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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 ","authors_text":"Pedro Lopes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-08-28T04:38:38Z","title":"The Minimization of the Number of Colors is Different at p=11"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6054","kind":"arxiv","version":3},"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":"sha256:2a9611b73c60eb2feb38195a64fc6e439559c7e613edb4c5ca710ae601be862e","target":"record","created_at":"2026-05-18T02:19:25Z","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":"f2615ba0f9632a689a8097051554add889241d1e290933a27b2d085df3615879","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-08-28T04:38:38Z","title_canon_sha256":"04352e3c68780be1709738909b0c5bc490820036ac5b2ca88281b18c69a551b0"},"schema_version":"1.0","source":{"id":"1308.6054","kind":"arxiv","version":3}},"canonical_sha256":"02d9fe7840af22c3ff5d82c636a1779faa60d613deca1b0e4aa7f5615ddaec16","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02d9fe7840af22c3ff5d82c636a1779faa60d613deca1b0e4aa7f5615ddaec16","first_computed_at":"2026-05-18T02:19:25.833072Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:25.833072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qaEsBpODhrcVlU1R7JbYN6mK4c2czlzEj1636YgYZKjbaIBlMSLZKpk5b1KV8nKufODKWQI144l1IDd9viBRAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:25.833904Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.6054","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a9611b73c60eb2feb38195a64fc6e439559c7e613edb4c5ca710ae601be862e","sha256:e93a886e9f0d8670abce4e9a7bcf91cf8d69f2cd3b15b5ac6182a1b618c2fce9"],"state_sha256":"6b5a98c465d00d3ec9280c3946f31d554f496b99a8edcf2cb819d494ef7d97ed"}