A packet's capacity is not its occupied energy
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Ranks describe the subspaces. Energies describe a particular input.
\[
x=\sum_{d\mid12}P_dx,\qquad\|x\|^2=\sum_{d\mid12}\|P_dx\|^2.
\]
The constant \(2\) contributes \(12\cdot2^2=48\) to order one. The cosine contributes \(54\) to order four. The Ramanujan component contributes \(48\) to order twelve. Keeping all six packets gives exact synthesis. Keeping only one packet performs a lossy selection.