Dual Structure of Five-Dimensional Solitonic Theory: Spectral-Solitonic Unification via Elliptic Interpolation

We establish the structural unity of the TS5D framework across the weak-field (particle)and strong-field (solitonic) regimes by identifying the elliptic modulus k ∈ (0,1) asa universal interpolation parameter. In the regime k → 0, the Jacobi solutions are periodicand the physics is spectral: particle masses emerge as discrete eigenvalues ofan elliptic projection hierarchy, with the exponential hierarchy involving the spectralfactor exp(−2kK’/K) combined with the Evans indexing and frequency skeleton. In theregime k → 1, the Jacobi period diverges and the cn/dn-type profiles become spatiallylocalized (sech-type), producing nonlinear strong-field configurations. The spectralfactor exp(−2kK’/K), inherited from the elliptic geometry of the particle-sector massformula, exhibits a suppression window centered around k ≈ 0.74 that serves as anatural crossover region between regimes. The Noether mass formula mc² = Q_θ ωapplies identically across all configurations. We derive concrete falsifiable predictionsfor the strong-field regime, including a minimal mass bound set by the orbifold compactificationscale and an inverse mass-radius relation. The framework requires noadditional postulates beyond the foundational field equation on M₄ × S¹/Z₆.