ronk wrote: My hope is/was to derive a proof that a MUG is always a deadly pattern as long as it is generated from a valid BUG-Lite. The generation method is to overlay all permutations of clue values for the BUG-Lite as shown earlier. Then pattern-by-pattern proofs of MUGs being deadly would not be required. The pattern I chose was just a starting point.

That conjecture seems to be eminently sensible. Here's a stab at a generalised proof:

In a BUG the pattern makes locked set in every house it covers which is what isolates it from the rest of the puzzle. This ensures that no single pattern candidate has a unique link to an external cell. When the various permutations of a BUG-Lite are overlaid therefore this property is preserved, but some houses will no longer contain locked sets.

Now each one of those 'unlocked' houses has a capacity for holding external instances of member digits, but when that capacity is exhausted the pattern cells will return to being locked sets. Repeating this for every unlocked house will inevitably restore the pattern to a completely locked state.

In this process it isn't necessary to consider any limitations on which particular combinations of member digits can be held in external cells or where they are located as at the end the reduced pattern will either be impossible or have two solutions.

All we need to find is any counter-examples to tell us if any additional provisos are needed.