diff --git a/engineering/skills/slo-architect/SKILL.md b/engineering/skills/slo-architect/SKILL.md
index e1758733..298f3d2f 100644
--- a/engineering/skills/slo-architect/SKILL.md
+++ b/engineering/skills/slo-architect/SKILL.md
@@ -99,7 +99,7 @@ Given target availability + window, computes:
 - Allowed downtime in the window
 - Multi-window burn-rate thresholds per Google SRE Workbook (Chapter 5):
   - **Fast burn** — page if 2% of monthly budget consumed in 1 hour
-  - **Slow burn** — page if 10% consumed in 6 hours, ticket if 10% in 3 days
+  - **Slow burn** — page if 5% consumed in 6 hours, ticket if 10% in 3 days
 - Recommended alerting rules (PromQL-shaped output)
 
 ```bash
@@ -140,8 +140,13 @@ See `references/sli_design.md` for examples and anti-patterns.
 
 For 99.9% SLO over 30 days:
 - Allowed unavailability: `0.1% × 30 × 24 × 60 = 43.2 minutes`
-- 1-hour fast-burn threshold (2% of monthly budget burned): `2% × 43.2 / 60 ≈ 1.44 ratio multiplier`
-- 6-hour slow-burn threshold (10% in 6h): `10% × 43.2 / 360 ≈ 0.6 ratio multiplier`
+- Burn rate is the observed bad-event fraction divided by the allowed bad-event fraction: `observed_bad_fraction / (1 - target_percent / 100)`.
+- Threshold for consuming a chosen budget fraction over an alert window: `budget_fraction × SLO_window_hours / alert_window_hours`.
+- 1-hour fast-burn threshold (2% of 30-day budget): `0.02 × 720 / 1 = 14.4`.
+- 6-hour slow-burn threshold (5% in 6h): `0.05 × 720 / 6 = 6`.
+- 3-day ticket threshold (10% in 72h): `0.10 × 720 / 72 = 1`.
+
+These are dimensionless burn-rate multipliers, not error-rate percentages. For a 99.9% target, a burn rate of 14.4 corresponds to a bad-event fraction of `14.4 × 0.001 = 0.0144` (1.44%). Thresholds scale with the SLO reporting window: the corresponding 28-day multipliers are 13.44, 5.6, and approximately 0.933.
 
 `error_budget_calculator.py` does this math for you and emits ready-to-paste alert rules.
 
diff --git a/engineering/skills/slo-architect/references/composition.md b/engineering/skills/slo-architect/references/composition.md
index 993b6096..94142302 100644
--- a/engineering/skills/slo-architect/references/composition.md
+++ b/engineering/skills/slo-architect/references/composition.md
@@ -27,7 +27,7 @@ abort_if: "p99 > 1000ms OR error_rate > 1%"
 
 After (SLO-driven):
 ```
-abort_if: "burn_rate.fast > 14.4 over 1h (per SLO checkout-success)"
+abort_if: "burn_rate.fast > 14.4 over 1h (per 30-day SLO checkout-success)"
 ```
 
 Wire-up:
@@ -79,7 +79,7 @@ Goal: ship a new checkout flow.
 2. **Compute burn-rate alerts** (slo-architect):
    ```bash
    error_budget_calculator.py --target 99.9 --window-days 28
-   # → fast_burn threshold = 14.4
+   # → fast_burn threshold = 13.44 (2% of a 28-day budget in 1h)
    ```
 
 3. **Define rollout** (feature-flags-architect):
@@ -91,7 +91,7 @@ Goal: ship a new checkout flow.
 
 4. **Wire the abort** (feature-flags-architect):
    ```yaml
-   abort_if: "burn_rate.fast > 14.4 (per SLO slo-checkout-svc-...)"
+   abort_if: "burn_rate.fast > 13.44 (per 28-day SLO slo-checkout-svc-...)"
    ```
 
 5. **Validate via chaos** before going wide (chaos-engineering):
diff --git a/engineering/skills/slo-architect/references/error_budget.md b/engineering/skills/slo-architect/references/error_budget.md
index 3b3d0a05..a5d9adcd 100644
--- a/engineering/skills/slo-architect/references/error_budget.md
+++ b/engineering/skills/slo-architect/references/error_budget.md
@@ -45,13 +45,17 @@ The alert fires only when BOTH windows show high burn. This filters spikes (only
 
 ### Recommended thresholds
 
+For a 30-day SLO reporting window:
+
 | Alert | Long window | Short window | Burn rate threshold | % budget at fire | Severity |
 |---|---|---|---|---|---|
 | Fast burn | 1h | 5m | 14.4 | 2% in 1h | page |
 | Slow burn | 6h | 30m | 6 | 5% in 6h | page |
 | Ticket | 3d | 6h | 1 | 10% in 3d | ticket |
 
-The numbers come from: `burn_rate × bad_event_rate > slo_target_violation_rate`.
+Burn rate is `observed_bad_fraction / allowed_bad_fraction`, where `allowed_bad_fraction = 1 - target_percent / 100`. To consume a chosen budget fraction over a long alert window, use `burn_rate_threshold = budget_fraction × SLO_window_hours / long_alert_window_hours`. An error-ratio alert compares `observed_bad_fraction > burn_rate_threshold × allowed_bad_fraction` in both its long and short windows.
+
+For 30 days (720 hours), the multipliers above are `0.02 × 720 / 1 = 14.4`, `0.05 × 720 / 6 = 6`, and `0.10 × 720 / 72 = 1`. For 28 days (672 hours), the same budget fractions and alert windows give 13.44, 5.6, and approximately 0.933. The target determines the allowed bad-event fraction; it does not change these multipliers.
 
 `error_budget_calculator.py` computes these for any target+window. Output is PromQL-shaped: