7.2 Interface discovery

Creative reuse often depends on discovering the interface rather than merely selecting the ingredients. Two theories may use different names for the same role, the same name for incompatible types, or different observational scales. An interface proposal must therefore answer three questions:

Alignment.

Which objects, operations, or invariants are being related?

Variance.

Which directions are preserved, reversed, forgotten, or aggregated by the relation?

Obligation.

Which diagrams must commute after the two domains are connected?

A useful interface may be a map already expressible in \(\mathbb S\). It may also require an intermediate object that neither source description contains. For example, two simulator modules may become composable only after introducing a common state variable and conversion law. In that case the creative act is not exhausted by composing old components: it includes proposing the mediating type through which they can communicate.

. When does an invented interface count as a combination inside the current theory, and when does it count as a transformation of that theory? The answer is relative to the declared representational package, not to the surface form of the output.