Temporal Memory in Repeating Fast Radio Bursts: Epsilon-Machine Reconstruction of Causal Structure in Burst Timing

The emission mechanism of fast radio bursts (FRBs) remains unknown. Whether the bursts from a repeating FRB arrive at random or in a structured sequence is a key constraint on that mechanism. We apply epsilon-machine reconstruction, a tool from computational mechanics that infers the minimal model capturing all predictive information in a stochastic process. Applied to the waiting-time sequences of three repeating FRBs (FRB 20121102A and FRB 20201124A from FAST; FRB 20220912A from CHIME), the method yields the statistical complexity C mu, the minimum number of bits required for optimal prediction. Both FAST sources carry roughly one bit of temporal memory (significant against permutation surrogates, p at most 0.01; per-source false-discovery-rate-adjusted p at most 0.028), while FRB 20220912A is consistent with memoryless emission. FRB 20201124A's memory spans hours-to-days across four sessions, FRB 20121102A's spans hours-to-weeks across thirty-nine, and neither source shows defensible within-session predictive memory. For FRB 20121102A the ordering of those sessions is itself predictive (session-shuffle p = 0.02), whereas FRB 20201124A's signal reflects the contrast between heterogeneous sessions rather than their order. A simulated windowing test shows that CHIME's short transit observations would suppress comparable structure in the FAST data, leaving FRB 20220912A's null result ambiguous. This first application of epsilon-machine reconstruction to astrophysical transients yields a model-independent constraint: the bursting of at least two of these repeaters is not memoryless, but is governed by a hidden state that occupies distinct activity-rate regimes varying across observing sessions, behaviour that any viable physical model must reproduce.