An Axiomatic Framework for Physical Symmetry Selection by Anonymous Partial Projection: Conditional Identification of E8 in an Eight-Component Two-Quartet Branch

This paper separates the solution space permitted by foundational axioms from the state space physically realized and formulates the latter as the image of an anonymous admissible partial projection. The proposed axiom does not name or preselect a symmetry group. As a nontrivial branch analysis, the paper assumes an eight-dimensional positive-definite readout space decomposed into two four-component subsystems, each with a local D4 transition lattice. A common-center neutrality projection on the two D4 discriminant groups permits only the diagonal glue classes (0,0), (v,v), (s,s), and (c,c). The resulting lattice is positive-definite, rank eight, even, and unimodular, hence isomorphic to the E8 lattice. Direct counting gives 240 norm-two vectors and therefore the dimension 8+240=248 for the associated complex simple Lie algebra; a Coxeter element has order 30. The result is explicitly conditional: the foundational axioms do not uniquely force E8, and the physical selector responsible for the eight-component, D4, and common-center branch remains an open problem.