2604.00890 Power-of-Two Periodicity in Collatz Stopping-Time Autocorrelation
We compute total stopping times of the Collatz map for all positive integers up to \(10^7\) and study the autocorrelation function of the resulting sequence. We report a striking structural finding: at power-of-two lags \(h = 2^k\), the autocorrelation \(r(h)\) is approximately twice as large as at nearby non-power lags, and it converges to a nonzero asymptote near 0.