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For every k-component oriented link L, every partition P of L into h:=|P| sublinks, and every labelling z of such a partition by the natural numbers z_1,...,z_n, the number of X-colorings of any diagram of (L,z) is a well-defined invariant of (L,P), of the form q^(a_X(L,P,z)+1) for some natural number a_X(L,P,z). Letting X and z vary in Q_F and among the labellings of P, we define a derived invariant A_Q(L,P)=sup a_X(L,P,z).\n  If P_M is such that |P_M|=k, we show that A_Q(L,P_M) is a lower bound for t(L","authors_text":"Riccardo Benedetti, Roberto Frigerio","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-04-20T13:36:39Z","title":"Alexander quandle lower bounds for link genera"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4018","kind":"arxiv","version":1},"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":"sha256:8a2236c845a7b55691e87ee991b963f8f8b1bf90b64719ba2c299ffb3ec930ee","target":"record","created_at":"2026-05-18T02:22:01Z","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":"1550cec6a0368882beb3ff75d31bf984c418a22b27427ade2f142e372abee74f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-04-20T13:36:39Z","title_canon_sha256":"6c79800d4eeac2415234ad34e4ee2b6a4f7dc9400512456e8197baeb490585c5"},"schema_version":"1.0","source":{"id":"1104.4018","kind":"arxiv","version":1}},"canonical_sha256":"50e4b4cd32f45f7dc30b0cbcb70c463ee1aa89ddef235445d4cdb690bcc13f63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50e4b4cd32f45f7dc30b0cbcb70c463ee1aa89ddef235445d4cdb690bcc13f63","first_computed_at":"2026-05-18T02:22:01.871890Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:01.871890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ArymUk1kiJOszcNReLeKVzAzl+VI7LJHYAtT+T/gBAbDjJ2osDNZV7jnUPRdBj7l0gG5wUONKAFd9uEi1nGpAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:01.872586Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.4018","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a2236c845a7b55691e87ee991b963f8f8b1bf90b64719ba2c299ffb3ec930ee","sha256:6c2f2ee192a79b9ba04500b5baec428f8cc2de55c3ed652876b57b0dd1b1b739"],"state_sha256":"b61348c40f75f3349d15480d064d161b39879509677fa944d7863eef0b5b78a9"}