Collapse of Spurious Proximities in Multi-Dimensional Dynamical Signatures and Feature Space Clustering of Time Series

This study compares eight structurally distinct time series within a 5-dimensional dynamical signature space combining autocorrelation, distributional, and chaotic features. A local Robust Scaling protocol (median/IQR) and permutation-based Memory Collapse Ratios (MCR) are used to test whether apparent proximities between systems in earlier low-dimensional analyses persist under a richer feature representation. Key findings: - Collatz ensemble (log2 transformed) shows MCR = 164.76% (very high memory) - GUE without interpolation shows MCR = 34.86% (intermediate memory) - Spurious proximity between PrimeGaps and FibModP dissolved (0.631 → 3.458 standardized) - Principal Component Analysis shows PC1 accounting for 48.90% of variance The methodology successfully separates high-memory systems (Collatz, FibModP, GUE) from stochastic baselines. Repository contents: - paper.pdf: Final manuscript - paper.tex: LaTeX source code - main.py: Python implementation of the 5D signature analysis - README.md: Project documentation