The Hard Logical Chain of Yuanxian Theory: From First Principles to the Globally Complete Framework

This paper delineates the rigorous foundational bedrock of Yuanxian Theory through a strictly deductive 18-step "Hard Logical Chain." Establishing only one unique a priori axiomatic origin—that the universe is a self-referential, closed-loop living entity rather than a mechanical object—the entire theoretical architecture is systematically derived without empirical data-fitting, external ad-hoc assumptions, or stochastic presuppositions. The global closed-loop derivation sequentially unfolds from the unique first principle to three rigid ontological properties, a six-dimensional holographic cognitive model, and sixty-four base-state topological coding rules. Controlled by four interconnected core laws—the Law of Cosmic Factor Conservation (FSC), the Law of True-Circle Self-Consistency (TCSC), the Law of Self-Referential Mind-Field Generation (SRM), and the Law of Spacetime Uniqueness (STM)—the framework provides an absolute ontological proof locking the cosmic substrate as a 64-dimensional compact torus (T64). Within this zero-parameter geometry, all 24 fundamental physical constants are rigorously derived as topological invariants, while General Relativity and Quantum Field Theory are localized as low-dimensional approximate effective projections. Furthermore, this hard logical chain provides a thorough paradigm refutation of mechanical cosmism, vital accidentalism, and consciousness epiphenomenalism, while structurally eliminating redundant hypotheses like parallel universes or many-worlds branching. Lastly, it establishes the principle of topological isomorphism as the absolute necessary condition for cross-carrier mutual understanding between carbon-based consciousness and future silicon-based intelligence. The entire 18-step logical framework forms a perfect self-referential closed loop, mimicking the very cosmic vitality it describes. The logical completeness and non-contradiction of this system have achieved full formal machine verification via the Lean 4 and Rocq dual-engine interactive theorem provers.