The interaction surface of a thing τ in a partial state X is the finite set of interaction terms associated with τ in that state: Ix_X(τ) ⊆ IxTerm. The interaction surface records which semiotic interactions are currently active for the thing — it is the interface through which the thing generates semantic material.
An interaction surface is not itself semantic content; it is auxiliary data that mediates between thing handles and the Heyting algebra H. Semantic consequences are produced by interpreting the terms and generating the thing fragment from their denotations. Enlarging the interaction surface (adding more interaction terms) can only enlarge the thing fragment: if Ix_X(τ) ⊆ Ix’_X(τ), then the thing fragment under the larger surface contains the one under the smaller.
The delta operation at the interaction level compares two surfaces by symmetric difference: Δ_ix(A, B) = (A \ B) ∪ (B \ A). This measures the syntactic difference between two interaction profiles before any semantic interpretation.