11 Geometric Causal Discovery

BRIDGE and SKFM

BRIDGE turns the infinitesimal-causality diagnostic of Chapter 5 into a causal-discovery front end. Regime changes produce estimated response fields. Directed influence proposes candidate arrows, while Lie-bracket residuals record failures of visible closure. A downstream causal learner then searches only inside the retained family. Spectral Kernel Flow Matching (SKFM) amortizes the fields and asks how much of the graph can be extracted directly from their geometry.

¹1. BRIDGE stands for Bracket Residuals for Interventional Discovery and Geometric Estimation. Its strongest present role is candidate generation, not stand-alone causal identification. ↩