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t/1......# Test 3 got: "0.814723691903055" (t/1.t at line 13)
#   Expected: "873847195.017769552"
...
# Test 4 got: "0.135477004107088" (t/1.t at line 14)
#   Expected: "2307073947.03889426"
[snip]

Adding a debugging printf to the C here:

...
and running

$ perl -MMath::Random::MT -e "Math::Random::MT->new(1)" > out

sub mt_init_seed {
    my ($self, $seed) = @_;
...
and running

perl -MMath::Random::MT::Perl -e "Math::Random::MT::Perl->new(1)" > ou
+tp

init 1: 1812433254
init 2: 3713160357
...
init 621: 1473334647
init 622: 2386671612
init 623: 2069268389