Current self-evolution methods mostly chase recall, they learn from any trajectory that ends with the right answer, even when the path relies on a "lucky guess". Such reasoning appears valid in-distribution but often fails the moment the task shifts slightly. We argue that robust evolution implies Structural Invariance: a reasoning path is valid only if its core dependency graph remains isomorphic under counterfactual perturbations. I-EDI enforces this with Verifiable Counterfactual Simulation (VCS). Instead of treating data generation as mere "sample and filter," we treat it as an intervention. Unlike standard rejection sampling, VCS acts as a structural stress test: it accepts a reasoning trace only if it remains valid across generated counterfactuals (e.g., numerical perturbations, context shifts). While this strict filtering reduces the volume of training data (trading recall for precision), our experiments on MATH and GSM8K show it effectively prevents hallucination accumulation, achieving superior out-of-distribution generalization compared to baselines.