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 $\varepsilon$-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, $p \leq 0.01$; per-source false-discovery-rate-adjusted $p \leq 0.028$), 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 $\varepsilon$-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.