Large language models (LLMs) are valuable digital assets, yet their weights can be easily modified after unauthorized acquisition, making model provenance difficult to verify. Model fingerprinting provides a promising solution for model ownership protection without modifying the model or embedding ownership information. However, parameter-based fingerprints can be sensitive to model transformations, limiting their robustness, while representation-based fingerprints may assign high similarity to unrelated models, limiting their uniqueness. To address these limitations, we propose TrFP, an intrinsic fingerprinting method based on computational trajectories. Instead of comparing model parameters or representations, TrFP captures how representations evolve across network depth and constructs compact fingerprints using permutation-invariant trajectory descriptors. Experiments across multiple LLM families show that TrFP reliably distinguishes related and unrelated models. It also remains robust under fine-tuning, pruning, quantization, model merging, parameter permutation, and adaptive attacks, while requiring less than 0.3 MiB of fingerprint storage. Overall, TrFP provides stronger provenance discrimination than several existing state-of-the-art methods, demonstrating the effectiveness of computational trajectories for reliable LLM provenance verification.

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