# F-076 — Architect: Link to frontend product + archive separate listing

## Current state

Admin products listing (`/products`) shows all products (active, archived, draft) in one table. No link to the frontend product page. No way to filter by state.

## Goal

1. **Frontend link**: Add a column with an external link icon that opens the product on the frontend (`http://192.168.18.93:3003/productos/[slug]`). Only shown for `state === 'active'` products.
2. **Archive listing**: Add a status filter (Todos / Activos / Archivados) to separate active from archived products.

## Scope IN

- `project/apps/admin/src/app/(dashboard)/products/page.tsx`:
  - Add `statusFilter` state: `'all' | 'active' | 'archived'`
  - Add filter buttons (Todos / Activos / Archivados) below the search bar
  - Add a new column "Tienda" (Frontend) with an external link icon for active products only
  - Filter `products` by `p.state` when `statusFilter !== 'all'`
  - Update total count to reflect filtered products
  - Use external link URL: `http://192.168.18.93:3003/productos/[slug]`

## Scope OUT

- No backend changes
- No new pages (filter is inline in the same page)
- No change to the product editor

## Design

Status filter buttons:
```tsx
<div className="flex gap-2 mb-4">
  {(['all', 'active', 'archived'] as const).map(f => (
    <button key={f} onClick={() => setStatusFilter(f)}
      className={`px-3 py-1.5 rounded-lg text-xs font-medium ${
        statusFilter === f ? 'bg-[#2D6A4F] text-white' : 'bg-white border border-gray-300 text-gray-600 hover:bg-gray-50'
      }`}>
      {f === 'all' ? 'Todos' : f === 'active' ? 'Activos' : 'Archivados'}
    </button>
  ))}
</div>
```

Frontend link column:
```tsx
{p.state === 'active' ? (
  <a
    href={`http://192.168.18.93:3003/productos/${p.slug}`}
    target="_blank"
    rel="noopener noreferrer"
    title="Ver en la tienda"
    className="inline-flex items-center justify-center w-8 h-8 rounded-lg bg-green-50 text-green-600 hover:bg-green-100 transition-colors"
    onClick={e => e.stopPropagation()}
  >
    <svg className="w-4 h-4" fill="none" viewBox="0 0 24 24" stroke="currentColor">
      <path strokeLinecap="round" strokeLinejoin="round" strokeWidth={2} d="M10 6H6a2 2 0 00-2 2v10a2 2 0 002 2h10a2 2 0 002-2v-4M14 4h6m0 0v6m0-6L10 14" />
    </svg>
  </a>
) : (
  <span className="w-8 h-8" />
)}
```

## Risk

- **Low risk**: purely frontend UX changes, no backend or DB changes
- URL is hardcoded to local dev URL (acceptable for admin panel)

## Verification

- `npx tsc --noEmit` admin
- `npx eslint` on changed file
- `./scripts/verify.sh` green