This framework is formulated directly in terms of the E_n hierarchy. The symmetry levels are labeled directly by E_n, with E_6, E_7, and E8 treated as finite-dimensional exceptional Lie groups and E_9, E_10, and higher labels treated, when invoked, as affine, hyperbolic, or more general indefinite E-type extensions whose precise generalized Cartan data must be specified. The exponentially weighted hypergeometric profile associated with an E_n level is written H_{n,n−1}(2ξ). Integral ft-{ht,lsr}-mGFT remains an analytic profile and field-equation solution architecture; internal symmetry is carried by explicit En Lie-algebra generators and representations; string/brane structure can be carried by Clifford factors; and physical masses arise from the quadratic fluctuation operator of a specified action. The framework does not use infinite summations to define a unifying interaction potential or universal particle-mass spectrum. The primary directional architecture is the reduction chain E_11 → E_10 → E_9 → E_8 → E_7 → E_6, with the reverse sequence treated as a constructive lift rather than an automatically invertible map. The phenomenological material is ordered by sector: the E_6 solar and hidden-particle benchmarks; the E_7 compact-object analysis; the E_9 affine/high-energy morphology sector; and the E_10 hyperbolic/solitonic sector. The supplemental verification layer supplies an effective benchmark action, residual-certified nonlinear fixed-point calculations, mesh convergence, and quadratic spectral extraction.