Geometric and Spectral Foundations of Five-Dimensional Solitonic Theory (TS5D): Noether Projection, Constructive Asymptotics, and Discrete-Sector Tests with Multi-Sector Numerical Validation

We present a five-dimensional solitonic framework in which particle masses arise as geometric Noether charges, without quantization postulates or empirical input. The mass law is derived from a factorization theorem for the elliptic monodromy function, while a Puiseux closure theorem shows that the exponent αα is a rational algebraic invariant rather than a fitted parameter. The resulting spectrum is discrete and sectorized, with explicit selection rules and falsifiable predictions. Numerical multi-sector analysis confirms the asymptotic relation ℓ∼3/k2 3/k²ℓ∼3/k2. This establishes a fully constrained geometric mechanism for mass generation.