Self-improving systems require environmental interaction for continuous adaptation. We introduce SPICE (Self-Play In Corpus Environments), a reinforcement learning framework where a single model acts in two roles: a Challenger that mines documents from a large corpus to generate diverse reasoning tasks, and a Reasoner that solves them. Through adversarial dynamics, the Challenger creates an automatic curriculum at the frontier of the Reasoner's capability, while corpus grounding provides the rich, near-inexhaustible external signal necessary for sustained improvement. Unlike existing ungrounded self-play methods that offer more limited benefits, SPICE achieves consistent gains across mathematical (+8.9%) and general reasoning (+9.8%) benchmarks on multiple model families. Our analysis reveals how document grounding is a key ingredient in SPICE to continuously generate its own increasingly challenging goals and achieve them, enabling sustained self-improvement.