feat(analyze): time an event at the step it was detected and report the quartiles

an obligation that never discharges is reported when the run ends, and timing it by the step that armed it recorded a liveness failure flushed at the budget as a violation found on step 1. the survival analysis now measures the detected step, falling back to the origin for campaigns written before the field existed, and says how many events that moved. the report gains the first and third quartiles beside the median.

cmd/internal-tools/analyze/analysis.go

@@ -20,7 +20,10 @@ type armSummary struct {
 	ExcludedByReason            map[string]int  `json:"excluded_by_reason,omitempty"`
 	MissingSeeds                []int64         `json:"missing_seeds,omitempty"`
 	EventsHeldAtBudget          int             `json:"events_held_at_budget"`
+	EventsDetectedAfterOrigin   int             `json:"events_detected_after_origin"`
 	MedianStepsToFirstViolation *float64        `json:"median_steps_to_first_violation"`
+	FirstQuartileSteps          *float64        `json:"first_quartile_steps_to_first_violation"`
+	ThirdQuartileSteps          *float64        `json:"third_quartile_steps_to_first_violation"`
 	SurvivalCurve               []survivalPoint `json:"survival_curve,omitempty"`
 	ViolationRate               *float64        `json:"violation_rate"`
 	TotalSteps                  int             `json:"total_steps"`
@@ -154,6 +157,9 @@ func summarize(current arm) armSummary {
 		if item.ClampedToBudget {
 			summary.EventsHeldAtBudget++
 		}
+		if item.Violated && item.EventStep > item.OriginStep {
+			summary.EventsDetectedAfterOrigin++
+		}
 		if item.Violated {
 			summary.Violated++
 		} else {
@@ -170,6 +176,12 @@ func summarize(current arm) armSummary {
 	if median, ok := medianSurvival(summary.SurvivalCurve); ok {
 		summary.MedianStepsToFirstViolation = &median
 	}
+	if lower, ok := quantileSurvival(summary.SurvivalCurve, 0.25); ok {
+		summary.FirstQuartileSteps = &lower
+	}
+	if upper, ok := quantileSurvival(summary.SurvivalCurve, 0.75); ok {
+		summary.ThirdQuartileSteps = &upper
+	}
 	if summary.Usable > 0 {
 		rate := float64(summary.Violated) / float64(summary.Usable)
 		summary.ViolationRate = &rate