11.8 What the experiments establish

The ten-node study uses six independently generated nonlinear DAGs (seeds 21–26), each with three injected latent-confounded visible pairs. The geometric screen is evaluated by candidate-arrow recall; a local Gaussian scorer, using the Bayesian information criterion (BIC), then selects parent sets inside that mask. The generator’s topological order is supplied to this final step, and the best row from a small fixed hyperparameter grid is reported for each seed. It is therefore a screen-and-parent-selection test, not an order-free identification result. The Sachs diagnostic uses 853 measurements of 11 proteins and a 17-arrow canonical reference graph; its ordered parent-set row likewise uses a reference order, while pooled greedy equivalence search (GES) is the order-free comparator.

Experiment: BRIDGE/SKFM nonlinear-DAG sweep

On the ten-node nonlinear random-DAG sweep, the selected graphs average 12.8 arrows, precision \(0.834\), recall \(0.907\), and directed \(F_1=0.864\). Direct SKFM extraction is less stable on these harder graphs even when the learned fields are accurate; the order-to-adjacency step is the principal bottleneck. This retained failure establishes the current division of labor: use geometry for high-recall compression and a score-based, latent-aware, or differentiable method for global selection.