Large language models (LLMs) have transformed natural language processing, yet their capabilities remain uneven across languages. Most multilingual models are trained primarily on high-resource languages, leaving many languages with large speaker populations underrepresented in both training data and evaluation benchmarks. This imbalance is particularly visible in the Turkic language family. This paper proposes a theoretical framework for studying cross-lingual transfer and parameter-efficient adaptation of multilingual LLMs within the Turkic language family, focusing on Azerbaijani, Kazakh, UResearch goal: How does parameter-efficient fine-tuning impact zero-shot cross-lingual transfer accuracy for low-resource Turkic languages on the XCOPA and XNLI benchmarks compared to full-model fine-tuning?Autonomous synthesis report generated by Assignee Research. Tribunal consensus score: 7.6/10.