created_at":"2026-05-18T02:42:39Z","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":"b34edd186937c428ad7199aa148cf2d1620292f784e41579233705e3125198f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-30T02:10:16Z","title_canon_sha256":"e7eff18c1fea96fea056a2923ad9905653a57f501b7d8a99dbd5297920926486"},"schema_version":"1.0","source":{"id":"1309.7705","kind":"arxiv","version":2}},"canonical_sha256":"fdcaccbfefe4be22435eeb38b44f9211642373d5bf000c69c626e62d4621132e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fdcaccbfefe4be22435eeb38b44f9211642373d5bf000c69c626e62d4621132e","first_computed_at":"2026-05-18T02:42:39.605734Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:39.605734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HSStahFnyywyvphownQfFie+aJnWeUCr3rX1u15NNYaCW1hPrZgsKwRId/gXQeG+eACbbSSy95hgPQmfcaAhDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:39.606374Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.7705","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7bf3865e21ca5b3fd071441d8faa47f135e2d860266c437a26c1b0dba4afaf99","sha256:42f5e44548c12faa538de06fafef837ab88dfccb0deb3b134f19207e1f26c284"],"state_sha256":"672bc1b1f12d2dd070f6037dbe7e0b81efec8e7d467b28eb9aef8292ffab5989"}