Ink Underline Contact Form

Build a "Ink Underline Contact Form" React component.

CONCEPT: A letter-style contact form with three fields (name, email, message). Labels float on focus or when filled, and a cobalt underline draws across under the focused field.

LAYOUT & CONTENT:
- Fields sit on 1px charcoal baselines, no boxes. Labels in small grotesk; floating state shrinks to 10px mono uppercase.
- Submit: charcoal pill 'Send letter' with arrow. Success replaces the form with 'Thank you. We reply within a day.' in italic serif.

INTERACTIONS & MOTION:
- Label: animate y (0 → -18) and scale (1 → 0.8) when focused or non-empty, spring stiffness 500 damping 35.
- Underline: absolutely positioned 2px cobalt line scaleX 0 → 1 origin-left on focus.
- Submit: on click the arrow translates x 40 and fades, then form crossfades to success state (AnimatePresence mode='wait'). Validate email with a simple regex and shake the field (x keyframes [0,-6,6,-4,4,0]) if invalid.

DESIGN SYSTEM (non-negotiable):
- Palette: paper background #FAF9F6, deep charcoal #121212 for text and 1px borders, ONE warm accent: cobalt #1D4ED8 or terracotta #D9534F. Secondary surface #F2EFE8.
- Typography: Swiss / editorial. A tight grotesk for UI (Instrument Sans, Inter Tight or similar) with negative tracking on display sizes; an italic serif (Instrument Serif) used sparingly for one emphasized word.
- NO dark-mode neon, NO glow, NO glassmorphism, NO backdrop blur, NO purple-to-blue gradients, NO emoji icons. Solid fills, hairline rules, honest shadows (hard offset or none).
- Motion: Framer Motion with spring physics (type: "spring", stiffness 300-500, damping 20-35). Animate transform and opacity only. Respect prefers-reduced-motion via useReducedMotion().
- Icons: lucide-react, 1.5px stroke.
- Accessibility: real <button>/<a>/<label> elements, visible focus ring (2px cobalt, 3px offset), keyboard operable, aria attributes where state changes.

OUTPUT: one self-contained React component file (Tailwind CSS v4 utility classes, framer-motion, lucide-react), no external images, default export, ready to paste into a Next.js App Router page with "use client".