Certified Fairness Auditing of Artificial Intelligence Subseasonal Heat-Wave Forecasts Under Unequal Station Density: Coverage Bounds and Public-Health Alert Equity

Subseasonal heat-wave forecasts increasingly drive public-health alerting, yet the statistical guarantees attached to those alerts are rarely audited for equity across unequally instrumented regions. The framework combines a station-density-weighted coverage functional, a distribution-free bound on the gap between nominal and realised alert coverage, and a calibration condition that links forecast reliability to the demographic composition of the alert-receiving population. A replication-based evaluation of the ['Intercept', 'exposure', 'group', 'severity'] estimator was conducted: 600 data sets of N = 500 were drawn from a declared data-generating process (intercept 12.0, exposure 0.42, group -3.1, severity 1.35, error SD 4.2). The study characterises the behaviour of the ordinary least squares estimator under the stated process. Across 600 replications the estimated bias was -0.03987 for the intercept and 0.00063 for the exposure coefficient, with RMSE 0.87652 and 0.01587 respectively; empirical coverage of the nominal 95% intervals was 1.0 for both parameters. The framework proposes that certified auditing can make alert-equity claims falsifiable, and it identifies the station-density threshold below which coverage bounds become too wide to support equitable-alert certification.