feat(lead-gen): inline math captcha field

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

ui/src/components/lead-forms/MathCaptcha.tsx

@@ -0,0 +1,45 @@
+"use client";
+
+import { useEffect, useState } from "react";
+
+import { Input } from "@/components/ui/input";
+import { Label } from "@/components/ui/label";
+
+interface MathCaptchaProps {
+  // Called whenever validity changes, so the parent can enable/disable submit.
+  onValidChange: (valid: boolean) => void;
+  id?: string;
+}
+
+// Dead-simple anti-spam: "What is X + Y?". Generated client-side on mount.
+// Math.random is allowed in browser runtime (this is not a workflow script).
+export function MathCaptcha({ onValidChange, id = "math-captcha" }: MathCaptchaProps) {
+  const [a, setA] = useState(0);
+  const [b, setB] = useState(0);
+  const [answer, setAnswer] = useState("");
+
+  useEffect(() => {
+    setA(Math.floor(Math.random() * 8) + 1);
+    setB(Math.floor(Math.random() * 8) + 1);
+  }, []);
+
+  useEffect(() => {
+    onValidChange(answer.trim() !== "" && parseInt(answer, 10) === a + b);
+  }, [answer, a, b, onValidChange]);
+
+  return (
+    <div className="space-y-1.5">
+      <Label htmlFor={id}>
+        Quick check: what is {a} + {b}?
+      </Label>
+      <Input
+        id={id}
+        inputMode="numeric"
+        value={answer}
+        onChange={(e) => setAnswer(e.target.value)}
+        placeholder="Answer"
+        className="w-32"
+      />
+    </div>
+  );
+}