Local Kinetic Quantum Theory with Hidden Variables: Reinterpretation of Bell Inequality and Entanglement from Eulerian Causal-Kinetic Locality

Quantum theory (QT) reproduces microscopic measurements with extraordinary accuracy, yet its standard formalism separates deterministic evolution, measurement, and the physical mechanism of non-factorizable correlations. We develop kinetic quantum theory (KQT), a local nonlinear phase-space framework in which quantization, spin, interference, entanglement, and many-particle exchange emerge from microscopic single quantum fluctuations (SQFs) organized within virtual multi-quantum fluctuations (VMQFs) through local kinetic states, nonlinear redistribution, and transported correlations.SQFs evolve in continuous canonical angle-action variables $(s,J)$, with a 4π internal gyration s. The KQT-to-QT reduction follows the same reduction architecture as gyrokinetic: microscopic gyration is integrated out while its action and directional moments survive. The sequence fQ(s,J) → (J, J\,k) → (nKQT,SKQT) → ψₖKQT → ψQT → WQT[ψQT] derives the complex quantum state from a positive kinetic state. Closure of the hidden kinetic stress by the quantum potential yields exactly the Schr\"odinger equation. Angular integration also generates an exact Bessel hierarchy whose momentum-chord argument recovers the Wigner Bessel argument.Bell locality only permits a generic connected correlation at the common source, PcorrBell(t₀,t₀)≠0, but after complete conditioning on the initial state λ₀≡λBell(t₀), Bell defines locality by screening-off the residual connected correlation, Pcorr^ Bell,λ₀(t₁,t₂)=0 for t₁,t₂>t₀. KQT instead defines causal locality by measurement independence, independent local observations, and operational no-signaling without superdeterminism, and preserves local causal propagation from t₀ to (t₁,t₂), so the source-generated correlation Pcorrλ₀(t₀,t₀)≠0 is consequently retained in P₁₂KQT(t₁,t₂)=P₁P₂+Pcorrλ₀(t₁,t₂)≠ P₁P₂ instead of being set to zero by Bell screening-off.The same 4π SQF kinetics generates spin-$1/2$ and an antisymmetric two-particle sector equal to the Bell singlet projector. It reproduces the harmonic-oscillator spectrum, spin-$1/2$ probabilities, entangled Bell/CHSH and three-particle GHZ/Mermin correlations, the Tsirelson limit, and double-slit interference. Hidden kinetic harmonics further predict experimental discriminators through dense-angle Bell measurements and an entangled double-double-slit null test.KQT thus provides a positive local kinetic parent state from which the main closed-QT structures emerge by reduction while retaining experimentally testable microscopic channels beyond the closed QT branch.