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, scalar excess e, and successor direction, write D (x, x (+z) ) =x^2+e D_ (x, z). The directional discriminant packet is _ (q) = (_, _ D_), _= (ₗ, ₙ) D_. If the child coefficient order is _, then its scalar excess and residual symbol are determined exactly by e_=e+_-2_, xᵉ_ D_. 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=2₀+e₀ and =2₁+e₁-e₀. The exact scalar cone is 0 d; the projective directional-form fiber is the full (^ k²) in the interior and the hyperplane complement D_+ (z^) 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 ₁2 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.