Hi Jonathan, I have a question about how you are thinking about the relationships in \$$\mathbb N[S]\$$ and \$$\mathbb N[T]\$$. You say:
> For any particular \$$T\$$-complex \$$y\$$, the set of \$$T\$$-complexes less than it are all those with no more \$$T\$$-resources than \$$y\$$.

Does this mean that you are defining \$$\leq\$$ according to the amount of resources in each complex? I thought that we were using \$$\leq\$$ to represent possible reactions. Remember, \$$y \leq y'\$$ means that we can get \$$y\$$ from \$$y'\$$ not that there are fewer resources in \$$y\$$ than in \$$y'\$$. As an example:

\$[\textrm{yolk}] + [\textrm{white}] \leq [\textrm{egg}] \$ because you can get a yolk and a white from a whole egg. However \$[\textrm{egg}] \nleq 2[\textrm{egg}] \$ because you can't get exactly one egg from two eggs.

Maybe I'm misunderstanding your explanation or the definition of \$$\le\$$?