Cross‑Domain Validation of a Moving‑Average Divergence Framework in Atmospheric Science, Hydrology, Solar Physics, and Epidemiology

A moving-average framework developed from mathematical first principles — a gap-closure decomposition that measures whether a moving-average filter leads or lags its series (the filter-share S_W), a fast-minus-slow volatility-divergence operator, a persistence-sign rule that predicts the sign of the correlation between a fast-minus-slow level divergence and the future observable from the series' autocorrelation function (ACF), and the property that the divergence operator is a superset of classical critical-slowing-down (CSD) indicators — had previously been validated only on financial-market data (Kim 2026a,b,c,d). This paper tests whether the identical framework recovers the independently-known physical behavior of four natural-science domains: atmospheric science (station temperature anomalies), hydrology (river discharge), solar physics (sunspot numbers), and epidemiology (influenza-like illness). The decomposition and the persistence-sign rule are applied identically across all four domains; the volatility-divergence operator is adapted to each domain's natural innovation representation (log-returns, first-differences, or level), a choice we disclose rather than tune. Three results follow. First, the decomposition orders the four domains by restoring-force strength exactly as their physics predicts, from a near-random-walk weather benchmark (S_W band [2.5, 5.2]%) through deseasonalized rivers to mechanically-adapting influenza (153.7%), against a synthetic random-walk control that sits at 97.9 (band 86.5–115.0). Second, the persistence-sign rule predicts the sign of each divergence-to-future correlation from the ACF, and that predicted sign is what the data confirm: across a pre-registered 25-prediction grid, every one of the 13 predictions with enough signal to resolve keeps its predicted sign on both temporal halves of the data — a split that does not depend on any significance model, and the load-bearing result here. A parametric screen (13 of 13 screened predictions correct, 0 significant wrong-signed) is reported as a demoted cross-check only, because the subsampling makes it anti-conservative; clearing the in-paper falsifier under it is therefore a strict test rather than a lenient one. The grid includes two predicted sign flips: the Colorado River at horizon 252 days, where the flip arises because the near-lag mean ACF falls below the far-lag mean ACF while the ACF itself remains positive (it is not an ACF zero-crossing), and influenza at horizon 26 weeks, near the seasonal ACF structure whose zero-crossing sits at 14 weeks. Third, a divergence-based influenza-onset detector fires roughly 8.222 weeks earlier on average than a simple level-threshold rule across 27 seasons — an advantage that ranges from 5.286 to 9.731 weeks as the threshold is varied, with divergence leading in the large majority of seasons throughout — and supplies simultaneous dominant-strain identification, obtained with no epidemiological model. A unifying variable — the ACF of the observable — governs the sign of the divergence operator across every domain tested (the proven relationship) and tracks its magnitude, deseasonalization response, and failure modes. We register dated, reader-runnable 2026–27 influenza predictions as the headline falsifier; a single statistically significant prediction whose observed sign contradicts the ACF-predicted sign would falsify the central mechanism. A spatial-curvature peak-detection hypothesis was pre-registered and failed: spatial disaggregation of the national signal does not yield a robust causal lead on the national peak, and we report that honest negative alongside the onset result.Verified rebuild under the Research-to-Publication Standard v1.8: every load-bearing number is registered in a machine-checked ledger (claims.lock) and regenerated on demand by verify.py on hash-pinned inputs, then independently reproduced from a clean checkout; a capped single-round adversarial review under a fix-or-rebut protocol and a public corrections log are committed in the repository. Dated, reader-runnable 2026–27 influenza predictions are registered publicly as a prospective out-of-sample falsifier, to be resolved on finalized CDC FluView data at a fixed lock date. The paper is licensed CC BY-NC-ND 4.0; the accompanying reconstruction and verification code is MIT-licensed.