Fingerprinting Large Language Models (LLMs) is essential for provenance verification and model attribution. Existing methods typically extract post-hoc signatures based on training dynamics, data exposure, or hyperparameters -- properties that only emerge after training begins. In contrast, we propose a stronger and more intrinsic notion of LLM fingerprinting: SeedPrints, a method that leverages random initialization biases as persistent, seed-dependent identifiers present even before training. We show that untrained models exhibit reproducible token selection biases conditioned solely on their parameters at initialization. These biases are stable and measurable throughout training, enabling our statistical detection method to recover a model's lineage with high confidence. Unlike prior techniques, unreliable before convergence and vulnerable to distribution shifts, SeedPrints remains effective across all training stages and robust under domain shifts or parameter modifications. Experiments on LLaMA-style and Qwen-style models show that SeedPrints achieves seed-level distinguishability and can provide birth-to-lifecycle identity verification akin to a biometric fingerprint. Evaluations on large-scale pretrained models and fingerprinting benchmarks further confirm its effectiveness under practical deployment scenarios. These results suggest that initialization itself imprints a unique and persistent identity on neural language models, forming a true ''Galtonian'' fingerprint.

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