We present Recursive Mathematical Plasticity Entropy Architecture (RMPEA), a comprehensive framework for designing adaptive intelligence systems based on information-entropy optimization principles. Building on symbolic entropy collapse (SEC) theory and validated through extensive TinyCIMM-Euler mathematical reasoning experiments, RMPEA demonstrates how architectural plasticity can emerge naturally from entropy-guided recursive processes. Our framework reveals that optimal intelligence architectures exhibit mathematical plasticity--the ability to dynamically restructure information processing pathways based on problem complexity and entropy gradients. Through validation across mathematical reasoning domains including prime number theory, transcendental mathematics, and algebraic reasoning, we show that RMPEA enables systems to achieve >95% activation ancestry stability while maintaining adaptive responsiveness to novel complexity patterns. The architecture provides practical design principles for developing AI systems that balance efficiency with adaptability, offering entropy-minimized design patterns for next-generation intelligent systems with implications for both artificial and biological intelligence research.