{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:KHST3J64TH4IEIXGPEJFDECRII","short_pith_number":"pith:KHST3J64","schema_version":"1.0","canonical_sha256":"51e53da7dc99f88222e67912519051423d296f9975cf4659640ddb4445850b7c","source":{"kind":"arxiv","id":"1705.08150","version":1},"attestation_state":"computed","paper":{"title":"Total weight choosability for Halin graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Tsai-Lien Wong, Xuding Zhu, Yu-Chang Liang","submitted_at":"2017-05-23T09:34:04Z","abstract_excerpt":"A proper total weighting of a graph $G$ is a mapping $\\phi$ which assigns to each vertex and each edge of $G$ a real number as its weight so that for any edge $uv$ of $G$, $\\sum_{e \\in E(v)}\\phi(e)+\\phi(v) \\ne \\sum_{e \\in E(u)}\\phi(e)+\\phi(u)$. A $(k,k')$-list assignment of $G$ is a mapping $L$ which assigns to each vertex $v$ a set $L(v)$ of $k$ permissible weights and to each edge $e$ a set $L(e)$ of $k'$ permissible weights. An $L$-total weighting is a total weighting $\\phi$ with $\\phi(z) \\in L(z)$ for each $z \\in V(G) \\cup E(G)$. A graph $G$ is called $(k,k')$-choosable if for every $(k,k'"},"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":"1705.08150","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-23T09:34:04Z","cross_cats_sorted":[],"title_canon_sha256":"94f8896e241da61911208d5817f09b1b718e9dc1369f92cbc6a09a092a6f4655","abstract_canon_sha256":"42f1b42d3be69be3c95aa7b54fb594b376f878d639a31b350097e4bfd24bff64"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:49.203349Z","signature_b64":"wE5m3tOtbqtOQ2dkLhhTbY919Md5qIIJz55WRLqxZh0d7dUdQXHJnGdc3lifAbhAz4IBe3yyVW5bIc0Ks8XZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51e53da7dc99f88222e67912519051423d296f9975cf4659640ddb4445850b7c","last_reissued_at":"2026-05-18T00:43:49.202731Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:49.202731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Total weight choosability for Halin graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Tsai-Lien Wong, Xuding Zhu, Yu-Chang Liang","submitted_at":"2017-05-23T09:34:04Z","abstract_excerpt":"A proper total weighting of a graph $G$ is a mapping $\\phi$ which assigns to each vertex and each edge of $G$ a real number as its weight so that for any edge $uv$ of $G$, $\\sum_{e \\in E(v)}\\phi(e)+\\phi(v) \\ne \\sum_{e \\in E(u)}\\phi(e)+\\phi(u)$. A $(k,k')$-list assignment of $G$ is a mapping $L$ which assigns to each vertex $v$ a set $L(v)$ of $k$ permissible weights and to each edge $e$ a set $L(e)$ of $k'$ permissible weights. An $L$-total weighting is a total weighting $\\phi$ with $\\phi(z) \\in L(z)$ for each $z \\in V(G) \\cup E(G)$. A graph $G$ is called $(k,k')$-choosable if for every $(k,k'"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08150","kind":"arxiv","version":1},"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":"1705.08150","created_at":"2026-05-18T00:43:49.202816+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.08150v1","created_at":"2026-05-18T00:43:49.202816+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08150","created_at":"2026-05-18T00:43:49.202816+00:00"},{"alias_kind":"pith_short_12","alias_value":"KHST3J64TH4I","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"KHST3J64TH4IEIXG","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"KHST3J64","created_at":"2026-05-18T12:31:24.725408+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/KHST3J64TH4IEIXGPEJFDECRII","json":"https://pith.science/pith/KHST3J64TH4IEIXGPEJFDECRII.json","graph_json":"https://pith.science/api/pith-number/KHST3J64TH4IEIXGPEJFDECRII/graph.json","events_json":"https://pith.science/api/pith-number/KHST3J64TH4IEIXGPEJFDECRII/events.json","paper":"https://pith.science/paper/KHST3J64"},"agent_actions":{"view_html":"https://pith.science/pith/KHST3J64TH4IEIXGPEJFDECRII","download_json":"https://pith.science/pith/KHST3J64TH4IEIXGPEJFDECRII.json","view_paper":"https://pith.science/paper/KHST3J64","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.08150&json=true","fetch_graph":"https://pith.science/api/pith-number/KHST3J64TH4IEIXGPEJFDECRII/graph.json","fetch_events":"https://pith.science/api/pith-number/KHST3J64TH4IEIXGPEJFDECRII/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KHST3J64TH4IEIXGPEJFDECRII/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KHST3J64TH4IEIXGPEJFDECRII/action/storage_attestation","attest_author":"https://pith.science/pith/KHST3J64TH4IEIXGPEJFDECRII/action/author_attestation","sign_citation":"https://pith.science/pith/KHST3J64TH4IEIXGPEJFDECRII/action/citation_signature","submit_replication":"https://pith.science/pith/KHST3J64TH4IEIXGPEJFDECRII/action/replication_record"}},"created_at":"2026-05-18T00:43:49.202816+00:00","updated_at":"2026-05-18T00:43:49.202816+00:00"}