Directional Discriminant Packets and Bounded Scalar-Profile Loci for Primitive Binary Quadratic Germs

Let q=a u²+2buv+c v²∈ k[[x,y]]⊗²(V^*) be a primitive binary quadratic germ over an algebraically closed field of characteristic zero, and let D=(q)=b²-ac. Along a chosen path of point blowups, the lowest ²(V^*)-valued coefficient packets and the scalar discriminant lose different amounts of jet information. We show that the exceptional multiplicity and residual tangent divisor of D do not recursively determine the scalar label at a child center. The missing datum is a direction-dependent two-variable principal form. If a parent center has coefficient order μ, scalar excess e, and successor direction λ, write D(x,x(λ+z))=x2μ+e D_λ(x,z). The directional discriminant packet is _λ(q)=(σ_λ,[σ_λ D_λ]),σ_λ=(x,z) D_λ. If the child coefficient order is μ_λ, then its scalar excess and residual symbol are determined exactly by e_λ=e+σ_λ-2μ_λ, [xᵉσ_λ D_λ]. We give primitive pairs with identical parent coefficient packet, identical parent scalar excess and residual symbol, and identical child coefficient packet, but different child scalar excesses. For one scalar blowup, put d=2μ₀+e₀ and σ=2μ₁+e₁-e₀. The exact scalar cone is 0≤σ≤ d; the projective directional-form fiber is the full (^σ k²) in the interior and the hyperplane complement D₊(z^σ) on the outer face. We lift this cone to the low-cost coefficient types occurring in the previously classified square-cost-twelve paths. In particular, terminal moving-branch packets have fibers ⁴⁺ᵉ, while the branch-to-moving edge B₂→ M₂ has the exact profile band ₁/2≤ e₀≤ e₁+4 with projective interior fibers and a hyperplane-complement boundary fiber. For any fixed finite coefficient path and scalar bound, the paired coefficient--scalar realization locus is constructible in a finite jet space. Without a scalar bound, no uniform finite closure follows from coefficient square cost: scalar excess is unbounded already on a terminal square-cost-four family. All statements are path-local and make no sibling or whole-tree glueing claim.