What the exact tensor-product identity supplies

Proposition prop:K5exact supplies a defined kernel at the transition. It also supplies a valid distributional pullback representation there.

It does not, without a further theorem, supply:

1. a uniform amplitude space describing the diagonal and flow-out pieces together;

2. the estimates relating the noncharacteristic diagonal symbols to the separated flow-out symbols;

3. the uniform parameter dependence needed when the residual variable $z$ is retained in a subsequent joint composition.

An intersecting-relation calculus can, in other problems, encode more than one ordinary Lagrangian piece. The present paper does not invoke such a calculus to assert these three conclusions for the full tensor-valued $K_5$ kernel.

Nor is a resolved paired construction substituted for the selected route.