They basically are, the algorithm is something like:
At the beginning of january and july, observe the difference between UT1 and UTC. If the difference is >= 0.6s, a leap second will be inserted at the end of june/december. Publish the results here: https://hpiers.obspm.fr/eoppc/bul/bulc
This is true. They look at how much the earth spun, and whether it was more or less than 86400 seconds/day average. This can't be done without external data. It's not a pure mathematical algorithm.
At the beginning of january and july, observe the difference between UT1 and UTC. If the difference is >= 0.6s, a leap second will be inserted at the end of june/december. Publish the results here: https://hpiers.obspm.fr/eoppc/bul/bulc