```python
from typing import List, Dict

def cheapest_pass_plan(trip_days: List[int], passes: List[Dict[str, int]]) -> Dict[str, int]:
    if not trip_days or not passes:
        return {'total': 0, 'purchases': []}
    
    # Validate inputs
    for day in trip_days:
        if not isinstance(day, int) or day <= 0:
            raise ValueError("Trip days must be strictly increasing positive integers.")
    
    for pass_info in passes:
        span = pass_info.get('span', 0)
        cost = pass_info.get('cost', 0)
        
        if not isinstance(span, int) or span <= 0:
            raise ValueError("Pass spans must be positive integers.")
        if not isinstance(cost, int) or cost < 0:
            raise ValueError("Pass costs must be non-negative integers.")
    
    # Sort passes by cost and then by span
    passes.sort(key=lambda x: (x['cost'], x['span']))
    
    total_cost = 0
    purchases = []
    covered_days = set()
    
    for day in trip_days:
        if day in covered_days:
            continue
        
        cheapest_pass = None
        min_cost = float('inf')
        
        for pass_info in passes:
            start_day = pass_info['start']
            span = pass_info['span']
            
            # Check if the current day is within the pass's coverage
            if start_day <= day < start_day + span:
                cost = pass_info['cost']
                
                # Find the cheapest pass that covers the current day
                if cost < min_cost:
                    min_cost = cost
                    cheapest_pass = pass_info
        
        if cheapest_pass is None:
            raise ValueError("No pass can cover the trip day.")
        
        total_cost += min_cost
        purchases.append([cheapest_pass['start'], cheapest_pass['span']])
        covered_days.update(range(cheapest_pass['start'], cheapest_pass['start'] + cheapest_pass['span']))
    
    return {'total': total_cost, 'purchases': purchases}
```