Distinction Collapse and the Limits of Invariant Extension: A Categorical Analysis

This paper studies what happens when distinctions are transferred between domains. It shows that when a mapping collapses the differences these distinctions rely on, it becomes impossible to reconstruct them in an invariant way. This is not a technical limitation, but a structural one. The paper then shows how extension remains possible through transformation rather than preservation, using standard tools from category theory. This work is the formal part of a two-paper project. The companion paper (DOI: 10.5281/zenodo.19546894) develops the same problem at a conceptual level, showing how ontological distinctions depend on the domains in which they operate. The present paper provides the precise structural result behind that claim.