Definition: Declared matching interface

For each accessible input $a$ in a declared finite set ${\mathcal{A}}_{\mathrm{acc}}$, a proposed complete output has coordinates $z\in {\mathbb{R}}^{m_a}$ in a fixed developed presentation. The affine part of its matching test is

where $A_a,b_a$ are supplied finite matrices and vectors. Additional predicates specify seam, worldline, overlap, label, and guard compatibility.

Acceptance means that all declared checks hold. A matching certificate is the proposed output together with the data establishing those checks. It is not a rule selecting the right-hand side $b_a$ from an unknown matter state.