Hi! Thanks for this amazing library.

While reproducing the example notebook AustralianPrisonPopulation.ipynb, I noticed the comment:
"Since the hierarchy structure is not strict, we can't use methods such as TopDown or MiddleOut."

This raises a couple of questions:

1. Why is that? Is there a mathematical reason preventing their use? I’d particularly appreciate a conceptual clarification on this point.
2. Surprisingly, TopDown(method="forecast_proportions") can be used in the example. Why is forecast_proportions compatible with non-strict hierarchical structures, while average_proportions and proportion_averages are not?
3. Additionally, none of the three MiddleOut proportions variants seem to work. However, if TopDown method with forecast_proportions is allowed, why isn’t MiddleOut with forecast_proportions also supported?

Here’s the list of reconcilers I tested using the same dataset from the AustralianPrisonPopulation example notebook:

reconcilers = [
    # Used in the example notebook
    BottomUp(),    
    MinTrace(method='mint_shrink'), 
    
    # Added by me for testing
    TopDown(method="forecast_proportions"), # Works
    
    # The following raise ValueError: "Top-down reconciliation requires strictly hierarchical structures."
    # TopDown(method="average_proportions"),  
    # TopDown(method="proportion_averages"),  
    
    # The following raise ValueError: "Middle out reconciliation requires strictly hierarchical structures."
    # MiddleOut(middle_level="Country/Legal", top_down_method="forecast_proportions"),  
    # MiddleOut(middle_level="Country/Legal", top_down_method="average_proportions"),  
    # MiddleOut(middle_level="Country/Legal", top_down_method="proportion_averages"),  
]

I’d really appreciate any clarification on this!
Thanks in advance.