# FINAL_REVIEW — adversarial referee audit (Phase 11)

Three simulated review perspectives were applied to the manuscript and code. Each objection records (a) location, (b) correction made, (c) new proof/test if any, (d) residual limitation. Unresolved items are listed candidly at the end with the verdict.

# Referee A — theoretical econometrician

A1. "The centered random remainder of the jackknife is dropped in the prior draft's higher-order corollary." (a) Prior draft Cor. 6.1; paper §4.2, Lemma 4. (b) Lemma 3–4 bound the remainder with the explicit constant A_r = Σ|w_j|s_j and carry it through Theorem 1; the proof shows it never binds for q ≥ 1 and binds only via K = o(N) for q = 0. (c) tests/test_estimators.py::test_pilot_bias_orders_exponential; symbolic S8. (d) none.

A2. "Uniformity along the triangular array: Assumption A1 must hold with a common constant for every sub-block size; is that realistic?" (a) §3.3, ASSUMPTIONS.md. (b) The assumption is stated for the sub-sample family with n ≥ n₀ and a common C; it is verified exactly in the exponential model (C = 33θ0²/2, n₀ = 3, App. B) and discussed as implied by standard primitive conditions. (c) symbolic S2. (d) Primitive conditions for general models are cited (ZDW/HH-type moment conditions + validity of the formal expansion, Bhattacharya–Ghosh) but not re-derived; stated as such in §3.3.

A3. "Bias cancellation of expected coefficients does not give an L2 statement." (a) §4.2. (b) Lemma 2 (mean) and Lemma 3 (L2) are separate; Lemma 5 combines them. (d) none.

A4. "Constants may diverge with p or with the order r." (a) §3.3 remark, §11. (b) Stated explicitly: fixed p only; A_r and κ(V) tabulated (Table 2) and the conditioning discussion in §4.3. (d) No growing-p theorem; said so.

A5. "Is K = o(N^α) interpreted as a machine count?" (b) §5.2 and the remark after Assumption 4: triangular-array statement, not a fixed-N machine limit; Theorem 2(vi) shows what happens at and beyond the boundary. (d) none.

A6. "Necessity: the sharpness is for one model and one estimator family." (a) §6. (b) Stated in §6 and §11; Volgushev et al. cited as the template; exact pooling counterexample given. (d) No worst-case construction over a model class for general likelihoods (as Volgushev et al. do for QR); left open.

A7. "Coverage claims require a consistent variance estimator; the point-estimator result is not enough." (b) Corollary 1 states the requirement and the extra p(p+1)/2 upload for the sandwich; Monte Carlo coverage uses the observed information at the estimate, and the misspecified design compares Fisher vs sandwich at the centralized estimate. (d) Sandwich-based coverage of the distributed estimators themselves is only computed at the centralized point in the current driver (se_sand_central); noted in the Monte Carlo section.

A8. "The boundary regime m ≍ N^{1/8} is unreachable; the −4θ0c⁴ limit is of theoretical interest only." (b) Agreed and stated in §6 and in the boundary table; a finite-m prediction (exact bias + remainder variance) is reported and matches the Monte Carlo to three digits (Table boundary). (d) The (3,1) boundary (m ≍ N^{1/24}) is not approached at any feasible N; reported, not hidden.

A9. "Theorem 3(a) needs third derivatives; the stale-Hessian exponent is conditional on A4." (b) A4 stated; the proof is explicit about where it is used. (d) A4's fourth-moment block condition is assumed, not derived from primitives.

# Referee B — statistical optimization specialist

B1. "Huang–Huo already prove the one-step estimator; what is new?" (a) §2, Table 1. (b) HH19's stated regime is k = O(√N) from the plain average; their k⁴N⁻⁴ term implies 3/4 (not stated by them); the jackknife start and the joint frontier (7/8, 11/12, general α(r,q)) are not in HH19; said explicitly in §1 ("What is not claimed") and §2. (d) none.

B2. "Zhu–Li–Wang's TWLSE reaches 3/4 with one local step; CEASE gives a rounds frontier; Gu–Chen reach 2/3 with analytic debiasing." (b) All cited at theorem level (Table 1); Theorem 3(b) recovers CEASE's (t+1)/(t+2) and JLY's 2/3 exactly, which is presented as a consistency check rather than a new result. (d) none.

B3. "Why nested doubling splits? Dhaene–Jochmans show {2,3,…} is bias-optimal." (b) §4.3 and Table 2 compare (1,2,3) and (1,2,4): smaller |β₃| (6 vs 8) but larger A₃ (12 vs 8) and a coarser finest block; the ablation evaluates both patterns numerically (Table abl). (d) No optimality theorem for patterns; the choice is empirical.

B4. "Split-sample corrections have twice the higher-order variance of delete-one (Hahn et al. 2024)." (b) Cited in §2 and §11; exact Var J₂ in the exponential model shows the cost is O(m⁻³) there; Monte Carlo RMSE tables show the finite-sample ranking reversals. (d) No general higher-order variance expansion for the nested construction.

B5. "Newton steps are undamped; production code needs safeguards; the basin result shows divergence with positive probability." (b) Theorem 2(iv) and the failure gallery; the library solves linear systems (no inverse), flags singular curvature, and the Monte Carlo reports failed replications rather than discarding them; a damped variant is not analysed (said in §6). (d) The theory is for the undamped map only.

B6. "CSL baseline: is the implementation faithful?" (b) The full surrogate maximization (not only the quadratic step) is implemented with Newton on machine 1 and the exact global gradient; in the exponential model the surrogate maximizer equals the centralized MLE exactly (proved in the test), which is reported as a property of that model, not as a weakness of CSL. (d) CSL's proximal/regularized variants (CEASE) are not implemented; stated.

B7. "Quantization: relative rounding of Hessian entries is not a realistic compression scheme." (b) Theorem 3(c) is stated for relative precision ε on every transmitted entry, which upper-bounds any scheme with that relative accuracy; the ablation implements exactly that. (d) Lattice/stochastic quantizers (Alimisis et al.) are not analysed.

B8. "The cost model is not a theorem." (b) Proposition 5 is labelled conditional on the cost model; §9 says so. (d) none.

# Referee C — distributed-systems / reproducibility specialist

(to be completed after the benchmark runs; see the "Benchmarks" entry in PHASE_STATUS.md)

C1. "In-memory partitions are not a cluster." (b) §10 only reports runs of the TCP coordinator–worker protocol on physical hosts; Monte Carlo sections state that they are in-memory (no communication measured). C2. "Two communication phases are not one message." (b) §3.2 counts phases, messages, numbers and bytes separately (Table 2); measured bytes include headers. C3. "Stragglers, start-up and scheduler delay." (b) The protocol logs per-worker fit/derivative times and p50/p90/p99 reply latencies; benchmark tables report the slowest worker and latency percentiles. C4. "K partitions ≠ K hosts." (b) Designs include 16 workers on 1, 2, 4, 8, 16 hosts and 64/128 workers on 16 hosts. C5. "Raw-data reproducibility." (b) Every raw file has a manifest (git commit, versions, host, SHA-256); EXPERIMENT_MANIFEST.csv; seeds derived from a hash of the cell description; the prior draft's numbers are reproduced by a test.

# Formal audit checklist

# Verdict

(filled at delivery)

spb/wp28_uqo