{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:BBMQZHIUURU4ZEXNKYUMEDHUB3","short_pith_number":"pith:BBMQZHIU","schema_version":"1.0","canonical_sha256":"08590c9d14a469cc92ed5628c20cf40ed928cc1fdec05b63554b667a8b9d33e3","source":{"kind":"arxiv","id":"1202.4842","version":1},"attestation_state":"computed","paper":{"title":"Vectorial solutions to list multicoloring problems on graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"IMATH), Jean-Christophe Godin (IMATH), Olivier Togni (Le2i), Yves Aubry (IML","submitted_at":"2012-02-22T07:38:01Z","abstract_excerpt":"For a graph $G$ with a given list assignment $L$ on the vertices, we give an algebraical description of the set of all weights $w$ such that $G$ is $(L,w)$-colorable, called permissible weights. Moreover, for a graph $G$ with a given list $L$ and a given permissible weight $w$, we describe the set of all $(L,w)$-colorings of $G$. By the way, we solve the {\\sl channel assignment problem}. Furthermore, we describe the set of solutions to the {\\sl on call problem}: when $w$ is not a permissible weight, we find all the nearest permissible weights $w'$. Finally, we give a solution to the non-recolo"},"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":"1202.4842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-02-22T07:38:01Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"1c5ccf890a3b8b609692f9f0e12d9a61438ea62b51c031a753ffa559abfde73e","abstract_canon_sha256":"a5a426f4bf537579396398eb4f3d7e0db9c126aa1b6e3b2f0037bbf1cb90bd6c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:25.983363Z","signature_b64":"qb6gTWOjIDAXB+Msla8Er4pZNW5KfBYlnaX6CL8pFGkZWZZwxvxS1TULVJsEe9QpUyEVvj5Gn+vDiEoK28rcDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08590c9d14a469cc92ed5628c20cf40ed928cc1fdec05b63554b667a8b9d33e3","last_reissued_at":"2026-05-18T03:30:25.982599Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:25.982599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vectorial solutions to list multicoloring problems on graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"IMATH), Jean-Christophe Godin (IMATH), Olivier Togni (Le2i), Yves Aubry (IML","submitted_at":"2012-02-22T07:38:01Z","abstract_excerpt":"For a graph $G$ with a given list assignment $L$ on the vertices, we give an algebraical description of the set of all weights $w$ such that $G$ is $(L,w)$-colorable, called permissible weights. Moreover, for a graph $G$ with a given list $L$ and a given permissible weight $w$, we describe the set of all $(L,w)$-colorings of $G$. By the way, we solve the {\\sl channel assignment problem}. Furthermore, we describe the set of solutions to the {\\sl on call problem}: when $w$ is not a permissible weight, we find all the nearest permissible weights $w'$. Finally, we give a solution to the non-recolo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4842","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":"1202.4842","created_at":"2026-05-18T03:30:25.982740+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.4842v1","created_at":"2026-05-18T03:30:25.982740+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4842","created_at":"2026-05-18T03:30:25.982740+00:00"},{"alias_kind":"pith_short_12","alias_value":"BBMQZHIUURU4","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"BBMQZHIUURU4ZEXN","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"BBMQZHIU","created_at":"2026-05-18T12:26:58.693483+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/BBMQZHIUURU4ZEXNKYUMEDHUB3","json":"https://pith.science/pith/BBMQZHIUURU4ZEXNKYUMEDHUB3.json","graph_json":"https://pith.science/api/pith-number/BBMQZHIUURU4ZEXNKYUMEDHUB3/graph.json","events_json":"https://pith.science/api/pith-number/BBMQZHIUURU4ZEXNKYUMEDHUB3/events.json","paper":"https://pith.science/paper/BBMQZHIU"},"agent_actions":{"view_html":"https://pith.science/pith/BBMQZHIUURU4ZEXNKYUMEDHUB3","download_json":"https://pith.science/pith/BBMQZHIUURU4ZEXNKYUMEDHUB3.json","view_paper":"https://pith.science/paper/BBMQZHIU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.4842&json=true","fetch_graph":"https://pith.science/api/pith-number/BBMQZHIUURU4ZEXNKYUMEDHUB3/graph.json","fetch_events":"https://pith.science/api/pith-number/BBMQZHIUURU4ZEXNKYUMEDHUB3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BBMQZHIUURU4ZEXNKYUMEDHUB3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BBMQZHIUURU4ZEXNKYUMEDHUB3/action/storage_attestation","attest_author":"https://pith.science/pith/BBMQZHIUURU4ZEXNKYUMEDHUB3/action/author_attestation","sign_citation":"https://pith.science/pith/BBMQZHIUURU4ZEXNKYUMEDHUB3/action/citation_signature","submit_replication":"https://pith.science/pith/BBMQZHIUURU4ZEXNKYUMEDHUB3/action/replication_record"}},"created_at":"2026-05-18T03:30:25.982740+00:00","updated_at":"2026-05-18T03:30:25.982740+00:00"}