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)

This protocol pre-registers a preliminary real-data study of beyond-pairwise ordinal dependence in four-variable environmental time series from Puerto Rico. It was finalized before any real-data outcome was computed. Systems. Confirmatory: (S2) daily mean discharge at four USGS gauges in 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), combined with airport wind. Estimators. Bandt–Pompe symbols of order 3 (delay 1). The proxy excess3 = 0.6 Syn + 0.4 Surp uses fixed weights and joint-tuple counting (nested-recd 0.2.3); the pooled counting of nested-recd 0.2.2 and earlier is retained only as a reproducibility note. No-dependence references for the proxy are fitted-pairwise, independence and independent-series. Res_pair is the Kullback–Leibler divergence of the joint ordinal law from its pairwise maximum-entropy projection, obtained by iterative proportional fitting. Windows span 13 symbols; event blocks span 52 symbols. Hypotheses. H1: bias-adjusted Res_pair in blocks straddling Hurricane María (20 Sep 2017), Hurricane Fiona (18 Sep 2022) and the June 2020 Saharan dust event (Puerto Rico peak 23 Jun 2020) exceeds that of calendar-matched placebo blocks. H2: the null-referenced proxy (excess3 minus its fitted-pairwise reference) carries no information about bias-adjusted Res_pair beyond joint-symbol support (equivalence test, margin 0.30). Inference. The protocol specifies Holm multiplicity control, negative-control anchors, sensitivity analyses and decision rules. An i.i.d. parametric bootstrap from the block-fitted pairwise law is not used, because it rejected a true null in 100% of simulated 52-symbol blocks (the fitted law has far smaller support than the true law). A series-wise year-shift randomization test of cross-series independence is included as a secondary analysis; on true-null simulations at α = 0.05 its empirical size was 5.0% for chaotic and 6.7% for near-periodic independent series (pooled 5.8% over 600 tests). Negative results will be reported. Status. The pipeline has been verified on simulated coupled logistic maps only. The real-data runner remains locked until registration. Protocol revisions, including correction of a counting error in the Syn term of nested-recd identified during re-analysis of simulated data, are logged in Section 16 of the protocol; all were made before any real-data outcome was computed.