Sure, you’re right if your filter is absolutely reliable, you can skip entire ranges like 444... that violate the rule, which does save a lot of computation.
But remember, this only works if you’re certain the filter will always hold true for any future puzzle. Otherwise, you risk missing possible solutions.
I also stated the same theory in previous posts, but it was useless and not accepted by users.
It's not a theory, it's just basic logic, if a whole range violates a strict filter, it can be skipped, no need to generate or check those keys at all.
People who reject this are just ignoring the fundamentals. Filtering entire subranges is standard practice, not some controversial idea.
So why does everyone take sides on this rule and consider it useless at the very beginning of the discussion in the forum, causing the discussion to be fruitless and not continue its process?