{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:55QGUPGQMJHTYIRLTKWJTAI7XH","short_pith_number":"pith:55QGUPGQ","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"},"canonical_sha256":"ef606a3cd0624f3c222b9aac99811fb9f110ca1a0f0319566d5d72e205576697","source":{"kind":"arxiv","id":"1805.02189","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.02189","created_at":"2026-05-18T00:00:30Z"},{"alias_kind":"arxiv_version","alias_value":"1805.02189v4","created_at":"2026-05-18T00:00:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.02189","created_at":"2026-05-18T00:00:30Z"},{"alias_kind":"pith_short_12","alias_value":"55QGUPGQMJHT","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"55QGUPGQMJHTYIRL","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"55QGUPGQ","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:55QGUPGQMJHTYIRLTKWJTAI7XH","target":"record","payload":{"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"},"canonical_sha256":"ef606a3cd0624f3c222b9aac99811fb9f110ca1a0f0319566d5d72e205576697","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"},"source_kind":"arxiv","source_id":"1805.02189","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:00:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aEWUCictMANY9c5vLDY+9grhSzjBHYMzn23DWZoG+6fy6C0AgfhGHIx2zavzFLMxQCOh4k5edpcd6NUz6Vt7CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:44:30.610866Z"},"content_sha256":"e62a80b851afaf1e590acb018d140f94b16c1b9f696c6bb2c6b73d0ea6dd4102","schema_version":"1.0","event_id":"sha256:e62a80b851afaf1e590acb018d140f94b16c1b9f696c6bb2c6b73d0ea6dd4102"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:55QGUPGQMJHTYIRLTKWJTAI7XH","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:00:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kh3mvrVS4abqseoBIte4ZVJopBkQbQ8yBcu4CxG6AHJ7Ffvaa5SUOoVq1kftQZq99z/02VdQp0zSd9fSxzrkAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:44:30.611451Z"},"content_sha256":"da85667dbfd1ae56617f0961f5efefbcba95f00ba022ed26c7a0c2f6fd93bad8","schema_version":"1.0","event_id":"sha256:da85667dbfd1ae56617f0961f5efefbcba95f00ba022ed26c7a0c2f6fd93bad8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/55QGUPGQMJHTYIRLTKWJTAI7XH/bundle.json","state_url":"https://pith.science/pith/55QGUPGQMJHTYIRLTKWJTAI7XH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/55QGUPGQMJHTYIRLTKWJTAI7XH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T01:44:30Z","links":{"resolver":"https://pith.science/pith/55QGUPGQMJHTYIRLTKWJTAI7XH","bundle":"https://pith.science/pith/55QGUPGQMJHTYIRLTKWJTAI7XH/bundle.json","state":"https://pith.science/pith/55QGUPGQMJHTYIRLTKWJTAI7XH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/55QGUPGQMJHTYIRLTKWJTAI7XH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:55QGUPGQMJHTYIRLTKWJTAI7XH","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":"94522c8205791deb00ef66939c061f6fbc0808f5e228d575e48201c711fe836f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-05-06T10:47:45Z","title_canon_sha256":"dfa685cd616698ea83de71f6fd7f7901aa53c39577c95bffc6dd2114adc51f89"},"schema_version":"1.0","source":{"id":"1805.02189","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.02189","created_at":"2026-05-18T00:00:30Z"},{"alias_kind":"arxiv_version","alias_value":"1805.02189v4","created_at":"2026-05-18T00:00:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.02189","created_at":"2026-05-18T00:00:30Z"},{"alias_kind":"pith_short_12","alias_value":"55QGUPGQMJHT","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"55QGUPGQMJHTYIRL","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"55QGUPGQ","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:da85667dbfd1ae56617f0961f5efefbcba95f00ba022ed26c7a0c2f6fd93bad8","target":"graph","created_at":"2026-05-18T00:00:30Z","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":"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 $","authors_text":"Lorenzo Traldi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-05-06T10:47:45Z","title":"Multivariate Alexander colorings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02189","kind":"arxiv","version":4},"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:e62a80b851afaf1e590acb018d140f94b16c1b9f696c6bb2c6b73d0ea6dd4102","target":"record","created_at":"2026-05-18T00:00:30Z","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":"94522c8205791deb00ef66939c061f6fbc0808f5e228d575e48201c711fe836f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-05-06T10:47:45Z","title_canon_sha256":"dfa685cd616698ea83de71f6fd7f7901aa53c39577c95bffc6dd2114adc51f89"},"schema_version":"1.0","source":{"id":"1805.02189","kind":"arxiv","version":4}},"canonical_sha256":"ef606a3cd0624f3c222b9aac99811fb9f110ca1a0f0319566d5d72e205576697","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef606a3cd0624f3c222b9aac99811fb9f110ca1a0f0319566d5d72e205576697","first_computed_at":"2026-05-18T00:00:30.351956Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:30.351956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4s9VbPqeunrwskeiT52Vxcvlbf/X3Ieyojyui4RidVURRxiKst2uq8+Ry5pE3362IogN6U7nJAnULDyXYbBOAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:30.352569Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.02189","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e62a80b851afaf1e590acb018d140f94b16c1b9f696c6bb2c6b73d0ea6dd4102","sha256:da85667dbfd1ae56617f0961f5efefbcba95f00ba022ed26c7a0c2f6fd93bad8"],"state_sha256":"439e5cf3ab5f3615056b13715fafe81a485a0f4f09967047dd51617d419bead3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sLEGfSFUoF4hq02RZwYhJ9PoRzKEsTrYno8Y+2Hoxqx+sLXw0V7CsPZxVH5mCUpyQXDSUE4qtHT5aT7C9QalAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T01:44:30.614463Z","bundle_sha256":"8bca20fd1c898b92710326f0943c642627f23c129584491072b742edc503a75c"}}