#!/usr/bin/env perl
use strict;
use warnings;
use feature 'say';
use Data::Printer;

my %hash = (
    alpha1 => [
        { beta => { gamma => 'theta', delta => 'lambda', } },
        { beta => { gamma => 'zeta', } },
    ],
    alpha2 => [
        { beta => { gamma => 'theta', delta => 'lambda', } },
    ],
);

say "## Original state:";
check_duplication();

push @{ $hash{alpha2} }, { beta => { gamma => 'theta', } };

say "## After pushing another element onto 'alpha2':";
check_duplication();

sub check_duplication {
    for ( keys %hash ) {
        if ( scalar @{ $hash{$_} } > 1 ) {
            say "$_ has a duplicate.";
        }
        else {
            say "$_ is unique.";
        }
    }
}

p %hash;