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/select.go

@@ -0,0 +1,46 @@
+package sampling
+
+import (
+	"math"
+	"math/rand"
+	"sort"
+)
+
+// Candidate is a question ID paired with its sampling weight.
+type Candidate struct {
+	ID     string
+	Weight float64
+}
+
+// SelectWeighted picks n distinct candidates using the A-Res weighted
+// reservoir algorithm (Efraimidis–Spirakis). Each item's selection
+// probability is proportional to its weight. O(m log m) time.
+func SelectWeighted(candidates []Candidate, n int, rng *rand.Rand) []Candidate {
+	if n >= len(candidates) {
+		out := make([]Candidate, len(candidates))
+		copy(out, candidates)
+		return out
+	}
+
+	type keyed struct {
+		c   Candidate
+		key float64
+	}
+
+	keys := make([]keyed, len(candidates))
+	for i, c := range candidates {
+		u := rng.Float64()
+		if u == 0 {
+			u = 1e-12 // avoid log(0) / pow weirdness
+		}
+		keys[i] = keyed{c, math.Pow(u, 1.0/c.Weight)}
+	}
+
+	sort.Slice(keys, func(i, j int) bool { return keys[i].key > keys[j].key })
+
+	out := make([]Candidate, n)
+	for i := range out {
+		out[i] = keys[i].c
+	}
+	return out
+}