{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:7WCIXMR37ZIGUMECN7ZLN4VCGT","short_pith_number":"pith:7WCIXMR3","schema_version":"1.0","canonical_sha256":"fd848bb23bfe506a30826ff2b6f2a234c3e2262c12a5c12fc4c5efe679b51453","source":{"kind":"arxiv","id":"1610.00424","version":1},"attestation_state":"computed","paper":{"title":"Algebraic properties of chromatic roots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Kerri Morgan, Peter J. Cameron","submitted_at":"2016-10-03T06:46:39Z","abstract_excerpt":"A \\emph{chromatic root} is a root of the chromatic polynomial of a graph. Any chromatic root is an algebraic integer. Much is known about the location of chromatic roots in the real and complex numbers, but rather less about their properties as algebraic numbers. This question was the subject of a seminar at the Isaac Newton Institute in late 2008. The purpose of this paper is to report on the seminar and subsequent developments.\n  We conjecture that, for every algebraic integer $\\alpha$, there is a natural number $n$ such that $\\alpha+n$ is a chromatic root. This is proved for quadratic integ"},"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":"1610.00424","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-03T06:46:39Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"b2c2030e960f4be9ad65e21d03ec54d055660555460a730df9e6540d869652ef","abstract_canon_sha256":"85a5f8e5fdbcbff17c7ad46b8efcdb25cb3075bed0913a818c1a20ac4885be09"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:43.629470Z","signature_b64":"bV1XLzVAD2hfv6lbeUezITfN3O3OI8OuRsnRjifS1TWool0zpSbwAsULODUn5hRYT+lq2ADRCyUpQCn9sJJ6Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd848bb23bfe506a30826ff2b6f2a234c3e2262c12a5c12fc4c5efe679b51453","last_reissued_at":"2026-05-17T23:44:43.629031Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:43.629031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebraic properties of chromatic roots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Kerri Morgan, Peter J. Cameron","submitted_at":"2016-10-03T06:46:39Z","abstract_excerpt":"A \\emph{chromatic root} is a root of the chromatic polynomial of a graph. Any chromatic root is an algebraic integer. Much is known about the location of chromatic roots in the real and complex numbers, but rather less about their properties as algebraic numbers. This question was the subject of a seminar at the Isaac Newton Institute in late 2008. The purpose of this paper is to report on the seminar and subsequent developments.\n  We conjecture that, for every algebraic integer $\\alpha$, there is a natural number $n$ such that $\\alpha+n$ is a chromatic root. This is proved for quadratic integ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00424","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":"1610.00424","created_at":"2026-05-17T23:44:43.629094+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.00424v1","created_at":"2026-05-17T23:44:43.629094+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00424","created_at":"2026-05-17T23:44:43.629094+00:00"},{"alias_kind":"pith_short_12","alias_value":"7WCIXMR37ZIG","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_16","alias_value":"7WCIXMR37ZIGUMEC","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_8","alias_value":"7WCIXMR3","created_at":"2026-05-18T12:30:04.600751+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/7WCIXMR37ZIGUMECN7ZLN4VCGT","json":"https://pith.science/pith/7WCIXMR37ZIGUMECN7ZLN4VCGT.json","graph_json":"https://pith.science/api/pith-number/7WCIXMR37ZIGUMECN7ZLN4VCGT/graph.json","events_json":"https://pith.science/api/pith-number/7WCIXMR37ZIGUMECN7ZLN4VCGT/events.json","paper":"https://pith.science/paper/7WCIXMR3"},"agent_actions":{"view_html":"https://pith.science/pith/7WCIXMR37ZIGUMECN7ZLN4VCGT","download_json":"https://pith.science/pith/7WCIXMR37ZIGUMECN7ZLN4VCGT.json","view_paper":"https://pith.science/paper/7WCIXMR3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.00424&json=true","fetch_graph":"https://pith.science/api/pith-number/7WCIXMR37ZIGUMECN7ZLN4VCGT/graph.json","fetch_events":"https://pith.science/api/pith-number/7WCIXMR37ZIGUMECN7ZLN4VCGT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7WCIXMR37ZIGUMECN7ZLN4VCGT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7WCIXMR37ZIGUMECN7ZLN4VCGT/action/storage_attestation","attest_author":"https://pith.science/pith/7WCIXMR37ZIGUMECN7ZLN4VCGT/action/author_attestation","sign_citation":"https://pith.science/pith/7WCIXMR37ZIGUMECN7ZLN4VCGT/action/citation_signature","submit_replication":"https://pith.science/pith/7WCIXMR37ZIGUMECN7ZLN4VCGT/action/replication_record"}},"created_at":"2026-05-17T23:44:43.629094+00:00","updated_at":"2026-05-17T23:44:43.629094+00:00"}