Algebra Selection from the Yield Corridor: Dimension Pressure, Central Phase, and the Non-Abelian Fork

Refinement-stable closure forces a non-Abelian symmetry class beyond phase-only structure. This paper continues the forced sequence by showing that if interaction residue is nontrivial, a purely Abelian (phase-only) representation cannot faithfully carry the independent residue content without information collision under refinement-stable encodings. To avoid representational collapse (word-explosion or collisions), the corridor forces representational expansion and a non-Abelian generator algebra closed under composition and residue formation. We further show that gauge/phase freedom must be bracket-silent with respect to physical generators, forcing the phase direction to be central and yielding a structural U(1) × (non-Abelian) split without assuming Lie theory, manifolds, or calculus primitives.