Structural Drift and Quantum Geometry

We establish an exact realization of the structural drift construction of the Negative-Entropy framework in a standard two-level quantum system. The abstract constraint operator J, its kernel L= J, and the associated orthogonal projector Π_L are realized precisely by the spectral eigenspace structure of the two-level Hamiltonian, with the identification J_-=H-E_-I=2d\,Π_+. The projector-drift identity of the earlier framework reduces exactly to Π_L=Π_-, and the resulting operator chain J_-→Π_-→Π_-→ K→(gᵢⱼ,Fᵢⱼ)→Γ_J connects the abstract construction to quantum geometric data through the Kato parallel-transport generator, the quantum metric, and the Berry curvature. We further prove a non-equivalence result within the original K_3 network-flow model: at a fixed active-set region where the structural projection is locally constant, the structural drift strength vanishes identically, while the multiplicative dynamical feedback strength remains strictly positive. This shows that structural drift is not a necessary mechanism for dynamical feedback in the original K_3 construction, and no linear operator factorizes the feedback response through the directional structural-change operator. The paper makes no empirical claims about consciousness, and does not assert a unified theory. The exact realization is an operator-level identification within the two-level spectral geometry. It does not introduce a new quantum dynamical law, nor does it establish a physical equivalence between the quantum geometric response and the network-flow feedback strength. The paper establishes a mathematically verifiable bridge between the abstract structural framework and a standard physical system, together with a rigorous boundary on where the bridge does not extend. Note on notation. The constraint matrix of the K_3 network-flow model is denoted B, while the scalar entry B of the dynamical matrix M_q retains the unadorned symbol B. Note on operator conventions. The framework is developed in finite-dimensional real or complex Hilbert spaces. The adjoint of a linear operator A is denoted A^; in the real case this coincides with the transpose A^. Projectors are orthogonal projectors with respect to the Hilbert-space inner product.