Private cells versus private occupation observables

Define the message-independent payload references

After occupation embedding, the single-cell channel comparison with

has half-diamond distance exactly ${q_i}^{J_i+1}$.

This comparison has two qualifications:

1. ${\xi }_i$ describes new degenerate payload degrees of freedom. It is not supplied by the scalar Hawking baseline;

2. count and mean matching concern $O_i$, not every observable of $r_i=O_i{C}_i$.

The payload energy and payload occupation are part of the finite energy ledger, but are not hidden inside the matched scalar number observable.