```python
from typing import List, Dict

def cheapest_pass_plan(trip_days: List[int], passes: List[Dict[str, int]]) -> Dict:
    if not trip_days or not passes:
        return {'total': 0, 'purchases': []}

    # Check for valid trips
    for day in trip_days:
        if not isinstance(day, int) or day <= 0:
            raise ValueError("Trip days must be positive integers.")

    # Sort pass kinds by span and then cost
    passes.sort(key=lambda x: (x['span'], x['cost']))

    total_cost = 0
    purchases = []
    trip_index = 0

    for i, pass_kind in enumerate(passes):
        span = pass_kind['span']
        cost = pass_kind['cost']

        # Find the cheapest way to cover remaining trips starting from trip_index
        while trip_index < len(trip_days) and total_cost + cost * (trip_days[trip_index] - trip_days[i]) >= 0:
            total_cost += cost * (trip_days[trip_index] - trip_days[i])
            purchases.append([trip_days[i], span])
            trip_index += span

    return {'total': total_cost, 'purchases': purchases}
```