6 · Match bounded functions with valuations

A chosen subring of bounded functions selects the valuations that give every one of those functions size at most one. Under the theorem's assumptions, the selected region also recovers the subring.

Try this. Add one bound at a time. Each new condition removes valuations that make the selected function too large. Compare the remaining region after every change.

This correspondence is Proposition 9.2. The plotted points are a simple model of independent valuation parameters, not the valuation space of a particular ring, so the picture shows inclusion only.