feat: Add math modules — stats, scale, epsilon, score, signal

Centralizes common math operations used across core/go-ai, core/go,
and core/mining into Poindexter as the math pillar (alongside Borg=data,
Enchantrix=encryption).

New modules:
- stats: Sum, Mean, Variance, StdDev, MinMax, IsUnderrepresented
- scale: Lerp, InverseLerp, Remap, RoundToN, Clamp, MinMaxScale
- epsilon: ApproxEqual, ApproxZero
- score: WeightedScore, Ratio, Delta, DeltaPercent
- signal: RampUp, SineWave, Oscillate, Noise (seeded RNG)

235 LOC implementation, 509 LOC tests, zero external deps, WASM-safe.

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

docs/plans/2026-02-16-math-expansion-design.md

@@ -0,0 +1,46 @@
+# Poindexter Math Expansion
+
+**Date:** 2026-02-16
+**Status:** Approved
+
+## Context
+
+Poindexter serves as the math pillar (alongside Borg=data, Enchantrix=encryption) in the Lethean ecosystem. It currently provides KD-Tree spatial queries, 5 distance metrics, sorting utilities, and normalization helpers.
+
+Analysis of math operations scattered across core/go, core/go-ai, and core/mining revealed common patterns that Poindexter should centralize: descriptive statistics, scaling/interpolation, approximate equality, weighted scoring, and signal generation.
+
+## New Modules
+
+### stats.go — Descriptive statistics
+Sum, Mean, Variance, StdDev, MinMax, IsUnderrepresented.
+Consumers: ml/coverage.go, lab/handler/chart.go
+
+### scale.go — Normalization and interpolation
+Lerp, InverseLerp, Remap, RoundToN, Clamp, MinMaxScale.
+Consumers: lab/handler/chart.go, i18n/numbers.go
+
+### epsilon.go — Approximate equality
+ApproxEqual, ApproxZero.
+Consumers: ml/exact.go
+
+### score.go — Weighted composite scoring
+Factor type, WeightedScore, Ratio, Delta, DeltaPercent.
+Consumers: ml/heuristic.go, ml/compare.go
+
+### signal.go — Time-series primitives
+RampUp, SineWave, Oscillate, Noise (seeded RNG).
+Consumers: mining/simulated_miner.go
+
+## Constraints
+
+- Zero external dependencies (WASM-compilable)
+- Pure Go, stdlib only (math, math/rand)
+- Same package (`poindexter`), flat structure
+- Table-driven tests for every function
+- No changes to existing files
+
+## Not In Scope
+
+- MLX tensor ops (hardware-accelerated, stays in go-ai)
+- DNS tools migration to go-netops (separate PR)
+- gonum backend integration (future work)

epsilon.go

@@ -0,0 +1,14 @@
+package poindexter
+
+import "math"
+
+// ApproxEqual returns true if the absolute difference between a and b
+// is less than epsilon.
+func ApproxEqual(a, b, epsilon float64) bool {
+	return math.Abs(a-b) < epsilon
+}
+
+// ApproxZero returns true if the absolute value of v is less than epsilon.
+func ApproxZero(v, epsilon float64) bool {
+	return math.Abs(v) < epsilon
+}

epsilon_test.go

@@ -0,0 +1,50 @@
+package poindexter
+
+import "testing"
+
+func TestApproxEqual(t *testing.T) {
+	tests := []struct {
+		name    string
+		a, b    float64
+		epsilon float64
+		want    bool
+	}{
+		{"equal", 1.0, 1.0, 0.01, true},
+		{"close", 1.0, 1.005, 0.01, true},
+		{"not_close", 1.0, 1.02, 0.01, false},
+		{"negative", -1.0, -1.005, 0.01, true},
+		{"zero", 0, 0.0001, 0.001, true},
+		{"at_boundary", 1.0, 1.01, 0.01, false},
+		{"large_epsilon", 100, 200, 150, true},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			got := ApproxEqual(tt.a, tt.b, tt.epsilon)
+			if got != tt.want {
+				t.Errorf("ApproxEqual(%v, %v, %v) = %v, want %v", tt.a, tt.b, tt.epsilon, got, tt.want)
+			}
+		})
+	}
+}
+
+func TestApproxZero(t *testing.T) {
+	tests := []struct {
+		name    string
+		v       float64
+		epsilon float64
+		want    bool
+	}{
+		{"zero", 0, 0.01, true},
+		{"small_pos", 0.005, 0.01, true},
+		{"small_neg", -0.005, 0.01, true},
+		{"not_zero", 0.02, 0.01, false},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			got := ApproxZero(tt.v, tt.epsilon)
+			if got != tt.want {
+				t.Errorf("ApproxZero(%v, %v) = %v, want %v", tt.v, tt.epsilon, got, tt.want)
+			}
+		})
+	}
+}

scale.go

@@ -0,0 +1,61 @@
+package poindexter
+
+import "math"
+
+// Lerp performs linear interpolation between a and b.
+// t=0 returns a, t=1 returns b, t=0.5 returns the midpoint.
+func Lerp(t, a, b float64) float64 {
+	return a + t*(b-a)
+}
+
+// InverseLerp returns where v falls between a and b as a fraction [0,1].
+// Returns 0 if a == b.
+func InverseLerp(v, a, b float64) float64 {
+	if a == b {
+		return 0
+	}
+	return (v - a) / (b - a)
+}
+
+// Remap maps v from the range [inMin, inMax] to [outMin, outMax].
+// Equivalent to Lerp(InverseLerp(v, inMin, inMax), outMin, outMax).
+func Remap(v, inMin, inMax, outMin, outMax float64) float64 {
+	return Lerp(InverseLerp(v, inMin, inMax), outMin, outMax)
+}
+
+// RoundToN rounds f to n decimal places.
+func RoundToN(f float64, decimals int) float64 {
+	mul := math.Pow(10, float64(decimals))
+	return math.Round(f*mul) / mul
+}
+
+// Clamp restricts v to the range [min, max].
+func Clamp(v, min, max float64) float64 {
+	if v < min {
+		return min
+	}
+	if v > max {
+		return max
+	}
+	return v
+}
+
+// ClampInt restricts v to the range [min, max].
+func ClampInt(v, min, max int) int {
+	if v < min {
+		return min
+	}
+	if v > max {
+		return max
+	}
+	return v
+}
+
+// MinMaxScale normalizes v into [0,1] given its range [min, max].
+// Returns 0 if min == max.
+func MinMaxScale(v, min, max float64) float64 {
+	if min == max {
+		return 0
+	}
+	return (v - min) / (max - min)
+}

scale_test.go

@@ -0,0 +1,148 @@
+package poindexter
+
+import (
+	"math"
+	"testing"
+)
+
+func TestLerp(t *testing.T) {
+	tests := []struct {
+		name    string
+		t_, a, b float64
+		want    float64
+	}{
+		{"start", 0, 10, 20, 10},
+		{"end", 1, 10, 20, 20},
+		{"mid", 0.5, 10, 20, 15},
+		{"quarter", 0.25, 0, 100, 25},
+		{"extrapolate", 2, 0, 10, 20},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			got := Lerp(tt.t_, tt.a, tt.b)
+			if math.Abs(got-tt.want) > 1e-9 {
+				t.Errorf("Lerp(%v, %v, %v) = %v, want %v", tt.t_, tt.a, tt.b, got, tt.want)
+			}
+		})
+	}
+}
+
+func TestInverseLerp(t *testing.T) {
+	tests := []struct {
+		name    string
+		v, a, b float64
+		want    float64
+	}{
+		{"start", 10, 10, 20, 0},
+		{"end", 20, 10, 20, 1},
+		{"mid", 15, 10, 20, 0.5},
+		{"equal_range", 5, 5, 5, 0},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			got := InverseLerp(tt.v, tt.a, tt.b)
+			if math.Abs(got-tt.want) > 1e-9 {
+				t.Errorf("InverseLerp(%v, %v, %v) = %v, want %v", tt.v, tt.a, tt.b, got, tt.want)
+			}
+		})
+	}
+}
+
+func TestRemap(t *testing.T) {
+	tests := []struct {
+		name                         string
+		v, inMin, inMax, outMin, outMax float64
+		want                         float64
+	}{
+		{"identity", 5, 0, 10, 0, 10, 5},
+		{"scale_up", 5, 0, 10, 0, 100, 50},
+		{"reverse", 3, 0, 10, 10, 0, 7},
+		{"offset", 0, 0, 1, 100, 200, 100},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			got := Remap(tt.v, tt.inMin, tt.inMax, tt.outMin, tt.outMax)
+			if math.Abs(got-tt.want) > 1e-9 {
+				t.Errorf("Remap = %v, want %v", got, tt.want)
+			}
+		})
+	}
+}
+
+func TestRoundToN(t *testing.T) {
+	tests := []struct {
+		name     string
+		f        float64
+		decimals int
+		want     float64
+	}{
+		{"zero_dec", 3.456, 0, 3},
+		{"one_dec", 3.456, 1, 3.5},
+		{"two_dec", 3.456, 2, 3.46},
+		{"three_dec", 3.4564, 3, 3.456},
+		{"negative", -2.555, 2, -2.56},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			got := RoundToN(tt.f, tt.decimals)
+			if math.Abs(got-tt.want) > 1e-9 {
+				t.Errorf("RoundToN(%v, %v) = %v, want %v", tt.f, tt.decimals, got, tt.want)
+			}
+		})
+	}
+}
+
+func TestClamp(t *testing.T) {
+	tests := []struct {
+		name       string
+		v, min, max float64
+		want       float64
+	}{
+		{"within", 5, 0, 10, 5},
+		{"below", -5, 0, 10, 0},
+		{"above", 15, 0, 10, 10},
+		{"at_min", 0, 0, 10, 0},
+		{"at_max", 10, 0, 10, 10},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			got := Clamp(tt.v, tt.min, tt.max)
+			if got != tt.want {
+				t.Errorf("Clamp(%v, %v, %v) = %v, want %v", tt.v, tt.min, tt.max, got, tt.want)
+			}
+		})
+	}
+}
+
+func TestClampInt(t *testing.T) {
+	if got := ClampInt(5, 0, 10); got != 5 {
+		t.Errorf("ClampInt(5, 0, 10) = %v, want 5", got)
+	}
+	if got := ClampInt(-1, 0, 10); got != 0 {
+		t.Errorf("ClampInt(-1, 0, 10) = %v, want 0", got)
+	}
+	if got := ClampInt(15, 0, 10); got != 10 {
+		t.Errorf("ClampInt(15, 0, 10) = %v, want 10", got)
+	}
+}
+
+func TestMinMaxScale(t *testing.T) {
+	tests := []struct {
+		name       string
+		v, min, max float64
+		want       float64
+	}{
+		{"mid", 5, 0, 10, 0.5},
+		{"at_min", 0, 0, 10, 0},
+		{"at_max", 10, 0, 10, 1},
+		{"equal_range", 5, 5, 5, 0},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			got := MinMaxScale(tt.v, tt.min, tt.max)
+			if math.Abs(got-tt.want) > 1e-9 {
+				t.Errorf("MinMaxScale(%v, %v, %v) = %v, want %v", tt.v, tt.min, tt.max, got, tt.want)
+			}
+		})
+	}
+}

score.go

@@ -0,0 +1,40 @@
+package poindexter
+
+// Factor is a value–weight pair for composite scoring.
+type Factor struct {
+	Value  float64
+	Weight float64
+}
+
+// WeightedScore computes the weighted sum of factors.
+// Each factor contributes Value * Weight to the total.
+// Returns 0 for empty slices.
+func WeightedScore(factors []Factor) float64 {
+	var total float64
+	for _, f := range factors {
+		total += f.Value * f.Weight
+	}
+	return total
+}
+
+// Ratio returns part/whole safely. Returns 0 if whole is 0.
+func Ratio(part, whole float64) float64 {
+	if whole == 0 {
+		return 0
+	}
+	return part / whole
+}
+
+// Delta returns the difference new_ - old.
+func Delta(old, new_ float64) float64 {
+	return new_ - old
+}
+
+// DeltaPercent returns the percentage change from old to new_.
+// Returns 0 if old is 0.
+func DeltaPercent(old, new_ float64) float64 {
+	if old == 0 {
+		return 0
+	}
+	return (new_ - old) / old * 100
+}

score_test.go

@@ -0,0 +1,86 @@
+package poindexter
+
+import (
+	"math"
+	"testing"
+)
+
+func TestWeightedScore(t *testing.T) {
+	tests := []struct {
+		name    string
+		factors []Factor
+		want    float64
+	}{
+		{"empty", nil, 0},
+		{"single", []Factor{{Value: 5, Weight: 2}}, 10},
+		{"multiple", []Factor{
+			{Value: 3, Weight: 2},  // 6
+			{Value: 1, Weight: -5}, // -5
+		}, 1},
+		{"lek_heuristic", []Factor{
+			{Value: 2, Weight: 2},   // engagement × 2
+			{Value: 1, Weight: 3},   // creative × 3
+			{Value: 1, Weight: 1.5}, // first person × 1.5
+			{Value: 3, Weight: -5},  // compliance × -5
+		}, -6.5},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			got := WeightedScore(tt.factors)
+			if math.Abs(got-tt.want) > 1e-9 {
+				t.Errorf("WeightedScore = %v, want %v", got, tt.want)
+			}
+		})
+	}
+}
+
+func TestRatio(t *testing.T) {
+	tests := []struct {
+		name        string
+		part, whole float64
+		want        float64
+	}{
+		{"half", 5, 10, 0.5},
+		{"full", 10, 10, 1},
+		{"zero_whole", 5, 0, 0},
+		{"zero_part", 0, 10, 0},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			got := Ratio(tt.part, tt.whole)
+			if math.Abs(got-tt.want) > 1e-9 {
+				t.Errorf("Ratio(%v, %v) = %v, want %v", tt.part, tt.whole, got, tt.want)
+			}
+		})
+	}
+}
+
+func TestDelta(t *testing.T) {
+	if got := Delta(10, 15); got != 5 {
+		t.Errorf("Delta(10, 15) = %v, want 5", got)
+	}
+	if got := Delta(15, 10); got != -5 {
+		t.Errorf("Delta(15, 10) = %v, want -5", got)
+	}
+}
+
+func TestDeltaPercent(t *testing.T) {
+	tests := []struct {
+		name      string
+		old, new_ float64
+		want      float64
+	}{
+		{"increase", 100, 150, 50},
+		{"decrease", 100, 75, -25},
+		{"zero_old", 0, 10, 0},
+		{"no_change", 50, 50, 0},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			got := DeltaPercent(tt.old, tt.new_)
+			if math.Abs(got-tt.want) > 1e-9 {
+				t.Errorf("DeltaPercent(%v, %v) = %v, want %v", tt.old, tt.new_, got, tt.want)
+			}
+		})
+	}
+}

signal.go

@@ -0,0 +1,57 @@
+package poindexter
+
+import (
+	"math"
+	"math/rand"
+)
+
+// RampUp returns a linear ramp from 0 to 1 over the given duration.
+// The result is clamped to [0, 1].
+func RampUp(elapsed, duration float64) float64 {
+	if duration <= 0 {
+		return 1
+	}
+	return Clamp(elapsed/duration, 0, 1)
+}
+
+// SineWave returns a sine value with the given period and amplitude.
+// Output range is [-amplitude, amplitude].
+func SineWave(t, period, amplitude float64) float64 {
+	if period == 0 {
+		return 0
+	}
+	return math.Sin(t/period*2*math.Pi) * amplitude
+}
+
+// Oscillate modulates a base value with a sine wave.
+// Returns base * (1 + sin(t/period*2π) * amplitude).
+func Oscillate(base, t, period, amplitude float64) float64 {
+	if period == 0 {
+		return base
+	}
+	return base * (1 + math.Sin(t/period*2*math.Pi)*amplitude)
+}
+
+// Noise generates seeded pseudo-random values.
+type Noise struct {
+	rng *rand.Rand
+}
+
+// NewNoise creates a seeded noise generator.
+func NewNoise(seed int64) *Noise {
+	return &Noise{rng: rand.New(rand.NewSource(seed))}
+}
+
+// Float64 returns a random value in [-variance, variance].
+func (n *Noise) Float64(variance float64) float64 {
+	return (n.rng.Float64() - 0.5) * 2 * variance
+}
+
+// Int returns a random integer in [0, max).
+// Returns 0 if max <= 0.
+func (n *Noise) Int(max int) int {
+	if max <= 0 {
+		return 0
+	}
+	return n.rng.Intn(max)
+}

signal_test.go

@@ -0,0 +1,103 @@
+package poindexter
+
+import (
+	"math"
+	"testing"
+)
+
+func TestRampUp(t *testing.T) {
+	tests := []struct {
+		name             string
+		elapsed, duration float64
+		want             float64
+	}{
+		{"start", 0, 30, 0},
+		{"mid", 15, 30, 0.5},
+		{"end", 30, 30, 1},
+		{"over", 60, 30, 1},
+		{"negative", -5, 30, 0},
+		{"zero_duration", 10, 0, 1},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			got := RampUp(tt.elapsed, tt.duration)
+			if math.Abs(got-tt.want) > 1e-9 {
+				t.Errorf("RampUp(%v, %v) = %v, want %v", tt.elapsed, tt.duration, got, tt.want)
+			}
+		})
+	}
+}
+
+func TestSineWave(t *testing.T) {
+	// At t=0, sin(0) = 0
+	if got := SineWave(0, 10, 5); math.Abs(got) > 1e-9 {
+		t.Errorf("SineWave(0, 10, 5) = %v, want 0", got)
+	}
+	// At t=period/4, sin(π/2) = 1, so result = amplitude
+	got := SineWave(2.5, 10, 5)
+	if math.Abs(got-5) > 1e-9 {
+		t.Errorf("SineWave(2.5, 10, 5) = %v, want 5", got)
+	}
+	// Zero period returns 0
+	if got := SineWave(5, 0, 5); got != 0 {
+		t.Errorf("SineWave(5, 0, 5) = %v, want 0", got)
+	}
+}
+
+func TestOscillate(t *testing.T) {
+	// At t=0, sin(0)=0, so result = base * (1 + 0) = base
+	got := Oscillate(100, 0, 10, 0.05)
+	if math.Abs(got-100) > 1e-9 {
+		t.Errorf("Oscillate(100, 0, 10, 0.05) = %v, want 100", got)
+	}
+	// At t=period/4, sin=1, so result = base * (1 + amplitude)
+	got = Oscillate(100, 2.5, 10, 0.05)
+	if math.Abs(got-105) > 1e-9 {
+		t.Errorf("Oscillate(100, 2.5, 10, 0.05) = %v, want 105", got)
+	}
+	// Zero period returns base
+	if got := Oscillate(100, 5, 0, 0.05); got != 100 {
+		t.Errorf("Oscillate(100, 5, 0, 0.05) = %v, want 100", got)
+	}
+}
+
+func TestNoise(t *testing.T) {
+	n := NewNoise(42)
+
+	// Float64 should be within [-variance, variance]
+	for i := 0; i < 1000; i++ {
+		v := n.Float64(0.1)
+		if v < -0.1 || v > 0.1 {
+			t.Fatalf("Float64(0.1) = %v, outside [-0.1, 0.1]", v)
+		}
+	}
+
+	// Int should be within [0, max)
+	n2 := NewNoise(42)
+	for i := 0; i < 1000; i++ {
+		v := n2.Int(10)
+		if v < 0 || v >= 10 {
+			t.Fatalf("Int(10) = %v, outside [0, 10)", v)
+		}
+	}
+
+	// Int with zero max returns 0
+	if got := n.Int(0); got != 0 {
+		t.Errorf("Int(0) = %v, want 0", got)
+	}
+	if got := n.Int(-1); got != 0 {
+		t.Errorf("Int(-1) = %v, want 0", got)
+	}
+}
+
+func TestNoiseDeterministic(t *testing.T) {
+	n1 := NewNoise(123)
+	n2 := NewNoise(123)
+	for i := 0; i < 100; i++ {
+		a := n1.Float64(1.0)
+		b := n2.Float64(1.0)
+		if a != b {
+			t.Fatalf("iteration %d: different values for same seed: %v != %v", i, a, b)
+		}
+	}
+}

stats.go

@@ -0,0 +1,63 @@
+package poindexter
+
+import "math"
+
+// Sum returns the sum of all values. Returns 0 for empty slices.
+func Sum(data []float64) float64 {
+	var s float64
+	for _, v := range data {
+		s += v
+	}
+	return s
+}
+
+// Mean returns the arithmetic mean. Returns 0 for empty slices.
+func Mean(data []float64) float64 {
+	if len(data) == 0 {
+		return 0
+	}
+	return Sum(data) / float64(len(data))
+}
+
+// Variance returns the population variance. Returns 0 for empty slices.
+func Variance(data []float64) float64 {
+	if len(data) == 0 {
+		return 0
+	}
+	m := Mean(data)
+	var ss float64
+	for _, v := range data {
+		d := v - m
+		ss += d * d
+	}
+	return ss / float64(len(data))
+}
+
+// StdDev returns the population standard deviation.
+func StdDev(data []float64) float64 {
+	return math.Sqrt(Variance(data))
+}
+
+// MinMax returns the minimum and maximum values.
+// Returns (0, 0) for empty slices.
+func MinMax(data []float64) (min, max float64) {
+	if len(data) == 0 {
+		return 0, 0
+	}
+	min, max = data[0], data[0]
+	for _, v := range data[1:] {
+		if v < min {
+			min = v
+		}
+		if v > max {
+			max = v
+		}
+	}
+	return min, max
+}
+
+// IsUnderrepresented returns true if val is below threshold fraction of avg.
+// For example, IsUnderrepresented(3, 10, 0.5) returns true because 3 < 10*0.5.
+func IsUnderrepresented(val, avg, threshold float64) bool {
+	return val < avg*threshold
+}

stats_test.go

@@ -0,0 +1,122 @@
+package poindexter
+
+import (
+	"math"
+	"testing"
+)
+
+func TestSum(t *testing.T) {
+	tests := []struct {
+		name string
+		data []float64
+		want float64
+	}{
+		{"empty", nil, 0},
+		{"single", []float64{5}, 5},
+		{"multiple", []float64{1, 2, 3, 4, 5}, 15},
+		{"negative", []float64{-1, -2, 3}, 0},
+		{"floats", []float64{0.1, 0.2, 0.3}, 0.6},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			got := Sum(tt.data)
+			if math.Abs(got-tt.want) > 1e-9 {
+				t.Errorf("Sum(%v) = %v, want %v", tt.data, got, tt.want)
+			}
+		})
+	}
+}
+
+func TestMean(t *testing.T) {
+	tests := []struct {
+		name string
+		data []float64
+		want float64
+	}{
+		{"empty", nil, 0},
+		{"single", []float64{5}, 5},
+		{"multiple", []float64{2, 4, 6}, 4},
+		{"floats", []float64{1.5, 2.5}, 2},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			got := Mean(tt.data)
+			if math.Abs(got-tt.want) > 1e-9 {
+				t.Errorf("Mean(%v) = %v, want %v", tt.data, got, tt.want)
+			}
+		})
+	}
+}
+
+func TestVariance(t *testing.T) {
+	tests := []struct {
+		name string
+		data []float64
+		want float64
+	}{
+		{"empty", nil, 0},
+		{"constant", []float64{5, 5, 5}, 0},
+		{"simple", []float64{2, 4, 4, 4, 5, 5, 7, 9}, 4},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			got := Variance(tt.data)
+			if math.Abs(got-tt.want) > 1e-9 {
+				t.Errorf("Variance(%v) = %v, want %v", tt.data, got, tt.want)
+			}
+		})
+	}
+}
+
+func TestStdDev(t *testing.T) {
+	got := StdDev([]float64{2, 4, 4, 4, 5, 5, 7, 9})
+	if math.Abs(got-2) > 1e-9 {
+		t.Errorf("StdDev = %v, want 2", got)
+	}
+}
+
+func TestMinMax(t *testing.T) {
+	tests := []struct {
+		name    string
+		data    []float64
+		wantMin float64
+		wantMax float64
+	}{
+		{"empty", nil, 0, 0},
+		{"single", []float64{3}, 3, 3},
+		{"ordered", []float64{1, 2, 3}, 1, 3},
+		{"reversed", []float64{3, 2, 1}, 1, 3},
+		{"negative", []float64{-5, 0, 5}, -5, 5},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			gotMin, gotMax := MinMax(tt.data)
+			if gotMin != tt.wantMin || gotMax != tt.wantMax {
+				t.Errorf("MinMax(%v) = (%v, %v), want (%v, %v)", tt.data, gotMin, gotMax, tt.wantMin, tt.wantMax)
+			}
+		})
+	}
+}
+
+func TestIsUnderrepresented(t *testing.T) {
+	tests := []struct {
+		name      string
+		val       float64
+		avg       float64
+		threshold float64
+		want      bool
+	}{
+		{"below", 3, 10, 0.5, true},
+		{"at", 5, 10, 0.5, false},
+		{"above", 7, 10, 0.5, false},
+		{"zero_avg", 0, 0, 0.5, false},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			got := IsUnderrepresented(tt.val, tt.avg, tt.threshold)
+			if got != tt.want {
+				t.Errorf("IsUnderrepresented(%v, %v, %v) = %v, want %v", tt.val, tt.avg, tt.threshold, got, tt.want)
+			}
+		})
+	}
+}