Have you paid attention to this part of the manual page:

BUGS
       1.  Adding or altering substructures to a hash value is
           not entirely transparent in current perl.  If you want
           to store a reference or modify an existing reference
           value in the DBM, it must first be retrieved and
           stored in a temporary variable for further modifica­
           tions.  In particular, something like this will NOT
           work properly:

                   $mldb{key}{subkey}[3] = 'stuff';        # won't wor
+k

           Instead, that must be written as:

                   $tmp = $mldb{key};                      # retrieve 
+value
                   $tmp->{subkey}[3] = 'stuff';
                   $mldb{key} = $tmp;                      # store val
+ue

           This limitation exists because the perl TIEHASH inter­
           face currently has no support for multidimensional
           ties.
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Abigail