PFUSRC-145 The Boundary Closure of the Narrow Hilbert's Sixth Problem and the Endpoint Signs of the Three-Dimensional Classical Paradigm

Deng Yu’s research team has completed rigorous long-timescale derivation for the narrow Hilbert’s Sixth Problem, marking a landmark mathematical physics achievement over the past century. Within the three-dimensional classical dilute hard-sphere gas framework, this work constructs a complete linear derivation chain linking microscopic Newtonian dynamics, Boltzmann kinetic equations and macroscopic Navier-Stokes fluid equations. This paper argues that the success of this proof stems not from refined mathematical techniques, but from the synchronous co-emergence of mass generation and double-cone topological structures, which establish system boundaries and pre-restrict the cosmic time arrow via intrinsic topology. When constrained by laboratory settings—3D flat continuous space, BG dilute limit, absent long-range interactions and structureless particles—multitudinous potential time arrows are truncated, leaving merely one near-linear evolutionary trajectory trackable. Deng Yu’s proof only verifies the traceability of this pre-existing linear channel instead of uncovering a disorder-to-order generative mechanism. This paper further states that authentic mathematical-physical closure requires unified convergence of mathematical constraints and physical boundaries in nature: mass, inertia, double-cone topology and spatial boundaries must arise simultaneously within a single structural event. Deng Yu’s derivation only realizes equation correspondence confined within preset boundaries; it neither explains boundary generation nor validates the integrity of linear evolution channels under natural cosmic closure. The three-dimensional classical paradigm has reached its theoretical and practical limits: its core theoretical framework is fully closed, and its engineering application efficiency ceiling has been hit. This paper acts as a sister work to PFUSRC-13B (Ontological Reconstruction of the Kakeya Needle). The two papers adopt separate research angles—Hilbert’s Sixth Problem and the Kakeya needle problem—to jointly complete a full boundary assessment of the three-dimensional classical physical paradigm, demonstrating that the era of paradigm shift has arrived.