There is no need to be excessively verbose when expounding on the subject at hand. It helps if you get the syntax right in your example code too.

for my $number (@{$arrays->{$array_name}}) { 
    $result->{$number}{$array_name} = 1;
}
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The @{...} is required to dereference the array reference which is the hash value. Without the dereference syntax @array is assigned (or the loop iterates over) a single element which is the reference to the array.