CRTI Empirical Validation Pipeline: A Pre-Registered, Falsification-First Test on the Peter Lake Regime-Shift Dataset

This document presents a fully specified, pre-registered empirical validation pipeline for testing the CRTI (Compression–Response/Resonance Thermodynamic Index) framework on a canonical ecological regime-shift dataset: the Peter Lake whole-ecosystem manipulation experiment (Carpenter et al., 2011).   The pipeline defines a reproducible workflow for constructing the state variables R (adaptive response capacity) and \Phi (structural compression) from multivariate time-series data, and for computing the composite index T = R/\Phi. All preprocessing steps, parameter choices, windowing strategies, and statistical tests are fixed ex ante and may not be modified post hoc.   The design is explicitly falsification-first. Primary and secondary hypotheses, as well as detailed failure criteria, are pre-specified and reported with equal prominence to positive outcomes. The document does not claim empirical validation of the CRTI framework; it defines a transparent and reproducible protocol for testing whether T carries early-warning information prior to a documented regime shift.   This pipeline provides a methodological foundation for fair comparison between CRTI-based metrics and classical early-warning signals under identical conditions.     early warning signals, regime shifts, ecological data, Peter Lake, pre-registration, reproducibility, falsification, time series analysis, dynamical systems, complex adaptive systems, structural compression, adaptive capacity, Kendall tau, covariance analysis, CRTI, critical transitions