ניתוח חד-מינימלי של תוצאות סופר-לוגיסטי

תקציר מקורי באנגליתarXiv:2608.26515v2 Announce Type: replace-cross Abstract: We determine the minimax cumulative log-loss regret of a finite-alphabet, exogenously driven source with genuinely infinite input memory: independent Rademacher inputs $(U_t)$ are observed sequentially and the next binary mark has logit $\sum_{j\ge1}\theta_jU_{t+1-j}$, the unknown coefficients obeying a summable envelope $|\theta_j|\le r_j$, $\sum_jr_j\le B$. At horizon $T$, lag $j$ can move the logit by at most $r_j$ and is exercised in only $n_{T,j}=(T-j+1)_+$ rounds, and the two limitations combine into the sum $\Gamma_T(r)=\sum_{j\le T}\log(1+n_{T,j}r_j^{2})$. One coordinate-localised Bayesian mixture achieves $R_T(r)\le C\Gamma_T(r)$ for \emph{every} summable envelope with $C$ universal. Our main result is a matching nonasympto