I am auditing a long public series of categorical draws with 19 symbols (coded 0–18). Draws occur about every 5 minutes. This is a methodological question about randomness quality / hypothesis comparison — not a request to analyze raw data for me, and not gambling advice. Observed structure in the history: In a daytime window (roughly 07:38–19:59 local), the empirical rate of immediate repeats (X_t = X_{t-1}) is essentially ~0%. Overnight, the repeat rate is about ~5%, closer to the independent Uniform{0,…,18} baseline of 1/19. Symbol "0" appears about ~10% less often than 1/19 across the day. Competing explanations: Mostly uniform draws, plus a daytime-only anti-repetition filter (reject/resample when equal to previous). A single biased or Markovian generator whose transition structure differs by time of day. Questions: What formal comparisons (likelihood ratio, Bayes factor, nested models, simulation-based tests) are appropriate to separate (1) vs (2) on a categorical series? For an alphabet of size 19, which dependence diagnostics are most useful beyond marginal chi-square — e.g. serial/runs tests on indicators, lagged mutual information, spectral checks for period, or battery tests (TestU01 / PractRand) after a stated encoding? How should one correct for multiple testing when scanning many time windows for a day/night change-point? I can provide anonymized contingency tables / summary counts if that helps the answer stay concrete. I am not asking anyone to recover a seed…

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