Geometric and Spectral Foundations of Five-Dimensional Solitonic Theory (TS5D): Noether Projection, Constructive Asymptotics, Discrete-Sector Tests, and a Call for Computational Closure of the Spectral Constants

We develop a framework in which particle masses emerge from the geometryof a five-dimensional manifold M4 ×S1/Z6, without invoking quantum postulates. A single complex scalar field with quartic self-interaction and curvaturecoupling admits solitonic solutions whose radial profiles are expressed exactlyin terms of Jacobi elliptic functions. The overdetermined projection systemPj = 0j≥0 discretizes the solution family and yields a universal asymptoticmass law m (ℓ) = M0 ℓα exp (−B/√ℓ), where ℓ = 6N + n labels the spectralindex and n ∈ 1, 2, 3, 4, 5 the orbifold sector. The exponential factor is establishedby a factorization theorem for the elliptic monodromy function G (k) ;the power-law exponent α is shown to be a rational algebraic invariant of theprojection system, constrained to α ∈ (0, 1/2) by a Puiseux closure theorem. We interpret mass as a Noether charge projection along the compact dimension (mc2 = Qe ω), requiring no quantization hypothesis. An overdeterminedalgebraic inversion yields α = 0. 4200 and B = 5. 969 with structured residualsdecaying as ℓ−1. 3, consistent with the analytic bounds. After calibration onthe electron mass, the asymptotic law reproduces the global mass hierarchy ofbenchmark states; the cross-sector ratio mJ/ψ/mτ = 1. 743 is predicted to foursignificant figures without calibration input. An independent computationalverification confirms the partial ab initio values (B ≈ 5. 04, αlead ≈ 0. 03)