{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RBBHIOR7AQGRGNIXG27U3SEZB4","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":"086f4d4cfbac37f5653dcb1bdd1444d25b86a4316c2f31ea0787e2f76c2e4616","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-04T18:21:52Z","title_canon_sha256":"c831db0e3f061a4c70cd0a8760b5224a69e67264caba030d710baad848e5b1d0"},"schema_version":"1.0","source":{"id":"1808.02018","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.02018","created_at":"2026-05-17T23:56:35Z"},{"alias_kind":"arxiv_version","alias_value":"1808.02018v2","created_at":"2026-05-17T23:56:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.02018","created_at":"2026-05-17T23:56:35Z"},{"alias_kind":"pith_short_12","alias_value":"RBBHIOR7AQGR","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RBBHIOR7AQGRGNIX","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RBBHIOR7","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:c91e9c92ff8ceab66d548935c2d737fc874d561491889e29dc1d1d8ed14a35f6","target":"graph","created_at":"2026-05-17T23:56:35Z","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":"In 2003 Kostochka, Pelsmajer, and West introduced a list analogue of equitable coloring called equitable choosability. A $k$-assignment, $L$, for a graph $G$ assigns a list, $L(v)$, of $k$ available colors to each $v \\in V(G)$, and an equitable $L$-coloring of $G$ is a proper coloring, $f$, of $G$ such that $f(v) \\in L(v)$ for each $v \\in V(G)$ and each color class of $f$ has size at most $\\lceil |V(G)|/k \\rceil$. Graph $G$ is said to be equitably $k$-choosable if an equitable $L$-coloring of $G$ exists whenever $L$ is a $k$-assignment for $G$. In this note we study the equitable choosability ","authors_text":"Ezekiel Thornburgh, Isaac Kadera, Jeffrey A. Mudrock, Madelynn Chase, Tim Wagstrom","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-04T18:21:52Z","title":"A Note on the Equitable Choosability of Complete Bipartite Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02018","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:cebd499926b494c0a9fe3bfa1cebc4de2339ef9a083d544f1165c91b7055de65","target":"record","created_at":"2026-05-17T23:56:35Z","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":"086f4d4cfbac37f5653dcb1bdd1444d25b86a4316c2f31ea0787e2f76c2e4616","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-04T18:21:52Z","title_canon_sha256":"c831db0e3f061a4c70cd0a8760b5224a69e67264caba030d710baad848e5b1d0"},"schema_version":"1.0","source":{"id":"1808.02018","kind":"arxiv","version":2}},"canonical_sha256":"8842743a3f040d13351736bf4dc8990f3330983313a4e86c1063d9c3c48a5668","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8842743a3f040d13351736bf4dc8990f3330983313a4e86c1063d9c3c48a5668","first_computed_at":"2026-05-17T23:56:35.095243Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:35.095243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gDbZMIhU0L2+TJBROQZcTH1L4oRukcI0VUQH0OM5hkUPT4rlW1V3thzhZhjzuIts6ku3ulvsFStQJ5iDpddcDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:35.095900Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.02018","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cebd499926b494c0a9fe3bfa1cebc4de2339ef9a083d544f1165c91b7055de65","sha256:c91e9c92ff8ceab66d548935c2d737fc874d561491889e29dc1d1d8ed14a35f6"],"state_sha256":"b1ed28051d50d1d4881621db335b3c2781d09f989e476388a54880cfe3c4086b"}