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  "Title": "Cayley Graph Analysis for Permutation Puzzles",
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    "analyze_top_combinations",
    "apply_operations",
    "apply_operations_batch_gpu",
    "bidirectional_bfs",
    "breakpoint_distance",
    "calculate_angular_distance_z",
    "calculate_differences",
    "calculate_midpoint_z",
    "cayley_gpu_available",
    "cayley_gpu_free",
    "cayley_gpu_init",
    "cayley_gpu_status",
    "check_duplicates",
    "convert_digits",
    "convert_LRX_to_celestial",
    "create_state_store",
    "find_best_random_combinations",
    "find_closest_to_coords",
    "find_combination_in_states",
    "find_path_bfs",
    "find_path_iterative",
    "generate_state",
    "generate_unique_states_df",
    "get_reachable_states",
    "get_reachable_states_light",
    "invert_path",
    "manhattan_distance",
    "manhattan_distance_matrix_gpu",
    "reconstruct_bfs_path",
    "reverse_prefix",
    "reverse_prefix_simple",
    "save_bridge_states",
    "select_unique",
    "shift_left",
    "shift_left_simple",
    "shift_right",
    "shift_right_simple",
    "short_path_bfs",
    "short_position",
    "sparse_bfs",
    "state_store_size",
    "store_add_from_df",
    "store_analyze_combos",
    "store_analyze_combos_gpu",
    "store_clear_opd",
    "store_combos_for_state",
    "store_filter_middle",
    "store_find_best_match",
    "store_find_intersections",
    "store_get_meta",
    "store_get_state",
    "store_lookup",
    "store_reconstruct_path",
    "store_set_opd",
    "store_to_dataframe",
    "validate_and_simplify_path"
  ],
  "_help": [
    {
      "page": "analyze_top_combinations",
      "title": "Analyze Top Operation Combinations",
      "topics": [
        "analyze_top_combinations"
      ]
    },
    {
      "page": "apply_operations",
      "title": "Apply Sequence of Operations",
      "topics": [
        "apply_operations"
      ]
    },
    {
      "page": "apply_operations_batch_gpu",
      "title": "Apply operations to batch of states on GPU",
      "topics": [
        "apply_operations_batch_gpu"
      ]
    },
    {
      "page": "bidirectional_bfs",
      "title": "Bidirectional BFS Shortest Path",
      "topics": [
        "bidirectional_bfs"
      ]
    },
    {
      "page": "breakpoint_distance",
      "title": "Breakpoint Distance Between Two States",
      "topics": [
        "breakpoint_distance"
      ]
    },
    {
      "page": "calculate_angular_distance_z",
      "title": "Angular Distance Between Two Celestial Points",
      "topics": [
        "calculate_angular_distance_z"
      ]
    },
    {
      "page": "calculate_differences",
      "title": "Calculate Manhattan Distances for All States",
      "topics": [
        "calculate_differences"
      ]
    },
    {
      "page": "calculate_midpoint_z",
      "title": "Midpoint Between Two Celestial Coordinates",
      "topics": [
        "calculate_midpoint_z"
      ]
    },
    {
      "page": "cayley_gpu_available",
      "title": "Check if GPU acceleration is available",
      "topics": [
        "cayley_gpu_available"
      ]
    },
    {
      "page": "cayley_gpu_free",
      "title": "Free GPU backend resources",
      "topics": [
        "cayley_gpu_free"
      ]
    },
    {
      "page": "cayley_gpu_init",
      "title": "Initialize GPU backend",
      "topics": [
        "cayley_gpu_init"
      ]
    },
    {
      "page": "cayley_gpu_status",
      "title": "Get GPU status information",
      "topics": [
        "cayley_gpu_status"
      ]
    },
    {
      "page": "check_duplicates",
      "title": "Find Duplicate States Between Two Tables",
      "topics": [
        "check_duplicates"
      ]
    },
    {
      "page": "convert_digits",
      "title": "Convert String to Integer Vector of Digits",
      "topics": [
        "convert_digits"
      ]
    },
    {
      "page": "convert_LRX_to_celestial",
      "title": "Convert LRX Counts to Celestial Coordinates",
      "topics": [
        "convert_LRX_to_celestial"
      ]
    },
    {
      "page": "create_state_store",
      "title": "Create a New State Store",
      "topics": [
        "create_state_store"
      ]
    },
    {
      "page": "find_best_random_combinations",
      "title": "Find Best Random Operation Sequences",
      "topics": [
        "find_best_random_combinations"
      ]
    },
    {
      "page": "find_closest_to_coords",
      "title": "Find Closest State to Target Coordinates",
      "topics": [
        "find_closest_to_coords"
      ]
    },
    {
      "page": "find_combination_in_states",
      "title": "Find a State in Reachable States Table",
      "topics": [
        "find_combination_in_states"
      ]
    },
    {
      "page": "find_path_bfs",
      "title": "Find Path via BFS Highways",
      "topics": [
        "find_path_bfs"
      ]
    },
    {
      "page": "find_path_iterative",
      "title": "Iterative Path Finder Between Permutation States",
      "topics": [
        "find_path_iterative"
      ]
    },
    {
      "page": "generate_state",
      "title": "Generate Reachable Random State",
      "topics": [
        "generate_state"
      ]
    },
    {
      "page": "generate_unique_states_df",
      "title": "Generate Data Frame of Unique Random States",
      "topics": [
        "generate_unique_states_df"
      ]
    },
    {
      "page": "get_reachable_states",
      "title": "Find Cycle in Permutation Group",
      "topics": [
        "get_reachable_states"
      ]
    },
    {
      "page": "get_reachable_states_light",
      "title": "Find Cycle Length (Lightweight Version)",
      "topics": [
        "get_reachable_states_light"
      ]
    },
    {
      "page": "invert_path",
      "title": "Invert a Path of Operations",
      "topics": [
        "invert_path"
      ]
    },
    {
      "page": "manhattan_distance",
      "title": "Manhattan Distance Between Two States",
      "topics": [
        "manhattan_distance"
      ]
    },
    {
      "page": "manhattan_distance_matrix_gpu",
      "title": "Compute Pairwise Manhattan Distance Matrix on GPU",
      "topics": [
        "manhattan_distance_matrix_gpu"
      ]
    },
    {
      "page": "reconstruct_bfs_path",
      "title": "Reconstruct path from sparse BFS result",
      "topics": [
        "reconstruct_bfs_path"
      ]
    },
    {
      "page": "reverse_prefix",
      "title": "Reverse First k Elements (with Coordinates)",
      "topics": [
        "reverse_prefix"
      ]
    },
    {
      "page": "reverse_prefix_simple",
      "title": "Reverse First k Elements (Simple)",
      "topics": [
        "reverse_prefix_simple"
      ]
    },
    {
      "page": "save_bridge_states",
      "title": "Save Bridge States to CSV",
      "topics": [
        "save_bridge_states"
      ]
    },
    {
      "page": "select_unique",
      "title": "Select Unique States by V-columns",
      "topics": [
        "select_unique"
      ]
    },
    {
      "page": "shift_left",
      "title": "Shift State Left (with Coordinates)",
      "topics": [
        "shift_left"
      ]
    },
    {
      "page": "shift_left_simple",
      "title": "Shift State Left (Simple)",
      "topics": [
        "shift_left_simple"
      ]
    },
    {
      "page": "shift_right",
      "title": "Shift State Right (with Coordinates)",
      "topics": [
        "shift_right"
      ]
    },
    {
      "page": "shift_right_simple",
      "title": "Shift State Right (Simple)",
      "topics": [
        "shift_right_simple"
      ]
    },
    {
      "page": "short_path_bfs",
      "title": "Shorten Path via Depth-Limited BFS Hopping",
      "topics": [
        "short_path_bfs"
      ]
    },
    {
      "page": "short_position",
      "title": "Simplify Operation Path",
      "topics": [
        "short_position"
      ]
    },
    {
      "page": "sparse_bfs",
      "title": "Sparse BFS with Look-ahead and Hybrid Selection",
      "topics": [
        "sparse_bfs"
      ]
    },
    {
      "page": "state_store_size",
      "title": "Get State Store Size",
      "topics": [
        "state_store_size"
      ]
    },
    {
      "page": "store_add_from_df",
      "title": "Add States to Store from Data Frame",
      "topics": [
        "store_add_from_df"
      ]
    },
    {
      "page": "store_analyze_combos",
      "title": "Analyze Combinations Directly into Store",
      "topics": [
        "store_analyze_combos"
      ]
    },
    {
      "page": "store_analyze_combos_gpu",
      "title": "Analyze Combinations into Store Using GPU Batch Operations",
      "topics": [
        "store_analyze_combos_gpu"
      ]
    },
    {
      "page": "store_clear_opd",
      "title": "Clear All OPD Filters",
      "topics": [
        "store_clear_opd"
      ]
    },
    {
      "page": "store_combos_for_state",
      "title": "Find Combo Numbers Containing a State in a Cycle",
      "topics": [
        "store_combos_for_state"
      ]
    },
    {
      "page": "store_filter_middle",
      "title": "Filter Middle States for a Cycle",
      "topics": [
        "store_filter_middle"
      ]
    },
    {
      "page": "store_find_best_match",
      "title": "Find Best Match by Manhattan Distance",
      "topics": [
        "store_find_best_match"
      ]
    },
    {
      "page": "store_find_intersections",
      "title": "Find Intersections Between Two Stores",
      "topics": [
        "store_find_intersections"
      ]
    },
    {
      "page": "store_get_meta",
      "title": "Get Metadata for a State",
      "topics": [
        "store_get_meta"
      ]
    },
    {
      "page": "store_get_state",
      "title": "Get State from Store",
      "topics": [
        "store_get_state"
      ]
    },
    {
      "page": "store_lookup",
      "title": "Lookup State Indices by State Vector",
      "topics": [
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    },
    {
      "page": "store_reconstruct_path",
      "title": "Reconstruct Path from Store",
      "topics": [
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    },
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      "page": "store_set_opd",
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      "topics": [
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