Theorem: L.7 summary

Assume (R1)–(R3). The root-attached coefficient ${{\mathcal{C}}^{{\mathfrak{R}}_{\mathrm{L}}}}_{\mathrm{L}}$ exists, has compactly supported integrand, is bilinear and jointly continuous, agrees off the diagonal with the unextended graph, restricts exactly to XVI-K's ${{\mathcal{C}}^{{\mathfrak{R}}_{\mathrm{K}}}}_{C_2,\mathrm{fv}}$ on the $C_2$-only sector and exactly to XVI-J's ${{\mathcal{C}}^{\mathfrak{R}}}_{2e}$ on the further constant-slot truncation, and has propagated coherent ambiguity (eq:L-deltaCL) and propagated scale variation (eq:L-dCLmu) with net sign $+1$. The unrooted changes are collision-local; their propagated images are given by the root pairing. Locality or nonlocality of those functionals is not established here.

Proof. Lemmas lem:Lattach, lem:Lambprop, lem:Lscaleprop; Theorems thm:Lmain; Propositions prop:LtoK, prop:LtoJ; Remark rem:Lloc.