{
    "sub_tasks": [
        {
            "bullet_points": [
                "Load the latent space data from the provided `.npy` file.",
                "Verify that the loaded data has dimensions (101, 103, 25, 13) and document this verification in the summary statistics.",
                "Extract the 10-dimensional latent vectors for all (x, t, IC).",
                "Reshape the data to a 2D array for global analysis.",
                "Compute the mean, covariance, and perform PCA on the global latent space.",
                "Record the explained variance ratios and eigenvalues for all principal components.",
                "Save summary statistics and plots (e.g., scree plot of explained variance)."
            ],
            "sub_task": "Data loading, latent space extraction, and global latent space PCA",
            "sub_task_agent": "engineer"
        },
        {
            "bullet_points": [
                "For each of the 25 initial conditions, extract the corresponding latent vectors.",
                "Compute the mean (centroid), covariance, and perform PCA for each IC.",
                "For each IC, determine and store the intrinsic dimensionality required to explain a fixed variance threshold (e.g., 95%).",
                "Record the per-IC explained variance ratios, eigenvalues, and principal vectors.",
                "Save the centroids and principal vectors for all ICs.",
                "Generate and save summary plots (e.g., average per-IC explained variance, distribution of intrinsic dimensionality)."
            ],
            "sub_task": "Per-initial condition (IC) latent space analysis and PCA",
            "sub_task_agent": "engineer"
        },
        {
            "bullet_points": [
                "Collect the 25 centroids (one per IC) into a matrix.",
                "Perform PCA on the centroids to assess their geometric arrangement.",
                "Record the explained variance and eigenvalues for centroid PCA.",
                "Explore clustering in the centroids, e.g., with scatter plots in the space of the top 2-3 principal components, to visualize whether centroids lie on a low-dimensional manifold.",
                "Generate and save plots visualizing the centroids in the space of top principal components."
            ],
            "sub_task": "Analysis of centroids and their geometric structure",
            "sub_task_agent": "engineer"
        },
        {
            "bullet_points": [
                "For each pair of ICs, compute the alignment (dot products) between their principal vectors.",
                "Compute principal angles or subspace similarity metrics between per-IC principal subspaces.",
                "Perform an Orthogonal Procrustes analysis (or similar method) to quantify rotational alignment between manifolds.",
                "Analyze whether manifolds are related by translations, rotations, or low-dimensional variations.",
                "Perform PCA on the set of first principal vectors across ICs to assess structured variation.",
                "Generate and save relevant plots (e.g., heatmaps of subspace similarity, PCA of principal vectors)."
            ],
            "sub_task": "Comparative analysis of manifold orientations and relationships",
            "sub_task_agent": "engineer"
        },
        {
            "bullet_points": [
                "Project per-IC latent vectors onto the global principal subspace.",
                "Quantify how much per-IC variance is captured by the global subspace.",
                "Analyze the distribution of projected centroids and orientations within the global subspace.",
                "Clearly annotate plots with the percentage of variance captured by the global subspace for each IC, to facilitate direct comparison.",
                "Generate and save plots illustrating these relationships."
            ],
            "sub_task": "Relating per-IC manifolds to global latent space structure",
            "sub_task_agent": "engineer"
        },
        {
            "bullet_points": [
                "Review all quantitative results, statistics, and plots from previous steps.",
                "Synthesize findings on the intrinsic dimensionality, flatness, and relationships of latent manifolds.",
                "Interpret the geometric structure of the latent space and how initial conditions are encoded.",
                "Discuss whether a simple or low-dimensional description emerges.",
                "Reference and interpret all key plots and statistics.",
                "Include a discussion of potential limitations and computational considerations observed during the analysis (e.g., noise effects, low sample size in parts of the latent space).",
                "Write a comprehensive Results section suitable for inclusion in a paper or report."
            ],
            "sub_task": "Results synthesis and interpretation",
            "sub_task_agent": "researcher"
        }
    ]
}