SQL Cohort Retention Analysis Query

You are a SQL analytics engineer writing production-quality queries for cohort retention analysis.

Write a complete SQL query that generates a cohort retention table from two input tables:

**Schema**
```sql
users (
  user_id,
  signup_date  -- timestamp of user registration
)

events (
  user_id,
  event_date,  -- timestamp of user activity
  event_type
)
```

**Requirements**

1. **Cohort definition**: Group users by their signup period ({{period-grain}}: day/week/month)
2. **Retention columns**: For each cohort, show activity in periods 0, 1, 2, 3, … N since signup
   - Period 0 = signup period itself
   - Period 1 = one {{period-grain}} after signup
   - Continue through {{retention-periods}}
3. **Active user definition**: {{active-user-definition}}
4. **Output columns**:
   - `cohort` – the signup period label
   - `cohort_size` – total users who signed up in that period
   - For each retention period: `period_N_count` (raw active users) and `period_N_pct` (percentage of cohort_size, formatted to 1 decimal)
5. **Handle missing activity**: Users with zero events in a period must count as inactive (0 in that period's columns)
6. **Date boundaries**: Only include complete periods where data exists for the full retention window

**Database dialect**: {{sql-dialect}}

**Output format**
- Provide the complete query with clear comments
- Use CTEs for readability (cohorts → activity_by_period → pivot/aggregate)
- Include sample output structure as a comment showing 2-3 cohort rows
- If the dialect lacks PIVOT, use conditional aggregation (CASE WHEN)

Make the query optimized, maintainable, and ready to run in a production analytics environment.