We introduce the honeycomb hierarchy, a representation-theoretic framework that gives new asymptotic upper bounds on R2(δ). Its first level is the two-row hyperoctahedral representation graph associated with type S(n−k,k). Retaining every two-row irreducible and every coordinate box-transfer channel, together with a moving-projection theorem, yields an explicit four-parameter exponent κHC
Nearby in the stack
. The earlier whole-cube exponent
κH
is a boundary restriction of this optimization, whereas the fully optimized second MRRW exponent
M2
is an exact symmetric slice. The prior best curve is the combined
κbin=min{κCW,κH}
, which uses a constant-weight branch
κCW
. Replacing only the whole-cube branch by the honeycomb bound gives
The hierarchy has two further directions. Increasing the representation depth replaces scalar by matrix-valued transfers on the hive. Increasing the anchor depth localizes it in a stable-set hierarchy. The resulting bounds are monotone in both directions and eventually recover
A2(n,d)
. A complementary Horn--channel hierarchy gives matrix optimizations whose
2×2
level is
κHC
and whose
3×3
level is a stronger bound. Already at low levels, they can be used to improve the strongest previous general bounds, while the honeycomb framework provides a route towards tighter bounds.