Explore the fundamental principles of holography through the lens of state-counting methods in this 53-minute conference talk delivered at ICBS2025. Delve into the mathematical frameworks that underpin holographic theories and discover how state-counting approaches provide crucial insights into the nature of holographic dualities. Learn about the connections between microscopic degrees of freedom and macroscopic gravitational phenomena, examining how counting quantum states reveals the deep structure of holographic correspondences. Gain understanding of advanced theoretical physics concepts including the holographic principle, entropy calculations, and the statistical mechanics foundations that support holographic theories in modern theoretical physics.