Truth Precedes Verification: Cognitive Logic and Scientific Positioning under the Paradigm of Yuanxian Theory — An Epistemological Elevation and Machine-Verified Ontological Reconstruction

Traditional empirical science adheres to an inductive trajectory of "hypothesis--verification--revision--establishment," positioning empirical observation as the ultimate arbiter of truth. This paper systematically elucidates the cognitive paradigm of "Truth Precedes Verification" proposed by Yuanxian Theory (YXT). Rather than invalidating scientific methodology, this paradigm executes a structural elevation of epistemology. Yuanxian Theory selects the high-dimensional topological ontology of the 64-dimensional compact torus (T^64) as its axiomatic point of departure, leveraging the dual engines of Lean 4 and Rocq (Coq) to execute machine-grade formal verification, thereby anchoring the formal truth-value of the theory prior to the implementation of empirical experiments. Within this framework, empirical observation is restored from its role as an "arbiter of truth" to that of an "empirical attestation of theoretical deduction," whose utility is restricted to high-dimensional parameter calibration, mathematical error correction, and engineering boundary expansion; it possesses no validity to falsify the underlying foundational axioms. This paper further clarifies that falsifiability criteria are intended to delineate the effective domain of applicability of a theory within low-dimensional spacetime, rather than to overthrow logically self-consistent ontological axioms. Yuanxian Theory actualizes a fundamental paradigm shift from empirical induction to axiomatic deduction.