R code implementing finite-step probabilistic upper bounds for iterated Pearson correlation dynamics. From uniform -1,1 initialization, constructs state-dependent functions controlling contraction ratios conditional on normalized step size. Implements conditional quantile bounds via logarithmic binning, deterministic enlargement families, and out-of-sample validation. Computes expansion thresholds below which contraction is guaranteed with a given probability, and worst-case envelope bounds. Includes replication scripts for all figures and tables. Validated for matrix dimensions three to two thousand.
Ishrak Alhajj Hassan (Sat,) studied this question.