feat: add captcha verification to contact form

Added math-based captcha system to prevent spam on the contact form:
- Created captcha API endpoint with simple arithmetic questions
- Added captcha UI component with refresh functionality
- Integrated captcha verification into contact form submission
- Relaxed spam filters since captcha provides better protection

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

lib/captcha.ts

@@ -0,0 +1,93 @@
+import { randomInt } from 'crypto'
+
+interface CaptchaChallenge {
+  answer: number
+  expires: number
+}
+
+// Simple in-memory store for captcha challenges
+const captchaStore = new Map<string, CaptchaChallenge>()
+
+// Clean up expired captchas every 5 minutes
+setInterval(() => {
+  const now = Date.now()
+  for (const [key, value] of captchaStore.entries()) {
+    if (value.expires < now) {
+      captchaStore.delete(key)
+    }
+  }
+}, 5 * 60 * 1000)
+
+function generateCaptchaId(): string {
+  return `captcha_${Date.now()}_${randomInt(10000, 99999)}`
+}
+
+export interface CaptchaData {
+  captchaId: string
+  question: string
+}
+
+export function generateCaptcha(): CaptchaData {
+  // Generate simple math problem
+  const num1 = randomInt(1, 20)
+  const num2 = randomInt(1, 20)
+  const operations = ['+', '-', '×'] as const
+  const operation = operations[randomInt(0, operations.length)]
+
+  let answer: number
+  let question: string
+
+  switch (operation) {
+    case '+':
+      answer = num1 + num2
+      question = `${num1} + ${num2}`
+      break
+    case '-':
+      // Ensure positive result
+      const larger = Math.max(num1, num2)
+      const smaller = Math.min(num1, num2)
+      answer = larger - smaller
+      question = `${larger} - ${smaller}`
+      break
+    case '×':
+      // Use smaller numbers for multiplication
+      const small1 = randomInt(2, 10)
+      const small2 = randomInt(2, 10)
+      answer = small1 * small2
+      question = `${small1} × ${small2}`
+      break
+  }
+
+  const captchaId = generateCaptchaId()
+
+  // Store captcha with 10 minute expiration
+  captchaStore.set(captchaId, {
+    answer,
+    expires: Date.now() + 10 * 60 * 1000
+  })
+
+  return {
+    captchaId,
+    question
+  }
+}
+
+export function verifyCaptcha(captchaId: string, answer: string | number): boolean {
+  const stored = captchaStore.get(captchaId)
+
+  if (!stored) {
+    return false
+  }
+
+  if (stored.expires < Date.now()) {
+    captchaStore.delete(captchaId)
+    return false
+  }
+
+  const isValid = parseInt(answer.toString()) === stored.answer
+
+  // Delete captcha after verification (one-time use)
+  captchaStore.delete(captchaId)
+
+  return isValid
+}