Axiomatic Emergence W; The Physical Origin of Analytic Mathematics

This paper reconstructs the core system of modern analytic mathematics fromthe ground up, based on a foundational framework of physical principles centeredon information conservation and finite-step computability. The research demonstrates that structures such as the macroscopic arrow of time, Lebesgue measure,probability axioms, algorithmic complexity, function spaces, and stochastic process theory can all be regarded as the natural mathematical manifestations of theabove principles when describing information evolution and process simulation. Byclearly distinguishing the three levels of mathematical construction, physical modeling, and empirical testing, and with the aid of a set of bridge assumptions, thispaper systematically deduces the emergence path from discrete information dynamics to continuous mathematical descriptions. To ensure the falsifiability of thetheory, specific experimental verification schemes connecting cosmological observations and quantum computing experiments are designed for each core structure.The entire work endeavors to show that the main architecture of analytic mathematics is the most suitable language induced by the fundamental constraints ofinformation processing in the physical world.