Internal GEP Carrier Derived, Dynamical Orientation Not Yet Selected

The preceding Stone-2 study established that a faithful four-band Q₈-linked Qi–Wu–Zhang proxy can support a gapped irreducible Chern bulk and a compensated chiral edge-to-core pump. Its central microscopic limitation remained explicit: the four-state internal carrier and its orbital Pauli matrices were inserted rather than derived from Granular Entropic Physics (GEP). Stone 2B isolates and resolves that local kinematic question. Let V ≅ ℂ² be the fundamental spinor representation of the binary tetrahedral group 2T ⊂ SU(2). Writing the local three-spinor space as V ⊗ V ⊗ V, its restriction to 2T decomposes as V ⊗ V ⊗ V ≅ 2·𝟐 ⊕ 𝟐′ ⊕ 𝟐″. Its 2T-equivariant endomorphism algebra is A₆ = End₂T(V ⊗ V ⊗ V) ≅ M₂(ℂ) ⊕ ℂ ⊕ ℂ. A central character projector P₀ canonically selects the doubled fundamental isotypic component of rank four: P₀(V ⊗ V ⊗ V) ≅ W ⊗ M, dim(W) = dim(M) = 2. The normal subgroup Q₈ ◁ 2T acts faithfully and irreducibly on W, while the 2T commutant supplies the complete matrix algebra M₂(ℂ) on the independent multiplicity factor M. Exact reconstructed channel operations S and R belong to A₆ and satisfy S² = I, R³ = I, SRS = R⁻¹. A channel reflection and the normalized oriented-cycle difference R − R⁻¹ generate three Hermitian operators satisfying the exact Pauli–Clifford relations on the rank-four carrier. Together with the faithful Q₈ factor, these operators generate the full matrix algebra M₂(ℂ) ⊗ M₂(ℂ) = M₄(ℂ), with a scalar joint commutant. An orientation-symmetrized negative control collapses to scalar operators, demonstrating that the noncommuting Pauli structure specifically requires oriented rewiring. The established result is an exact local kinematic bridge: the four-state carrier and complete internal matrix algebra used by the Stone-2 chiral proxy have a representation-theoretic realization inside the locked local GEP construction. This is not yet a derivation of dynamical chirality. The paper does not derive energetic isolation of the carrier, physical two-dimensional gluing, dynamical selection of R over R⁻¹, the QWZ hopping coefficients or mass, a GEP Chern phase, a Kaplan-type higher-dimensional wall, or Standard-Model anomaly consistency. No numerical calculation is used.