The results of the Questionnaire algorithm on the parameter axis are analyzed, where each space-time matrix is now a data point (500 data points total). While we sampled from a 1D parameter space by varying the parameter K, the Questionnaire algorithm recovers a 2D manifold in a 3D space (Figure ), represented by κ a and κ b . Upon close inspection, we observe that the embedding is locally 1D: coloring the data points by K reveals a tight spiral. It would require a denser sampling of K to recover the 1D arc length of this spiral, but since we don't have such data, we instead retain the 2D embedding of our parameter space. This approach also demonstrates that our framework can adapt to multi-dimensional parameter spaces. Although the true K is one-to-one with the tight spiral, we justify our 2D parameter embedding as follows: the radius roughly corresponds to the coupling strength value, and the angle describes the isochron or the direction of agent synchronization (i.e., for large K values, where the position of the high-value ReW is in the phase-space plot).