{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:YFHLK54UM2QFIAQPRZP5IRXLTY","short_pith_number":"pith:YFHLK54U","schema_version":"1.0","canonical_sha256":"c14eb5779466a054020f8e5fd446eb9e38896d3083f4607c1435d43801ebfd5b","source":{"kind":"arxiv","id":"1001.1334","version":2},"attestation_state":"computed","paper":{"title":"Minimum Number of Fox Colors for Small Primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"J. Matias, P. Lopes","submitted_at":"2010-01-08T18:50:19Z","abstract_excerpt":"This article concerns exact results on the minimum number of colors of a Fox coloring over the integers modulo r, of a link with non-null determinant. Specifically, we prove that whenever the least prime divisor of the determinant of such a link and the modulus r is 2, 3, 5, or 7, then the minimum number of colors is 2, 3, 4, or 4 (respectively) and conversely. We are thus led to conjecture that for each prime p there exists a unique positive integer, m, with the following property. For any link L of non-null determinant and any modulus r such that p is the least prime divisor of the determina"},"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":"1001.1334","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-01-08T18:50:19Z","cross_cats_sorted":[],"title_canon_sha256":"6051e713758d5efb53b1553d49c3faa4c057e513fa9ca1465f0bb59f2d49aeb5","abstract_canon_sha256":"4443d4df6a7e0fcf229a6616215ab48f4bd0979e1a94506dbc73d610f94ea0e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:43.897855Z","signature_b64":"O9NKyWmMGfLW6AVDL6ILZSIVAIBTOdz8uIFlOVEw4z2rao7Yuyuu/WHDDjcL4VRiBFo57PY9nQF4pfWukLA0Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c14eb5779466a054020f8e5fd446eb9e38896d3083f4607c1435d43801ebfd5b","last_reissued_at":"2026-05-18T04:24:43.897502Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:43.897502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimum Number of Fox Colors for Small Primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"J. Matias, P. Lopes","submitted_at":"2010-01-08T18:50:19Z","abstract_excerpt":"This article concerns exact results on the minimum number of colors of a Fox coloring over the integers modulo r, of a link with non-null determinant. Specifically, we prove that whenever the least prime divisor of the determinant of such a link and the modulus r is 2, 3, 5, or 7, then the minimum number of colors is 2, 3, 4, or 4 (respectively) and conversely. We are thus led to conjecture that for each prime p there exists a unique positive integer, m, with the following property. For any link L of non-null determinant and any modulus r such that p is the least prime divisor of the determina"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.1334","kind":"arxiv","version":2},"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":"1001.1334","created_at":"2026-05-18T04:24:43.897557+00:00"},{"alias_kind":"arxiv_version","alias_value":"1001.1334v2","created_at":"2026-05-18T04:24:43.897557+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.1334","created_at":"2026-05-18T04:24:43.897557+00:00"},{"alias_kind":"pith_short_12","alias_value":"YFHLK54UM2QF","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"YFHLK54UM2QFIAQP","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"YFHLK54U","created_at":"2026-05-18T12:26:17.028572+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/YFHLK54UM2QFIAQPRZP5IRXLTY","json":"https://pith.science/pith/YFHLK54UM2QFIAQPRZP5IRXLTY.json","graph_json":"https://pith.science/api/pith-number/YFHLK54UM2QFIAQPRZP5IRXLTY/graph.json","events_json":"https://pith.science/api/pith-number/YFHLK54UM2QFIAQPRZP5IRXLTY/events.json","paper":"https://pith.science/paper/YFHLK54U"},"agent_actions":{"view_html":"https://pith.science/pith/YFHLK54UM2QFIAQPRZP5IRXLTY","download_json":"https://pith.science/pith/YFHLK54UM2QFIAQPRZP5IRXLTY.json","view_paper":"https://pith.science/paper/YFHLK54U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1001.1334&json=true","fetch_graph":"https://pith.science/api/pith-number/YFHLK54UM2QFIAQPRZP5IRXLTY/graph.json","fetch_events":"https://pith.science/api/pith-number/YFHLK54UM2QFIAQPRZP5IRXLTY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YFHLK54UM2QFIAQPRZP5IRXLTY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YFHLK54UM2QFIAQPRZP5IRXLTY/action/storage_attestation","attest_author":"https://pith.science/pith/YFHLK54UM2QFIAQPRZP5IRXLTY/action/author_attestation","sign_citation":"https://pith.science/pith/YFHLK54UM2QFIAQPRZP5IRXLTY/action/citation_signature","submit_replication":"https://pith.science/pith/YFHLK54UM2QFIAQPRZP5IRXLTY/action/replication_record"}},"created_at":"2026-05-18T04:24:43.897557+00:00","updated_at":"2026-05-18T04:24:43.897557+00:00"}