PCG64
PCG64 (Permuted Congruential Generator, 64-bit output) is a family of pseudo-random number generators that produce statistically excellent, fast, and reproducible random sequences from a given seed.
The math
state_{n+1} = state_n × multiplier + increment (mod 2^128)The 64-bit output is produced by applying a "permutation" function to the 128-bit internal state, giving much better statistical quality than raw LCG output.
Why it matters
Pancake bootstrap and permutation tests both use NumPy's default_rng(), which uses PCG64 internally. This means that given the same seed, the identical 10,000 resamples are generated on Ubuntu, macOS, and Windows — producing byte-identical CIs across runs and across machines. O'Neill (2014) describes the full PCG family; the Harvey Mudd technical report is freely available.
PCG64 is a pseudo-random generator, not a true random one — given the same seed it is perfectly deterministic. This is a feature for reproducibility but means Pancake bootstrap CIs are not "statistically independent" if the seed is guessable. The seed for each run is derived from the result_hash (see batter), making seed prediction negligible in practice.