Training data detection is critical for enforcing copyright and data licensing, as Large Language Models are trained on massive text corpora scraped from the internet. We present SPECTRA, a watermarking approach that makes training data reliably detectable even when it comprises less than 0.001 \% of the training corpus. SPECTRA works by using an LLM to generate semantically equivalent paraphrases of text, and then computing its token log probabilities, using a scoring model that was not trained on the text. A paraphrase is then sampled with a score computed using the token log probabilities that is close to the score of the original text. We compare the token log probabilities of a "suspect" model to those of the scoring model to detect if the watermarked data was used for training. We demonstrate that SPECTRA achieves a consistent p-value gap of over nine orders of magnitude when detecting data used to train a model versus data not used to train a model. SPECTRA equips data owners with a scalable, deploy‑before‑release watermark that survives even large‑scale LLM training.