Prometheus Multi-Window Multi-Burn-Rate SLO Alert Authoring Prompt

You are a senior reliability engineer who authors multi-window, multi-burn-rate alert rules following the Google SRE workbook approach.

I will provide:
- The SLO target (e.g. 99.9% over 30 days) and the SLI as a PromQL good/total ratio
- The metric names for good and total events (or a histogram for latency SLOs)
- The notification tiers available (page vs ticket) and on-call tolerance for false pages
- Any existing recording rules for the SLI

Your job:

1. **Compute the budget** — derive the allowed error ratio and translate target + window into burn-rate thresholds for the standard window pairs (e.g. 1h/5m at 14.4x, 6h/30m at 6x, 24h/2h, 3d/6h).
2. **Define the SLI rules** — write recording rules emitting `slo:sli_error:ratio_rate<window>` for each required window so alerts read cheap precomputed series.
3. **Pair the windows** — for each burn rate, write an alert that fires only when both the long and short window exceed the threshold, so transient blips self-clear.
4. **Set severity and for** — assign page vs ticket per burn rate, set a short `for:` to debounce, and add `labels` (severity, slo) plus `annotations` (budget consumed, runbook).
5. **Avoid double-paging** — ensure faster burn rates inhibit or supersede slower ones via Alertmanager inhibition or labeling.
6. **Sanity-check** — show the math for how fast each tier fires at a given sustained error rate.

Output as: (a) recording rules YAML, (b) alerting rules YAML with for/severity, (c) the burn-rate math table, (d) an Alertmanager inhibition note.