Authenticator

Recreate the "Authenticator" screen in React Native using LumioUI.

Goal: Two-factor codes with the current one shown large above a draining timer bar. When the code rolls over, the new digits light up one by one, and a tap confirms it was copied while your app does the copying. Match the reference implementation's layout, behavior, and motion exactly — this is a production screen, not a mockup.

## Setup

Fastest path — install the screen plus its component deps:

```bash
npx @lumioui/cli add pro/core-authenticator
```

Or pull just the components: `npx @lumioui/cli add icon search-input text`

Native packages:
- react-native-reanimated@*
- react-native-safe-area-context@*
- react-native-svg@*

Stack assumptions: Expo SDK 54 / RN 0.81, Reanimated 4, NativeWind v4, TypeScript strict, Expo Go compatible.

## Components — how, where, when

### `icon` — Icon set drawn on one consistent grid, sized and coloured from your theme. The heart, star and bookmark can fill in place inside their outline, then fade back out.
- `<Icon>` ×4

### `search-input` — Search field with a clear button and a busy indicator while results load. Focus brightens the field, matching text in results can be highlighted, and a frosted glass style is included.
- `<SearchInput>` ×1

### `text` — Themed type scale from caption to display that follows light and dark mode. Includes a pull-quote style with an accent rule and a quieter dimmed tone for secondary text.
- `<Text>` ×14

## Conventions (non-negotiable)

- Styling via NativeWind `className` with semantic tokens only: `bg-background`, `text-foreground`, `bg-card`, `text-card-foreground`, `bg-secondary`, `bg-muted`, `text-muted-foreground`, `bg-accent`, `bg-destructive`, `border-border`. Hard-coded colors only inside media overlays (`text-white`, `bg-black/N`).
- Motion via the token presets from `@lumioui/core` (`spring.press`, `spring.surface`, `spring.glide`, `timing.fast`, `timing.slow`, …) — no bespoke spring configs or durations.
- Gate transform motion behind `useReducedMotion()`; keep opacity/color feedback, drop travel and overshoot.
- Haptics via `useHaptic()`: `light` on press, `selection` on toggle/select, `warning` on invalid input. Never import expo-haptics directly.
- Press feedback via `usePressAnimation()` (~0.97 scale), not `activeOpacity` tricks.
- a11y: `accessibilityRole` + `accessibilityLabel` on every control, touch targets ≥44pt.
- Entrance choreography: staggered `Mount` wrappers (delay 0/60/120…) so regions land in sequence instead of popping in at once.
- Wrap the screen in `SafeAreaView`; keep dark mode working via the semantic tokens.

## Deliverable

One file: `screens/core/authenticator.tsx` exporting AuthenticatorScreen. Preserve the props interface — the host app wires the callbacks (navigation, submit handlers) through them.

## Reference implementation

This is a LumioUI Pro item: its source is not published in the docs. Install it with a Pro license key
(set `LUMIO_LICENSE_KEY`; keys are on lumioui.com/account) and read the installed file as the reference:

```bash
npx @lumioui/cli add pro/core-authenticator
```

The source lands at `screens/core/authenticator.tsx`.

Screen: https://lumioui.com/screens/core-authenticator