This paper introduces a statistical framework for making valid scientific discoveries using synthetic data, specifically addressing concerns that artificially generated data can be biased or noisy. The authors propose a new technical condition called task exchangeability, which allows researchers to calibrate synthetic results by comparing them to historical tasks where both real and synthetic data are available. By measuring the discrepancy between real and synthetic outcomes in these past cases, the method can adjust confidence intervals for new tasks where only synthetic data exists. The researchers demonstrate that this approach provides provable validity guarantees across various fields, including social science surveys and AI evaluation. Experiments show that while naive synthetic-only intervals are often severely biased and overconfident, the task-exchangeability method consistently covers the true values. Ultimately, this framework enables scientists to use LLM-generated "silicon samples" and automated raters to accelerate discovery without sacrificing statistical rigor.