Well, the Manhattan project is a good example of something that remained secret from the public for far longer than any formula would predict, given the gigantic amount of people involved (though of course other state actors knew about it long before).

I guess it depends on your definition of "remained secret from the public". For example, Kodak figured it out pretty quickly after the first tests because the radiation particles in the atmosphere were carried from the Southwest US to their factories in Rochester, NY, and affected their film production.

The details of the Teller-Ulam design are still quite secret despite being known to several hundred people for 50+ years.

If that calculation was completely wrong, how would anyone know? We never get a perfect snapshot of the world to compare with.

What that stat really says is any conspiracy involving 10+ people, if the details manages to stay secret for 20 years, will likely never come to light.

With the US at least, it can probably be loosely tested by comparing declassified records (50 years on) with program size at the time.

This is Grimes' "On the Viability of Conspiratorial Beliefs" (https://doi.org/10.1371/journal.pone.0147905).

Bummer I was excited for a scholarly paper by Claire Boucher.