Code for: Volcanic Eruptions Reorganize Climate Teleconnections: Detection via Riemannian Covariance Fingerprinting

Analysis code and data for the manuscript “Volcanic Eruptions Reorganize Climate Teleconnections: Detection via Riemannian Covariance Fingerprinting” (Geophysical Research Letters, 2026GL124297R). The method applies tangent-space regression on the symmetric positive definite (SPD) matrix manifold SPD(8) to detect volcanic, solar, and anthropogenic forcing signals in the rolling covariance structure of eight teleconnection indices (Niño 3.4, SOI, PDO, AMO, NAO, AO, PNA, HadCRUT5 GMTA; 1983–2024). Volcanic forcing is detected at p < 0.001, equivalent to z = 6.3σ above a block-permutation surrogate null (count-robust z-score, 4999 surrogates). The covariance (full-fingerprint) detector substantially outperforms a Euclidean mean-only optimal-fingerprinting baseline, indicating that the volcanic signal lives predominantly in the reorganization of teleconnection covariance rather than in the global-mean response. The energy-budget versus reorganization decomposition (V⁺) is reported as a qualitative diagnostic: V⁺ = 0.009 (volcanic), 0.026 (anthropogenic), 0.091 (solar). None of these are statistically distinguishable from the surrogate null V⁺ distribution (median ≈ 0.06; V⁺ p = 0.19 / 0.30 / 0.56). The qualitative ordering—volcanic forcing carrying the smallest energy-budget component—is consistent with a reorganization-dominated response and is corroborated, though not individually confirmed, by a CMIP6 GISS-E2-1-G hist-nat model test (natural-forcing V⁺ = 0.017 at d = 8). This version supersedes the original deposit. During peer review the originally archived V⁺ numbers were found not to be reproducible from the archived code, owing to (i) a post-submission change to the V⁺ ratio formula—the squared form V⁺ = ‖B⁺‖²F/‖B‖²F defined in the paper’s Methods is the correct one—and (ii) a near-zero fingerprint trace in the first submission that no longer obtains. The detection result (volcanic p < 0.001) is fully intact and robust; the V⁺ mechanism claim has been downgraded from a statistically significant near-zero result to a qualitative diagnostic. The full audit is included as AUDIT_vplus_grl.md, and every number is reproduced by a single canonical driver (analysis/grl_canonical_numbers.py) from the bundled input caches—no download step required. Contents: the SPD detection-and-attribution library (core/); public-data download scripts (data_download/); canonical reproduction drivers for every number, figure, SI table, and model test (analysis/); the exact processed input data used to produce the published numbers (cache/); the revised manuscript and supporting information in LaTeX and PDF (paper/); and the V⁺ reproducibility audit. See README.md for a complete file guide and reproduction instructions. All data sources (NOAA/CPC, NOAA/NCEI, NOAA/ESRL, UK Met Office, NASA ASDC GloSSAC v2.22, Pangeo/ESGF CMIP6) are publicly available. Code released under the MIT License.