Definition: Target I and Target II

Target I (unrooted counterterm matching). Determine which coherent contact assignments of ${\mathfrak{R}}_{\mathrm{L}}$ produce collision tensors that arise as variations of local metric or insertion functionals, without using the root hypotheses (R1)–(R3). Target II (gravitational perturbative-sector interpretation). Interpret those matched functionals inside a specified gravitational action, insertion, gauge choice, ghost content, and diagram inventory.