Dark Matter as Topological Phase Persistence of the Existence Equation

Evidence Paper V of the Existence Equation series In the Existence Equation [1], the deviation field Ψ = AeiΦ carries two degrees of freedom. The gradient energy decomposes exactly: |∇Ψ|² = |∇A|² + A²|∇Φ|². The first term is the amplitude-gradient energy. The second is the phase-gradient energy. The two are independent contributions to the stress-energy tensor — both gravitate equally — but they couple differently to electromagnetic probes. The amplitude |Ψ| is gauge-invariant and determines all observable emission, absorption, and scattering. The phase Φ is gauge-dependent; electromagnetic probes do not see it. Now add topology. When the phase winds by 2πn around a closed loop, the winding number n is an…