What a later quantum construction must still supply

A later quantum-product proposal on this carrier must specify:

1. an actual domain for every contracted kernel operation, not merely a carrier for its hoped-for output;

2. agreement with the fixed old product on its common domain;

3. extension and normalization data for the selected singular graphs and all required subsequent multiplications;

4. closure and the required topology estimates on the same output space;

5. associativity and descent through all actual-functional relations;

6. separate time-ordered, retarded, interacting, and switched-gauge constructions where claimed.

No assertion that every candidate must fail is proved. Conversely, a finite part for one numerical expression or membership of one output in ${\mathcal{P}}_{\Sigma }$ passes none of these remaining gates automatically.

The broader distinction between free products, causal products, and interaction maps is retained FR,CheungIXB,CheungIXD. No conclusion here reverses a separately versioned later partial construction; it simply makes no transfer from it.