Structural Limits of Orientation Scheduling in Byte-Local GF(2) Diffusion Layers

Orientation scheduling varies linear coefficients across rounds while preserving byte locality, invertibility, the branch-number floor, and the surrounding substitution-permutation network. For independently applied 8×8 invertible maps over GF(2), active-byte support is invariant at the matrix step; this elementary block-diagonal fact is used here as a screening invariant rather than as a new algebraic theorem. The restriction does not extend to linear layers whose coefficients couple byte positions. Under the standard Markov-cipher model, a 128-state transfer computation over a deterministic panel of 256 matrix contexts finds a small separation between temporally constant and round-dependent schedules. At 16 rounds, the oracle-maximized geometric-mean class probabilities are about 2−78.2 to 2−78.5, and the rotor-minus-static periodic-rate contrast is 0.00881 bits/round on the primary panel. Prefix and independently labeled panel checks give contrasts of the same order. The one-step ordering reverses under the periodic operator, an observation consistent with temporal-alignment effects but not sufficient to identify a unique mechanism. Reduced-round fixed-key calibration also shows that deviations from the Markov surrogate can be much larger than the schedule separation. The numerical difference is therefore resolvable but numerically small within the transfer model and is not presented as a fixed-key security advantage. The aggregate weight-one class exceeds the best individual trail by about 228 in mean log-domain gap. The resulting design lesson is structural: coefficient diversity can change local transition quality and ordering, but within a byte-local layer it cannot substitute for diffusion width.