Decomposition Before Assembly

Prove that whenever a regular computation is achievable by the paper’s graphical operations, an equivalent computation exists in which every gluing operation is performed only after all decomposition operations.

Background

The proposed identification algorithm follows an extract–decompose–assemble pattern: it extracts identifiable kernels, decomposes them into smaller graphical components, and finally glues those components into the target kernel. The conjecture asks whether this prescribed ordering loses no computational power. Together with the other completeness conjectures, it is intended to support the claimed if-and-only-if characterization of the algorithm.