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 system{Pj = 0}j≥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)