We prove Born-almost-sure completeness for a score-plus-Hessian (SH) damping of the spinless Deotto–Ghirardi law on polynomial-Gaussian Schrödinger solutions satisfying quantitative full-configuration transversality throughout a small-value region of the polynomial. A trace identity controls the added current without imposing a rank condition on individual particle blocks. The result covers nondegenerate complex-linear polynomials times isotropic Gaussians and two-particle data (X+iY+F0(q1))e−|q|2/2 under free and unit-oscillator evolution, for every finite-degree complex polynomial in the three coordinates of particle one. This graph family includes entangled moving nodes whose added current has no C1 extension. Separately, a local rank hierarchy characterizes sufficient conditions for flat nodal extension: score damping works at particle rank two, and SH damping works at any nonzero particle block of a transversal node. An active rank-zero block can obstruct extension while retaining complete trajectories. Controlled high-frequency tails give vanishing standard Bohmian velocities but divergent or separated modified velocities. Local strong-H4 convergence restores an L2 velocity estimate in three dimensions under an amplitude floor. Born-weighted norms quantify the transition to strong suppression as the damping lengths approach the preparation width; an exact Hessian minimum determines the Hessian damping envelope for the example.

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