Genomic language models generate long nucleotide continuations from short prefixes, exposing a direct route for studying training-sequence extraction through the generation interface. We present an output-only black-box attack on Evo 2 that selects convergent groups of repeated generations without gradients, token likelihoods, or training-corpus access during candidate selection. Recovered content is then scored by an evaluator combining aligned length, nucleotide identity, match multiplicity, and sequence complexity. Across 304 runs on Evo 2 7B with bacteriophage and plasmid prefixes, the attack yields 888 candidate clusters, of which 85 match training segments of at least 500 bp, giving a cluster-level attack success rate of 9.57%. Final filtering retains 22 uniquely matched extraction events at the 500-bp threshold and 15 at 1,000 bp, covering 14 and 7 distinct training-sequence regions, respectively. Within-category source-homology screening retains 11 of the 22 events at a 99% exclusion threshold and four at 98%, with the latter mapping to two reference regions. The results establish convergence among repeated nucleotide generations as a practical output-only signal for recovering long training-sequence segments and characterize how recovery depends on prefix length, cluster size, perplexity, early stopping, and sequence domains.

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