The other two maps

At every cut, a name $a$ has a prescribed port location $\ell (a)\in U$. The name-to-rod map is

Quantum factors may be grouped into three named collections for bookkeeping, but this grouping does not derive three-dimensional geometry.

The schedule has a port-event map

Every permitted dependency edge is required to map to a future-causal pair. Therefore the scheduled ancestors of an output map into its metric past. This is an order-preserving containment, not an equality between ancestry and actual influence.