"Synthetic Neuromotor Variability Dataset with Conserved Variability Budget Across Functional States"

"We present a synthetic neuromotor dataset designed to study movement variability as an actively regulated property of motor control rather than as unstructured noise. The dataset models motor behavior as a high-dimensional stochastic dynamical system operating under a constrained total variability budget, formalized as the trace of the covariance matrix of the motor state. This formulation enables systematic investigation of how variability can be redistributed across degrees of freedom without changing its global magnitude and how pathological states emerge when this conservation principle is violated.The dataset consists of long multivariate time series (10,000 samples per condition) in a 10-dimensional motor state space, decomposing variability into irreducible noise (constant across conditions) and regulated noise (task and context-dependent). Five conditions are simulated: healthy baseline, task-constrained performance, high environmental uncertainty, pathological variability collapse and post-rehabilitation recovery. In all non-pathological conditions, total variability is conserved while variance is reallocated across dimensions; in the pathological condition, the total variability budget is reduced to model rigid and low-entropy motor dynamics.For each condition, we provide time-series data, covariance matrices, eigenspectra, power spectral density estimates and multivariate entropy measures, along with structured metadata. The dataset is suitable for analysis using statistical learning, signal processing and dynamical systems methods and supports research on motor learning, neuromotor disorders, rehabilitation and variability-based biomarkers. By offering an open, reproducible and computationally lightweight benchmark, this dataset enables principled exploration of conserved variability, dimensional reorganization and recovery dynamics in neuromotor control."