Coordinative structures as scale-free networks: Cascade and percolation dynamics in motor learning with empirical validation.

Coordinative structures are the functional groupings of degrees of freedom that simplify motor control. Decades of research have documented them well, yet they remain mechanistically unexplained. How they emerge and why they are hierarchically organized are both unresolved questions. This study proposes scale-free network topology as the missing mechanism. Systematic simulations compared random networks, small-world networks, and scale-free networks. Scale-free organization reproduced the defining features of coordinative structures more completely than either alternative. Those features are a hub-periphery hierarchy, ordered hub-first recruitment, an abrupt onset of global coordination, and a balance between stability and flexibility. Four formal correspondences connect these features to established coordination phenomena. A coupled learning model reproduced the characteristic curve of skill acquisition, and scale-free networks reached the coordination threshold fastest. The model was then validated against published data from five independent studies spanning motor learning, bimanual coordination, brain networks, and joint coordination. It yields eleven testable predictions with explicit quantitative thresholds, together with five criteria that would disconfirm it. Network topology therefore offers a principled account of how coordinative structures form through structural constraints and experience. That account is empirically grounded and open to falsification.