Dynamical Independence as Causal Projection: A Fisher-Geometric Bridge with Topological Shielding at Criticality

We establish a formal bridge between dynamical independence (DI) and the causal Fisher metric for Gaussian VAR(1) processes, proving that dynamical dependence equals the squared Frobenius norm of the causal leakage operator weighted by the conditional Fisher metric. Three corollaries follow: DI-optimal projections minimize causal leakage ("Causal PCA"), the geometric-precision index decomposes into DI-mode contributions, and at criticality macroscopic autonomy saturates while microscopic complexity diverges (topological shielding). Numerical verification on 54 parameter combinations and n=50 random networks confirms all predictions.