From Philosophical Speculation to Scientific Cognition -- How Yuanxian Theory Achieves Their Complete Commensurability

The historical chasm between philosophical speculation and empirical scientific cognition has long been regarded as an insurmountable barrier in modern intellectual history. Philosophy, relying on intuition and speculative metaphysics, addresses the "why" of ontological substance; science, driven by empirical measurement, maps the "how" of phenomenological behavior. This divergence has led to structural incommensurability, freezing dialogue between the two essential modes of human understanding. This paper formally demonstrates that Yuanxian Theory (YXT) provides a rigorous, formalized framework that achieves the complete commensurability of philosophical speculation and scientific cognition. Transitioning from over three decades of ontological formulation in True-Circle Holographic Philosophy, the system has successfully completed a triple leap through the axiomatization of four core cosmic laws ( Cosmic Factor Conservation, True-Circle Self-Consistency, Self-Referential Mind-Field Generation, and Spacetime Uniqueness), a 15-stage globally closed deductive chain, and interactive machine verification via the Lean 4 and Rocq interactive theorem provers. By anchoring reality upon a 64-dimensional compact torus topology (T64) and utilizing a self-referential mind-field as its primary vector, this monograph proves that philosophical insight and scientific precision are isomorphic projections of the exact same high-dimensional truth. The apparent "incommensurability" is revealed to be a mere artifact of low-dimensional cognitive architectures. Through this formal synthesis, philosophy receives absolute deductive constraints and convergence, while empirical science obtains a foundational, non-accidental ontological root, marking a profound paradigm shift towards absolute cognitive unity.