Magnifying Dock Bar

Build a "Magnifying Dock Bar" React component.

CONCEPT: A floating bottom navigation dock inspired by desktop docks but in a flat, editorial style. Icons grow according to the pointer's horizontal distance.

LAYOUT & CONTENT:
- Dock: cream pill with 1px charcoal border, hard 3px shadow. Six items: Home, Search, Inbox, Calendar, Bookmark, Settings (lucide icons).
- Each icon sits in a 40px square tile; tiles alternate cream and paper-2; the active one is cobalt.

INTERACTIONS & MOTION:
- Track mouseX on the dock (useMotionValue, Infinity when outside). For each tile compute distance to tile center; width = useTransform(distance, [-120, 0, 120], [40, 64, 40]) then useSpring mass 0.1 stiffness 170 damping 12.
- Tooltip label appears above hovered tile with y 6 → 0 and opacity.
- Click sets active with a small bounce (y [0,-8,0]).

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".