analyze_top_combinations
                        Analyze Top Operation Combinations
apply_operations        Apply Sequence of Operations
apply_operations_batch_gpu
                        Apply operations to batch of states on GPU
bidirectional_bfs       Bidirectional BFS Shortest Path
breakpoint_distance     Breakpoint Distance Between Two States
calculate_angular_distance_z
                        Angular Distance Between Two Celestial Points
calculate_differences   Calculate Manhattan Distances for All States
calculate_midpoint_z    Midpoint Between Two Celestial Coordinates
cayley_gpu_available    Check if GPU acceleration is available
cayley_gpu_free         Free GPU backend resources
cayley_gpu_init         Initialize GPU backend
cayley_gpu_status       Get GPU status information
check_duplicates        Find Duplicate States Between Two Tables
convert_LRX_to_celestial
                        Convert LRX Counts to Celestial Coordinates
convert_digits          Convert String to Integer Vector of Digits
find_best_random_combinations
                        Find Best Random Operation Sequences
find_closest_to_coords
                        Find Closest State to Target Coordinates
find_combination_in_states
                        Find a State in Reachable States Table
find_path_bfs           Find Path via BFS Highways
find_path_iterative     Iterative Path Finder Between Permutation
                        States
generate_state          Generate Reachable Random State
generate_unique_states_df
                        Generate Data Frame of Unique Random States
get_reachable_states    Find Cycle in Permutation Group
get_reachable_states_light
                        Find Cycle Length (Lightweight Version)
invert_path             Invert a Path of Operations
manhattan_distance      Manhattan Distance Between Two States
manhattan_distance_matrix_gpu
                        Compute Pairwise Manhattan Distance Matrix on
                        GPU
reconstruct_bfs_path    Reconstruct path from sparse BFS result
reverse_prefix          Reverse First k Elements (with Coordinates)
reverse_prefix_simple   Reverse First k Elements (Simple)
save_bridge_states      Save Bridge States to CSV
select_unique           Select Unique States by V-columns
shift_left              Shift State Left (with Coordinates)
shift_left_simple       Shift State Left (Simple)
shift_right             Shift State Right (with Coordinates)
shift_right_simple      Shift State Right (Simple)
short_path_bfs          Shorten Path via Greedy BFS Hopping
short_position          Simplify Operation Path
sparse_bfs              Sparse BFS with Look-ahead and Hybrid Selection
validate_and_simplify_path
                        Validate and Simplify a Path
