Decoder

A canonical geometric word determines:

1. $s=j{2}^{-d}$;

2. the exact function (eq:family);

3. the appropriate cellulation from Section sec:cells;

4. the affine chart table from Section sec:holonomy;

5. the fixed particle packet;

6. the auxiliary canonical reports.

For $j<0$, only incoming mode is valid; for $j>0$, only outgoing mode is valid. At $j=0$, the two mode values select the two declared germs.

The decoder reconstructs coordinates and exact lengths from the symbolic formulas, not from report words. It ignores retained implementation history. Intermediate compiler states are not assigned geometric interpretations.