{
  "image0": {
    "name": "centroid_pca_scree_plot_3_20250604-135958.png",
    "caption": "Scree plot showing the variance explained by principal components of the initial condition (IC) centroids. The first principal component captures over 99\\% of the variance, indicating that the centroids are arranged along an effectively one-dimensional structure in the latent space."
  },
  "image1": {
    "name": "global_pca_scree_plot_1_20250604-135555.png",
    "caption": "Scree plot showing the individual and cumulative explained variance from the global Principal Component Analysis of all latent vectors. The variance is highly concentrated in the first three components, which capture over 96\\%, revealing the low-dimensional structure of the global latent space."
  },
  "image2": {
    "name": "per_ic_avg_scree_plot_2_20250604-135804.png",
    "caption": "Average explained variance by principal components for the latent space of each initial condition, averaged across 25 initial conditions. Blue bars show the average individual explained variance per component; the red line shows the average cumulative explained variance with standard deviation (shaded). This analysis reveals that the latent representation for each initial condition is consistently low-dimensional, with the first three components capturing nearly 97.5\\% of the variance on average."
  },
  "image3": {
    "name": "dot_product_heatmaps_4_20250604-140218.png",
    "caption": "Heatmaps show the absolute dot product between corresponding principal vectors (PC1, PC2, PC3) from per-initial condition PCA for all pairs of initial conditions. High values (yellow) indicate strong alignment. The plots demonstrate substantial alignment across initial conditions, particularly for PC3, indicating that the 3D latent manifolds for different initial conditions are largely parallel."
  },
  "image4": {
    "name": "projected_centroids_3D_5_20250604-140503.png",
    "caption": "Centroids of the 25 per-initial\\ensuremath{\\_}condition (IC) latent manifolds projected onto the first three global principal components (PCs). Points are colored by IC index (0-24). The centroids form a near-linear path, primarily along Global PC1, indicating that different initial conditions primarily translate the latent manifolds along this dominant direction in the global latent space."
  }
}