Mediterranean memory raises European warm-tail summer risk 8-11 points at 1-5 year horizons

The framework decomposes summer indicators into inherited slow-state memory, its predictable component, and contemporaneous innovation via finite causal filters and ridge-regularised logistic models. Mediterranean memory improved mean-temperature prediction over trend-only and ARX baselines, though gains over ARX were modest and multiple filter kernels performed similarly. Warm-tail risk showed the clearest signal: high memory loadings raised extreme-event odds consistently across 1-, 3-, and 5-year horizons in all 28 regions.

Circular-shift placebos produced one-sided probabilities of 0.05-0.14 that failed strict family-wise correction, leaving evidence moderate. The result aligns with documented increases in European heatwave persistence linked to soil-moisture and North-Atlantic temperature anomalies, yet isolates the inherited component more explicitly than prior observational studies. Regional bootstrap intervals remained positive, supporting physical interpretability of memory as a risk-loading variable.

Next steps include out-of-sample testing on CMIP6 ensembles and integration into seasonal forecast systems. Stronger evidence would require larger ensembles or targeted process-model experiments that isolate Mediterranean memory mechanisms.