When Do Learnable Coupling Matrices Pay Off? Task Temporal Structure as the Decisive Factor

English translation of the Chinese paper 'Task Temporal Structure Strength Determines the Value of Learnable Coupling Matrices' (v6.2, Chinese version DOI 10.5281/zenodo.23009758). Through controlled-variable experiments on MNIST (no temporal structure), Cartpole (weak), and Collision (strong), this paper establishes that the value of a learnable coupling matrix depends on the task's temporal-structure strength: G4→G5 gain on Collision is 69.3% (train)/66.0% (ood), winning on 11/11 seeds (Wilcoxon p=0.0005, permutation p=0.0006, Cohen dz=3.56); cross-lag structural std is 0.0099 (Collision) vs 0.0012 (Cartpole), an 8.25x ratio. Includes three testable follow-up predictions (ACF stratification / W_lag null-model control / lead_steps sweep).