Phase 6: take a test (weighted sampling + question flow)

- internal/sampling: ComputeWeight (Laplace-smoothed error rate + recency
  multiplier, floor 0.15) and SelectWeighted (A-Res reservoir algorithm).
  10k-run statistical test verifies weak questions appear >3x more often
  than mastered, and mastered questions still appear (floor exercised).
- GET/POST /test/new: source filter with live available-count JS update,
  n-questions input, weighted vs uniform mode radio.
- GET /test/{id}/q/{n}: deterministic answer shuffle per (test_id,
  question_id), progress bar, mobile-friendly large tap targets.
- POST /test/{id}/q/{n}: records answer + upserts stat; advances to next
  question or finishes test and redirects to results stub.
- GET /test/{id}/results: stub (Phase 7 will add full review).
- Ownership enforced: all test routes 404 for wrong user.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

internal/sampling/weight.go

@@ -0,0 +1,41 @@
+package sampling
+
+import (
+	"math"
+	"time"
+
+	"qbank/internal/models"
+)
+
+const (
+	FloorWeight      = 0.15 // mastered questions still appear at ~15% base rate
+	RecencyCapDays   = 30.0 // days until recency multiplier saturates
+	RecencyMaxMult   = 2.0  // peak recency multiplier
+	UnseenBaseWeight = 0.5  // base weight for questions with no stats row
+)
+
+// ComputeWeight returns the sampling weight for a question given its per-user
+// stat. A nil stat means the question has never been seen.
+func ComputeWeight(stat *models.UserQuestionStat, now time.Time) float64 {
+	if stat == nil {
+		// Unseen: mid-range base + full recency = 1.0
+		return UnseenBaseWeight * RecencyMaxMult
+	}
+
+	s := float64(stat.TimesSeen)
+	c := float64(stat.TimesCorrect)
+
+	// Laplace-smoothed error rate dampens noise from small samples.
+	errorRate := (s - c + 1) / (s + 2)
+	base := math.Max(FloorWeight, errorRate)
+
+	var daysSince float64
+	if stat.LastSeenAt.Valid {
+		daysSince = now.Sub(stat.LastSeenAt.Time).Hours() / 24
+	} else {
+		daysSince = RecencyCapDays
+	}
+	recency := 1 + math.Min(daysSince/RecencyCapDays, 1.0)
+
+	return base * recency
+}