Compact representatives on a finite TT plane

For the conical adaptation the selected bumps must fit the laboratory. If the laboratory was fixed earlier, positive Gram rank there is an additional admission condition. Independence on a full auxiliary slab is not silently replaced by independence on an arbitrary small patch.

The finite-plane ambiguity is exactly

On compact distributions,

is an idempotent projection onto $\mathrm{Ann}({\mathcal{V}}_2)$. Thus the interpolation problem has codimension two. It says nothing about uniform bounds or compatibility as the tested plane grows. This reproduces the finite-plane mechanism of V@1, not a dense-space extension CheungV.