All words are made up words.

And how many people doing "science" do code review, computer-aided proofs, or automated theorem proving to verify their code is correct? Very, very, very few.

This. In theory it’s open, but in reality, people just want to get this work done mostly.

Also, if something is that important, people can and do perform the same calculations using different packages or different algorithms.

Write two algorithms in MMA, or one in MMA and one in something else, and every so often spot check a few cases by hand.