Pre-registration protocol: beyond-pairwise ordinal dependence (Res_pair, excess3) in Puerto Rico environmental multivariate time series around documented regime shifts (Aim 3 preliminary study)

Abstract

Pre-registration protocol, written before any outcome was computed, for a preliminary real-data study of beyond-pairwise ordinal dependence in four-variable environmental time series from Puerto Rico. Systems. Confirmatory: (S2) daily mean discharge at four USGS gauges of the upper Río Grande de Loíza basin (50050900, 50051310, 50051800, 50055000; 1990–2025); (S4) TMAX, TMIN, AWND and WSF2 at San Juan Luis Muñoz Marín International Airport (GHCN-Daily RQW00011641; 1996–2025). Exploratory: (S1b) PM10, PM2.5 and SO2 at EPA AQS site 72-033-0004 (Cataño) with airport wind. Estimators. Bandt–Pompe symbols of order 3 (delay 1); excess3 = 0.6 Syn + 0.4 Surp with fixed weights and joint-tuple counting (corrected nested-recd 0.2.3, released on PyPI and Zenodo, doi:10.5281/zenodo.22970079; the pooled counting of nested-recd 0.2.2 and earlier is archived only as a reproducibility note); no-dependence references for the proxy (fitted-pairwise, independence, independent-series); Res_pair = KL divergence of the joint ordinal law from its pairwise maximum-entropy projection (IPF); window 13 symbols; event blocks of 52 symbols. Hypotheses. H1: the bias-adjusted Res_pair in blocks straddling Hurricane María (20 Sep 2017), Hurricane Fiona (18 Sep 2022) and the June 2020 Saharan dust event (PR peak 23 Jun 2020) exceeds calendar-matched placebo blocks. H2 (reworked in v0.2): the null-referenced proxy (excess3 minus its fitted-pairwise reference) carries no information about the bias-adjusted Res_pair beyond joint-symbol support (equivalence test, margin 0.30). Also specified: Holm multiplicity control, negative-control anchors, sensitivity analyses and decision rules. Negative results will be reported. Version 0.2 (25 Sep 2026) replaces draft v0.1 of the same day after a software counting error in the Syn term of nested-recd was found during re-analysis of simulated data; the changes are logged in Section 16 and were made before any real-data outcome was computed. Version 0.3 (25 Sep 2026) retires the i.i.d. parametric bootstrap from the block-fitted pairwise law, which rejected a true null in 100% of simulated 52-symbol blocks (the fitted law has far smaller support than the true law), and adds, as a secondary analysis, a series-wise year-shift randomization test of cross-series independence (empirical size at alpha = 0.05 on true-null simulations: 5.0% for chaotic and 6.7% for near-periodic independent series, pooled 5.8% of 600 tests). H1 (placebo ranks) and H2 are unchanged. Version 0.3.1 (5 Oct 2026; doi:10.5281/zenodo.23171841) revised wording only. Version 0.3.2 (6 Oct 2026) corrects the software citation: nested-recd 0.2.3, described in v0.3 and v0.3.1 as an unreleased local build, is released on PyPI (https://pypi.org/project/nested-recd/0.2.3/) and archived on Zenodo (doi:10.5281/zenodo.22970079); nested-recd 0.2.2 (doi:10.5281/zenodo.21937204) contains the Syn counting error and is not used. No scientific content was changed from v0.3. The pipeline was verified on simulated coupled logistic maps only. No dependence statistic has been computed on the real data; the real-data runner remains locked until the PI's explicit unlock instruction.