Noncommutative Transport Topology in the Rubik's Cube Representation

This paper studies direct off-diagonal transport relative to a fixed orthogonal sectorization. A spectral sectorization need not be preserved bythe operators whose transport it is used to analyze, and the resulting off-diagonal blocks define a direct support graph. The exact finite-dimensional layer establishes the Transport--Non-Invariance Identity: for a unitary operator and a completeorthogonal sectorization, the total outgoing off-diagonal Frobenius mass from a sector equals one half of the squared Frobenius norm of the correspondingprojector commutator. A separate block-locality theorem shows that direct transport vanishes between sectors with disjoint physical-block support whenboth the transport family and the sector projectors preserve the declared physical blocks. In the declared complex128 Rubik realization, the quarter-turn and half-turn averages register nine numerical joint-spectral sectors. The eighteenface-turn matrices produce a symmetric direct graph with ten edges and degree sequence (0, 2, 2, 2, 2, 5, 3, 1, 3). Nine registered Type I edges haveshared thresholded noncommutative block support. The same localizer identifies fifteen candidate pairs, six of which are nonedges, so shared support is not asufficient transport criterion. The remaining Type II edge is carried by the numerically commuting corner-permutation block. The computed edge-permutationaveraging algebra is computationally registered with four copies of the algebra of two-by-two complex matrices and four one-dimensional scalar components. Exact theorems, numerical registration, and finite mechanism labels are kept separate. Machine-zero commutators do not establish exact commutation. Type Iand Type II are labels for the declared finite census rather than universal transport mechanisms, and support-graph paths are not interpreted asprojected matrix compositions. Source repository: https://github.com/dooven-prime/rime-lite Paper II of the Representation-Induced Mechanics and Evolution (RIME) program. Independent researcher; no institutional affiliation.