The Unified Theorem of Correlation Determination: Mathematical and Physical Anatomy and Systematic Reconstruction of Bell's Theorem and CHSH Experiments

'God does not play dice–he decrees the rules' “上帝不掷骰子——他制定规则” Peering through the veil of a century of history, this study provides a profound anatomy and comprehensive reconstruction of Bell's theorem and the CHSH inequality from both mathematical and physical perspectives. Building upon this foundation, we establish the unified theorem of correlation determination (UTCD) for photon polarization. This framework profoundly reveals the underlying mechanism driving polarization correlation effects—including the long-mythologized phenomenon of quantum entanglement—comprehensively explains the physical phenomena and deep-seated paradoxes of CHSH experiments, and delivers a series of verifiable experimental predictions. The mathematical reconstruction presented in this study systematically closes the loop on the probability dimension previously lost in photon transmission events, while the physical reconstruction comprehensively encompasses a total understanding of the intrinsic properties of photons. The synergistic reconstruction of physics and mathematics fully demonstrates the inherent binding force of the UTCD theorem: the benchmark for determining the existence of correlation must be an objectively complete set of rules. Ultimately, the completeness of these objective rules provides the definitive closure to that historic dialogue of the century: 'God does not play dice–he decrees the rules.' In the subsequent phases of this work, the author will unveil the physical nature of probabilistic events alongside the probabilistic expression of physical events, interpreting both the microscopic realization and macroscopic unfoldment of mathematical probability. As the relevant research indicates, this opens a brand-new horizon for humanity's proper understanding of probabilistic physics: ‘The essence of interference and diffraction fringes in single-slit, double-slit, and all other wave-particle duality phenomena is merely the two-dimensional projection of probabilistic events onto the material world; if the dimension of time is added, we can furthermore witness the vibrant, breathtaking three-dimensional unfoldment of the probabilistic manifold!’ Standing upon the firm bedrock of natural laws and causality, the organic integration of classical and modern physics heralds a transformative new epoch in the advancement of human physics.