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Existing methods are limited by task specificity, fixed model sets, or strict assumptions about tokenizers or architectures. Inspired by biological DNA, we address these limitations by mathematically defining LLM DNA as a low-dimensional, bi-Lipschitz representation of functional behavior. We prove that LLM DNA satisfies inheritance and genetic determinism properties and establish the existence of DNA. Building on this theory, we derive a general, scalable, training-free pipeline for DNA extraction. In experiments across 305 LLMs, DNA aligns with prior studies on limited subsets and achieves superior or competitive performance on specific tasks. 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