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There is a pair of diagrams, one for 6_2 and the other one for 7_2, each of them admitting only non-trivial 11-colorings using 5 colors, but neither of them admitting being colored with the sets of 5 colors that color the other one. This is in full contrast with the behavior exhibited by links admitting non-trivial p-colorings over the smaller primes, p=2, 3, 5 or 7.\n  We also prove results concerning obstructions to the minimization "},"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":"1308.6054","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-08-28T04:38:38Z","cross_cats_sorted":[],"title_canon_sha256":"04352e3c68780be1709738909b0c5bc490820036ac5b2ca88281b18c69a551b0","abstract_canon_sha256":"f2615ba0f9632a689a8097051554add889241d1e290933a27b2d085df3615879"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:25.833904Z","signature_b64":"qaEsBpODhrcVlU1R7JbYN6mK4c2czlzEj1636YgYZKjbaIBlMSLZKpk5b1KV8nKufODKWQI144l1IDd9viBRAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02d9fe7840af22c3ff5d82c636a1779faa60d613deca1b0e4aa7f5615ddaec16","last_reissued_at":"2026-05-18T02:19:25.833072Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:25.833072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Minimization of the Number of Colors is Different at p=11","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Pedro Lopes","submitted_at":"2013-08-28T04:38:38Z","abstract_excerpt":"In this article we present the following new fact for prime p=11. For knots 6_2 and 7_2, mincol_{11} 6_2 = 5 = mincol_{11} 7_2, along with the following feature. There is a pair of diagrams, one for 6_2 and the other one for 7_2, each of them admitting only non-trivial 11-colorings using 5 colors, but neither of them admitting being colored with the sets of 5 colors that color the other one. This is in full contrast with the behavior exhibited by links admitting non-trivial p-colorings over the smaller primes, p=2, 3, 5 or 7.\n  We also prove results concerning obstructions to the minimization "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6054","kind":"arxiv","version":3},"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":"1308.6054","created_at":"2026-05-18T02:19:25.833209+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.6054v3","created_at":"2026-05-18T02:19:25.833209+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6054","created_at":"2026-05-18T02:19:25.833209+00:00"},{"alias_kind":"pith_short_12","alias_value":"ALM746CAV4RM","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_16","alias_value":"ALM746CAV4RMH725","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_8","alias_value":"ALM746CA","created_at":"2026-05-18T12:27:38.830355+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/ALM746CAV4RMH725QLDDNILXT6","json":"https://pith.science/pith/ALM746CAV4RMH725QLDDNILXT6.json","graph_json":"https://pith.science/api/pith-number/ALM746CAV4RMH725QLDDNILXT6/graph.json","events_json":"https://pith.science/api/pith-number/ALM746CAV4RMH725QLDDNILXT6/events.json","paper":"https://pith.science/paper/ALM746CA"},"agent_actions":{"view_html":"https://pith.science/pith/ALM746CAV4RMH725QLDDNILXT6","download_json":"https://pith.science/pith/ALM746CAV4RMH725QLDDNILXT6.json","view_paper":"https://pith.science/paper/ALM746CA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.6054&json=true","fetch_graph":"https://pith.science/api/pith-number/ALM746CAV4RMH725QLDDNILXT6/graph.json","fetch_events":"https://pith.science/api/pith-number/ALM746CAV4RMH725QLDDNILXT6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ALM746CAV4RMH725QLDDNILXT6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ALM746CAV4RMH725QLDDNILXT6/action/storage_attestation","attest_author":"https://pith.science/pith/ALM746CAV4RMH725QLDDNILXT6/action/author_attestation","sign_citation":"https://pith.science/pith/ALM746CAV4RMH725QLDDNILXT6/action/citation_signature","submit_replication":"https://pith.science/pith/ALM746CAV4RMH725QLDDNILXT6/action/replication_record"}},"created_at":"2026-05-18T02:19:25.833209+00:00","updated_at":"2026-05-18T02:19:25.833209+00:00"}