We introduce Apeiron, a scalable and extensible framework for addressing *amorphous* user demands through autonomous, full-lifecycle application synthesis. Apeiron models the unstructured app development process as a heuristic optimization problem combining (i) a Computer-Use Agent (CUA) evaluator that simulates personas and demands, (ii) an *Activity Tracer* that grounds feedback in code-level interaction traces, and (iii) a *Locality Controller* that constrains changes during continuous integration and delivery (CI/CD). Furthermore, we introduce an innovative data generation approach using CUA-as-a-Judge to tackle data scarcity. Across 300 app scenarios, 2,400 personas, and 46,338 demands, Apeiron outperformed baselines by 10.7% in CUA ratings and 27.8% in user-demand task scores. The optimization process enhances task scores by 64.7%, and the tracer contributes a 25.1% gain. In CI/CD, Apeiron effectively restores 96.9% of the pre-shift mean CUA rating in one optimization step with <30% code changes in response to 30% demand shifts. Finally, a user study (N=18) shows that our CUA ratings strongly correlate with human judgment (Spearman’s 𝜌=0.685) and that users prefer Apeiron-synthesized apps over baselines.