{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:CMACLBVRMYBTDO63PVJFHWCM7Q","short_pith_number":"pith:CMACLBVR","schema_version":"1.0","canonical_sha256":"13002586b1660331bbdb7d5253d84cfc13bfc39b325f99d7e6037d609b53f010","source":{"kind":"arxiv","id":"1210.6944","version":3},"attestation_state":"computed","paper":{"title":"Bounding the weight choosability number of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ben Seamone","submitted_at":"2012-10-25T18:50:04Z","abstract_excerpt":"Let $G = (V,E)$ be a graph, and for each $e \\in E(G)$, let $L_e$ be a list of real numbers. Let $w:E(G) \\to \\cup_{e \\in E(G)}L_e$ be an edge weighting function such that $w(e) \\in L_e$ for each $e \\in E(G)$, and let $c_w$ be the vertex colouring obtained by $c_w(v) = \\sum_{e \\ni v}w(e)$. We desire the smallest possible $k$ such that, for any choice of $\\{L_e \\,|\\, e \\in E(G)\\}$ where $|L_e| \\geq k$ for all $e \\in E(G)$, there exists an edge weighting function $w$ for which $c_w$ is proper. The smallest such value of $k$ is the weight choosability number of $G$.\n  This colouring problem, introd"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1210.6944","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-25T18:50:04Z","cross_cats_sorted":[],"title_canon_sha256":"04c8fc6154c75f404160dfe2187faa07505bec038b6ccc1cb0d2563fd1f09ba0","abstract_canon_sha256":"116773ed56ba358f14f80f58fb7d6df5aa3bc82d4f0549deda5c9bec82aef3d1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:11.034927Z","signature_b64":"1X/gKemyAeZj6qQ7UYoqYAbSikE48wEcLajLwd51rWOvJBHvC68c1FrsQgUpdxnitoy7sLPc3Sn4D/J4cXURDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13002586b1660331bbdb7d5253d84cfc13bfc39b325f99d7e6037d609b53f010","last_reissued_at":"2026-05-18T03:01:11.034186Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:11.034186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounding the weight choosability number of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ben Seamone","submitted_at":"2012-10-25T18:50:04Z","abstract_excerpt":"Let $G = (V,E)$ be a graph, and for each $e \\in E(G)$, let $L_e$ be a list of real numbers. Let $w:E(G) \\to \\cup_{e \\in E(G)}L_e$ be an edge weighting function such that $w(e) \\in L_e$ for each $e \\in E(G)$, and let $c_w$ be the vertex colouring obtained by $c_w(v) = \\sum_{e \\ni v}w(e)$. We desire the smallest possible $k$ such that, for any choice of $\\{L_e \\,|\\, e \\in E(G)\\}$ where $|L_e| \\geq k$ for all $e \\in E(G)$, there exists an edge weighting function $w$ for which $c_w$ is proper. The smallest such value of $k$ is the weight choosability number of $G$.\n  This colouring problem, introd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6944","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1210.6944","created_at":"2026-05-18T03:01:11.034305+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.6944v3","created_at":"2026-05-18T03:01:11.034305+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6944","created_at":"2026-05-18T03:01:11.034305+00:00"},{"alias_kind":"pith_short_12","alias_value":"CMACLBVRMYBT","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"CMACLBVRMYBTDO63","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"CMACLBVR","created_at":"2026-05-18T12:27:01.376967+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CMACLBVRMYBTDO63PVJFHWCM7Q","json":"https://pith.science/pith/CMACLBVRMYBTDO63PVJFHWCM7Q.json","graph_json":"https://pith.science/api/pith-number/CMACLBVRMYBTDO63PVJFHWCM7Q/graph.json","events_json":"https://pith.science/api/pith-number/CMACLBVRMYBTDO63PVJFHWCM7Q/events.json","paper":"https://pith.science/paper/CMACLBVR"},"agent_actions":{"view_html":"https://pith.science/pith/CMACLBVRMYBTDO63PVJFHWCM7Q","download_json":"https://pith.science/pith/CMACLBVRMYBTDO63PVJFHWCM7Q.json","view_paper":"https://pith.science/paper/CMACLBVR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.6944&json=true","fetch_graph":"https://pith.science/api/pith-number/CMACLBVRMYBTDO63PVJFHWCM7Q/graph.json","fetch_events":"https://pith.science/api/pith-number/CMACLBVRMYBTDO63PVJFHWCM7Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CMACLBVRMYBTDO63PVJFHWCM7Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CMACLBVRMYBTDO63PVJFHWCM7Q/action/storage_attestation","attest_author":"https://pith.science/pith/CMACLBVRMYBTDO63PVJFHWCM7Q/action/author_attestation","sign_citation":"https://pith.science/pith/CMACLBVRMYBTDO63PVJFHWCM7Q/action/citation_signature","submit_replication":"https://pith.science/pith/CMACLBVRMYBTDO63PVJFHWCM7Q/action/replication_record"}},"created_at":"2026-05-18T03:01:11.034305+00:00","updated_at":"2026-05-18T03:01:11.034305+00:00"}