1\section{Discussion and limitations}\label{sec:discussion}23\paragraph{What is known and what is new.} The local correction is the generalized jackknife, the global correction is the distributed one-step estimator, and the idea of debiasing before averaging has analytic, delete-one and subsampling versions in the literature (\cref{sec:lit}). The joint frontier of \cref{thm:frontier}, its sharpness in \cref{thm:exponential} and the inexact-curvature frontier with the bit requirement of \cref{thm:inexact} are the new statements; the Monte Carlo and the measured benchmarks are new evidence. We have found no prior statement of the exponents $7/8$ or $11/12$, of a frontier indexed by both $r$ and $q$, or of a sharpness result for a bias-corrected construction, but we have not been able to check every unpublished thesis (the replication package lists the sources that could not be read in full).45\paragraph{Fixed dimension.} All exponents are for fixed $p$. The constants $C$, $C_b$, $M_N$, $\Lambda_N$ in \cref{ass:lin,ass:bias,ass:newton} depend on $p$, the Hessian payload grows as $p^2$, and the number of observations in the finest sub-block is $m/s_r$, so that for $p$ comparable to $m/s_r$ the local MLEs fail to exist with non-negligible probability (\cref{sec:mc}, $p = 20$). The results do not transfer to $p_N \to \infty$ without a new analysis of how every constant scales, and we make no claim in that direction.67\paragraph{Finite samples versus exponents.} The frontier orders estimators by the exponent of the bias term alone. At moderate $m$ the centered random remainder, whose constant grows with $\Amp$, and the alternating signs of $\betar$ make the order-$3$ pilot worse than the order-$2$ pilot in RMSE for all but the smallest $m$ in our designs, and the one-step versions inherit part of this ranking. Doubling the local order to save a round is therefore not free statistically, in addition to its computational price; the higher-order variance results of \citet{hahn2024efficient} describe the same phenomenon for split-sample corrections of cross-section MLEs.89\paragraph{Adaptive order.} Choosing $r$ from the data (for instance by comparing successive pilots) changes the estimator, and nothing in \cref{thm:frontier} covers a data-dependent $r$. Sample splitting or a selection event with uniform bounds would be needed to restore a theorem; we leave this open and do not report an adaptive estimator.1011\paragraph{Asynchrony, failures and stragglers.} The theorems describe synchronized phases: every worker's derivatives are evaluated at the same broadcast point. Asynchronous or stale-iterate updates change the estimator and inherit no guarantee from the present analysis; worker failures were handled in the benchmarks by waiting, not by dropping workers, and the theory for dropped blocks is that of \citet[Corollary~3.7]{huang2019distributed} rather than ours.1213\paragraph{Lower bounds.} Nothing here is a minimax or communication lower bound. In exponential families the pooled sufficient statistic recovers $\thetaN$ exactly in one round of $\dim(T)$ numbers per worker, and the exponential model shows that the full surrogate-likelihood maximization is also exact there. The sharpness in \cref{thm:exponential} concerns the estimator family $\{\iter{r}{q}\}$, not all distributed procedures.1415\paragraph{Benchmarks.} Measured times are specific to one cluster, one implementation (Python/NumPy over TCP with pickle framing) and the designs run. They calibrate \eqref{eq:cost} and show which side of \eqref{eq:rule} the designs fall on; they do not establish a general speed advantage of any protocol, and we report no energy or monetary cost because none was measured.16