The achievable set's automatic V/2 symmetry

Filed as the mechanism behind a negative result. The negative result on its own — the density predictor fails — is a dead end. With the mechanism attached it explains why the successor predictor (central-representation count) succeeds, which is the useful content and is not recoverable from the failure alone.

The mechanism. The achievable set carries a symmetry about V/2 automatically — it is a property of the set's construction, not an assumption. A predictor keyed on density is therefore keyed on a quantity that symmetry has already fixed: density cannot discriminate, because the symmetry makes it (near-)constant across the cases the predictor was meant to separate. A predictor keyed on how central a representation is reads a quantity the symmetry does not fix, which is why it survives where density did not.

What it makes coherent. "Density failed, centrality worked" looks like trial and error. With the symmetry named it is a single fact with two consequences: the symmetry kills one predictor and licenses the other. One mechanism, two filed outcomes.

Scope, honestly. Stated in the source chat, recorded here as stated, not re-derived in this repo and not tested by any run. In particular this note does not establish that central-representation count is the best predictor, only that the symmetry explains the density predictor's failure and does not obstruct the successor.

What would falsify it. An achievable set constructed the same way that is not V/2-symmetric; or a density-keyed predictor that does discriminate, which would mean the symmetry is not what flattened it.

Matched pair. [[N-023]] is the same shape from the other side.