An interaction term is an expression built from thing handles and definable operators, interpreted into the Heyting algebra H. Interaction terms form the smallest set IxTerm generated by: t ::= τ | k(t₁, …, tₙ), where τ is a thing handle and k is a definable operator in Op^def.
Interpretation extends recursively: a handle τ interprets as its semantic seed η(τ), and an operator application k(t₁, …, tₙ) interprets as ⟦k⟧(⟦t₁⟧, …, ⟦tₙ⟧). This makes interaction terms the “semiotic touches” through which things produce semantic material in H — the only way external entities generate content in the Interactive Semioverse.
The finite collection of interaction terms associated with a thing in a given state is its interaction surface. The semantic interpretations of these terms generate the thing fragment, and closing that fragment under the state’s operators produces the footprint. If an interaction term is ill-formed or its application undefined, it interprets as ⊥ (the failure value) and is marked in the failure semantics.