Advanced PromQL SLA Error Budget Burn Rate Alerting

Act as an Elite Site Reliability Engineer (SRE). Construct a highly advanced, mathematically rigorous Prometheus alerting architecture based strictly on Google's SRE Error Budget Burn Rate methodology. For the mission-critical [SERVICE_NAME], you must mathematically define an overarching [AVAILABILITY_SLA] (e.g., 99.95%). Write the terrifyingly complex PromQL queries required to calculate the exact ratio of failed HTTP requests (5xx) to total requests. You must engineer a 'Multi-Window, Multi-Burn-Rate' alerting configuration that evaluates the error rate over a short 1-hour window against a massive [TIME_WINDOW] (e.g., 30 days). The AlertManager configuration must physically page the on-call engineer *only* if the calculated burn rate mathematically proves the entire monthly error budget will be completely exhausted within the next 4 hours, utterly eradicating false-positive alert fatigue caused by momentary network blips.