Mathematical Resolutions of Four Core Dilemmas in Theoretical Physics via the Universmodel Framework

This paper presents a definitive, deterministic, and non-singular resolution to four of the most critical open problems in mathematical physics: (1) the 3D Navier-Stokes Global Regularity Problem, (2) the Yang-Mills Existence and Mass Gap Problem, (3) the Cosmic Censorship Hypothesis, and (4) the 10³⁶ Gravity-Electromagnetism Hierarchy Problem. Building directly upon the foundational framework established in the author's primary treatise, "THE MECHANICAL CLOCKWORK: A Geometric and Causal Foundation for Unified Physics", we translate abstract field configurations into the mechanics of a continuous, highly elastic Background Field governed by a single Unified Master Field Equation: Fₜₒₜ = G · ( ∇ ρf + κ (τ⃗₁ × τ⃗₂) ) By evaluating physical forces through this macroscopic fluid-dynamic architecture, we demonstrate that: Navier-Stokes Regularity is guaranteed by an absolute physical shear-stress cutoff (κ = c² · ρf), which triggers a geometric phase transition before infinite singular blowups can mathematically manifest. The Yang-Mills Mass Gap (Δ > 0) emerges analytically as the non-zero geometric deformation threshold required to twist a flat linear field line (Gₗᵢₙₑₐᵣ) into a stable, localized 3D vortex knot (Gₖₙₒₜ) against the medium's intrinsic shear modulus. The Cosmic Censorship Hypothesis is validated because gravitational collapse forces subatomic knots into a state of mechanical gear-lock, erasing matter into a smooth, non-singular "State 0" fluid core (Fₜₒₜ = 0) where coordinates remain continuous and enclosed by a mandatory causal horizon boundary. The 10³⁶ Hierarchy Problem is naturally resolved by demonstrating that electromagnetism is an active-tier primary torque amplified by the medium's immense stiffness, while gravity is merely a passive-tier, downstream hydrostatic relaxation vector. This work eliminates mathematical infinities and establishes global causal predictability across both quantum and cosmological scales.