This preprint presents an operator-algebraic formulation of a Gauss-based multidimensional 15/16 sector-closure logic. The 15/16 structure is not introduced as a numerical analogy and is not derived from quantum mechanics. It is treated as a prior geometric result of the multidimensional Gauss-type sector logic, which is here lifted into a quantum-operator representation. The construction represents sixteen sector operators on C4 using the two-qubit Pauli basis Gamma_ab = sigma_a tensor sigma_b. One identity sector supplies the scalar U(1) channel, while the remaining fifteen traceless Hermitian operators close under commutator and generate su(4). The explicit closure certificate gives zero closure residual, zero Jacobi residual, commutator span rank 15, Killing rank 15, and a rank-three Cartan candidate: ZI, IZ, ZZ. Through the standard isomorphism su(4) ~= so(6), equivalently SU(4) ~= Spin(6), the same fifteen active sectors admit a six-coordinate rotation-plane interpretation. The purpose of the paper is not to prove the 15/16 structure from quantum physics, but to show that the Gauss-based multidimensional sector logic has a natural operator realization inside the formal language used by quantum mechanics and gauge theory. The QED/QM-compatible layer is formulated as an operator grammar: the ordinary derivative is replaced by a gauge-covariant derivative on an enlarged internal Hilbert space C4. The ordinary U(1) electromagnetic channel is preserved as the identity-sector channel, while the fifteen active sectors form an SU(4) non-Abelian operator channel. Setting the sector coupling to zero returns the ordinary QED/Schrodinger minimal-coupling limit. The TERRA/I-Z finite-readout logic is used as a proof-architecture discipline: a finite 15/16 sector count is not treated as proof by itself. It becomes proof-relevant only after explicit lift to an operator table and complete Lie-closure certification. The included NEW_DIFF_EQ smoke test confirms the ordinary Linear Schrodinger boundary and control PDE branches, while also showing that the current package is not yet a full matrix-valued SU(4) gauge solver. This work should be read as a mathematical preprint on operator closure and QED/QM-compatible formal grammar. It is not a claim of experimentally established new physics, nor a replacement of the Standard Model. Its contribution is to provide a reproducible operator-closure bridge from Gauss-based multidimensional sector logic to the recognized algebraic language of SU(4), Spin(6), and gauge-covariant quantum formalism.