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If $D$ is a diagram of a link $L$ with $\\mu$ components, then the colorings of $D$ with values in $M$ form a $\\Lambda_{\\mu}$-module $\\mathrm{Color}_A(D,M)$. Extending a result of Inoue [Kodai Math.\\ J.\\ 33 (2010), 116-122], we show that $\\mathrm{Color}_A(D,M)$ is isomorphic to the module of $\\Lambda_{\\mu}$-linear maps from the Alexander module of $L$ to $M$. In particular, suppose $"},"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":"1805.02189","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-05-06T10:47:45Z","cross_cats_sorted":[],"title_canon_sha256":"dfa685cd616698ea83de71f6fd7f7901aa53c39577c95bffc6dd2114adc51f89","abstract_canon_sha256":"94522c8205791deb00ef66939c061f6fbc0808f5e228d575e48201c711fe836f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:30.352569Z","signature_b64":"4s9VbPqeunrwskeiT52Vxcvlbf/X3Ieyojyui4RidVURRxiKst2uq8+Ry5pE3362IogN6U7nJAnULDyXYbBOAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef606a3cd0624f3c222b9aac99811fb9f110ca1a0f0319566d5d72e205576697","last_reissued_at":"2026-05-18T00:00:30.351956Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:30.351956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multivariate Alexander colorings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Lorenzo Traldi","submitted_at":"2018-05-06T10:47:45Z","abstract_excerpt":"We extend the notion of link colorings with values in an Alexander quandle to link colorings with values in a module $M$ over the Laurent polynomial ring $\\Lambda_{\\mu}=\\mathbb{Z}[t_1^{\\pm1},\\dots,t_{\\mu}^{\\pm1}]$. If $D$ is a diagram of a link $L$ with $\\mu$ components, then the colorings of $D$ with values in $M$ form a $\\Lambda_{\\mu}$-module $\\mathrm{Color}_A(D,M)$. Extending a result of Inoue [Kodai Math.\\ J.\\ 33 (2010), 116-122], we show that $\\mathrm{Color}_A(D,M)$ is isomorphic to the module of $\\Lambda_{\\mu}$-linear maps from the Alexander module of $L$ to $M$. In particular, suppose $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02189","kind":"arxiv","version":4},"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":"1805.02189","created_at":"2026-05-18T00:00:30.352051+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.02189v4","created_at":"2026-05-18T00:00:30.352051+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.02189","created_at":"2026-05-18T00:00:30.352051+00:00"},{"alias_kind":"pith_short_12","alias_value":"55QGUPGQMJHT","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_16","alias_value":"55QGUPGQMJHTYIRL","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_8","alias_value":"55QGUPGQ","created_at":"2026-05-18T12:32:05.422762+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/55QGUPGQMJHTYIRLTKWJTAI7XH","json":"https://pith.science/pith/55QGUPGQMJHTYIRLTKWJTAI7XH.json","graph_json":"https://pith.science/api/pith-number/55QGUPGQMJHTYIRLTKWJTAI7XH/graph.json","events_json":"https://pith.science/api/pith-number/55QGUPGQMJHTYIRLTKWJTAI7XH/events.json","paper":"https://pith.science/paper/55QGUPGQ"},"agent_actions":{"view_html":"https://pith.science/pith/55QGUPGQMJHTYIRLTKWJTAI7XH","download_json":"https://pith.science/pith/55QGUPGQMJHTYIRLTKWJTAI7XH.json","view_paper":"https://pith.science/paper/55QGUPGQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.02189&json=true","fetch_graph":"https://pith.science/api/pith-number/55QGUPGQMJHTYIRLTKWJTAI7XH/graph.json","fetch_events":"https://pith.science/api/pith-number/55QGUPGQMJHTYIRLTKWJTAI7XH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/55QGUPGQMJHTYIRLTKWJTAI7XH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/55QGUPGQMJHTYIRLTKWJTAI7XH/action/storage_attestation","attest_author":"https://pith.science/pith/55QGUPGQMJHTYIRLTKWJTAI7XH/action/author_attestation","sign_citation":"https://pith.science/pith/55QGUPGQMJHTYIRLTKWJTAI7XH/action/citation_signature","submit_replication":"https://pith.science/pith/55QGUPGQMJHTYIRLTKWJTAI7XH/action/replication_record"}},"created_at":"2026-05-18T00:00:30.352051+00:00","updated_at":"2026-05-18T00:00:30.352051+00:00"}