Proprietary language models and their reasoning traces are vulnerable to API-based distillation, where an adversary trains a student model on the teacher model's outputs. To obtain evidence of distillation, model providers can watermark the teacher's outputs, aiming to leave a radioactive signal in the student's outputs. Existing black-box detectors search for such radioactivity using token-level statistics of the suspect model's outputs. However, token-level signals are not always detectable, for instance when the distillation traces are sampled at a low temperature. In this work, we discover the watermark basin, a persistent signal that enables more reliable watermark detection: during fine-tuning, watermarked teacher traces embed a distinct, key-specific geometric signal in parameter space that lies orthogonal to the ordinary task-specific fine-tuning subspace. Building on this, we introduce Watermark Basin Alignment (WM-Basin), a black-box watermark detector that queries the suspect model through its API, without access to its weights or logits. WM-Basin maps generated text to gradient representations using a fixed clean probe model, projects out the ordinary fine-tuning task directions, and tests whether the residual gradient aligns with the watermark basin induced by the watermark key. We evaluate WM-Basin extensively across diverse teacher models and student architectures (from 135M to 8.2B parameters) distilled on mathematical reasoning. At a strict 0.1% false-positive rate, WM-Basin detects 79% of distilled models at n-gram=1 and 45% at n-gram=3, substantially improving over the state-of-the-art token-level baseline (29% and 1.3%, respectively). Because the watermark signal resides in a persistent basin, it survives post-distillation modifications including quantization, pruning, and reinforcement-learning post-training.

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