Exact Root-Label Realization Loci in Low-Cost Proximity-Decorated Binary Quadratic Paths

Let q∈ k[[x,y]]⊗²(V^*) be a primitive framed binary quadratic germ over an algebraically closed field of characteristic zero. A maximal primitive blowup path carries multiplicities, free/satellite proximity, and exceptional types B, M, and N, where a constant-root branch vertex B also carries an exact repeated-root class on the rank-one Veronese conic C=ν₂((V^*))⊂(²(V^*)). A preceding path-local classification under the square-cost bound ∑μᵢ²≤ 12 produced a $124$-row proximity-decorated envelope, with $119$ realizable rows and $5$ projective-transport obstructions. We now restore all exact constant-root labels and classify, for every row, the constructible locus of labels realized by one primitive germ. After quotienting only by the equalities already forced by projective-class transport, every nonempty row has at most two independent root-label components. The exact profile is 124=46\+45C+21ΔC+7(C²ΔC)+5 . The two-component part is sharp: $21$ rows realize only the diagonal orbit, $7$ only the ordered off-diagonal orbit, and no row realizes both. For free chains, the mechanisms are a Newton-support overlap forcing equality and a multiplicity-drop-one nonbranch pencil forcing inequality. For nonfree chains, the same degree-one anchor pencil $sP+tQ$ forces opposite conditions according as it is exposed at an interior B₁ vertex or at the terminal N₁ vertex. Explicit primitive nonzero-discriminant normal forms realize every allowed orbit. The classification is path-local; it does not assert sibling compatibility, whole-tree glueing, or a finite count of exact labelled assignments.