Xianwei Meng

Mathematical and Theoretical Foundations of the Basic Phase-Transport Equation: A Unified Differential, Covariant, and Path-Functional Theory

This paper studies phase formation, continuous comparison, and cross-state transport when the observation map varies with the state of an observer. Starting from the classical model y = h(x), we prove that a complete representation of a nontrivial family of observation maps requi...

From Primitive Observation Records to the Dual-Axis Axiom: Set-Theoretic Foundations of Observational Geometry

The problem considered here arose in information science: the relation that forms an observation need not remain fixed while the underlying state of interest is held fixed. Yet the argument begins before any particular information-theoretic, statistical, geometric, or physical mo...