Pre-Analysis Plan: Empirical Validation of the Compression–Resonance–Tension Index (CRTI) as an Early-Warning Signal in Ecological Regime Shifts

This document constitutes a pre-registered falsification protocol and empirical validation design for the Compression–Resonance–Tension Index (CRTI), a composite instability indicator developed within the Singularization Framework (von Mallinckrodt, 2024–2026).The CRTI hypothesis proposes that instability in complex adaptive systems emerges when structural compression C(t) exceeds adaptive resonance Res(t), formalised as the ratio T(t) = C(t) / Res(t). While the index has been evaluated on synthetic pre-transition time series, no empirical validation on real-world data has yet been conducted.This pre-analysis plan specifies, prior to any data analysis, the complete operationalisation of CRTI variables, preprocessing procedures, benchmark comparisons, statistical evaluation methods, sensitivity analyses, and pre-specified falsification criteria. The first empirical test is designed around the Peter Lake Whole-Ecosystem Phosphorus Manipulation Experiment (Carpenter et al., 2011, Science) — a publicly available dataset with experimentally documented transition timing, available via the Environmental Data Initiative (EDI, knb-lter-ntl.1).CRTI performance will be benchmarked against rolling variance, lag-1 autocorrelation, spectral reddening, and detrended fluctuation analysis (DFA), following the evaluation protocol of Dakos et al. (2012). Primary falsification criteria are fully pre-specified and include Kendall tau trend tests, surrogate testing, and ROC curve analysis with DeLong comparison against AR1. A six-category outcome taxonomy covers all possible results, including full falsification and operationalisation failure, both treated as scientifically informative outcomes. Robustness checks include sensitivity analysis across rolling window lengths, proxy weighting parameters, detrending methods (Gaussian and LOESS), and multiple-testing correction via Benjamini–Hochberg FDR.This preregistration is uploaded prior to any computation on the real-world dataset. The subsequent empirical paper will cite this document and disclose any deviations from protocol. CRTI, Compression-Resonance-Tension Index, early-warning signals, regime shifts, critical transitions, preregistration, pre-analysis plan, falsification protocol, resilience, complex adaptive systems, critical slowing down, shallow lake, Peter Lake, ecological regime shift, Singularization Framework, Mallinckrodt Cycle, composite indicator, Kendall tau, ROC analysis, rolling variance, lag-1 autocorrelation, detrended fluctuation analysis, DFA, spectral reddening, Benjamini-Hochberg, surrogate testing, empirical validation, complexity science