Why it is a question
THEORY-304 holds the scalings Trefethen, Trefethen, Reddy and Driscoll computed for the linearized shear flows in the energy norm. CLAIM-383 derives the lower bounds (growth at least cR, resonance at least cR², a destabilizing perturbation of norm at most CR⁻²). That growth is no more than order R, and the constants of Table 1, rest on that one computation, which credits the results to earlier work the record has not read.
What would answer it
An independent computation or review of the linearized plane Couette and Poiseuille operators, such as Reddy & Henningson (1993) or Schmid & Henningson’s monograph, read here and reproducing the O(R) transient growth, O(R²) resonance and O(R⁻²) minimal destabilizing perturbation with constants near those of Table 1. A correct computation in the energy norm showing growth bounded independently of R would refute the scalings; CLAIM-383 already excludes it. Experiments on transition cannot settle it: they bear on the transition conjecture, not on the linear scalings.