Calculation of the degree of nontrivial ultrametricity for RNA macrostates. PHYSICALLY RIGOROUS APPROACH: distance between basins via spectral decomposition of the transition rate matrix (Mahalanobis distance in the space of eigenvectors of the symmetrized matrix K). METHOD: A transition rate matrix K is built between all structures (N x N, where N ~ 2000) based on the Kramers formula. K is symmetrized taking detailed balance into account. The m smallest eigenvalues in magnitude and corresponding eigenvectors are computed (Lanczos method for sparse matrices). Automatic filtering of noise modes is performed by finding a spectral gap: if the ratio |λ_k| / |λ_{k-1}| exceeds a threshold (default 10^6), modes with indices < k are discarded as numerical noise. Each attraction basin is represented by a characteristic vector χ_A in the space of structures. The distance between basins A and B is defined as the weighted Euclidean distance between projections of χ_A and χ_B onto eigenvectors (Mahalanobis distance). The resulting distance matrix is a metric and is tested for ultrametricity. HANDLING DISCONNECTED GRAPHS: Before constructing the K_sym matrix, the connectivity of the structure graph is checked. If the graph contains multiple connected components, each component is processed separately: its own K_sym matrix is built, spectral decomposition is performed, and ultrametricity is checked. Components with fewer than 3 basins are skipped. STATISTICAL MODE (NUM_STAT > 1): When NUM_STAT > 1, NUM_STAT independent runs are performed for each sequence with different random samples of structures (seed varies: RANDOM_SEED, RANDOM_SEED+1, ..., RANDOM_SEED+NUM_STAT-1). Results are averaged, and the final table shows mean values and standard deviations (mean ± std). Integer quantities (number of structures, basins, connected components) are rounded to integers. OUTPUT MODES: VERBOSE = True — full log (steps, components, spectral analysis). VERBOSE = False — brief log: sequence header and parameters are printed once, then only RUN/COMPLETED, followed by a statistics block. ADVANTAGES: Takes into account all possible transition paths (via spectral decomposition). Context-independent (distance between A and B is determined only by them, not by the presence of other basins). Symmetric and guaranteed to be a metric. Automatically filters out numerical noise via spectral gap detection. Correctly handles disconnected structure graphs. Computational complexity O(m·N·E + K²·m), allowing processing of N ~ 2000 structures and K ~ 100 basins in seconds. STRUCTURE GENERATION MODE: Stochastic sampling (pbacktrack) from the Gibbs distribution. Dependencies: pip install viennarna numpy scipy biopython