# Version-bound scoped review record

Model: GPT-6 (Codex; exact runtime variant not exposed)
Date: 2026-10-17
Reviewer role: same Codex agent preparing this publication; not independent peer review.
Main-file SHA-256: f02ce29f4b79672a3b23bc88c7d29279ef1316bddd2c8bff355b2e239cafc0ca

## Task instruction (verbatim user message)

> author: eggtea      you can create the things that are missing include the experiment code  I accept

## Review scope set by the preparing agent

Review the supplied work to prepare truthful MathHub metadata, concise takeaways and verification. Inspect the source statements and evidence actually available, preserve assumptions and provenance, and disclose unperformed checks. No separate model/referee was invoked. This record contains the complete scoped review response below; it does not purport to reconstruct a historical review dialogue.

## Complete review response

I read abstract.tex, main_results.tex, variance_lower_bound.tex, appendix_proofs.tex, experiment instructions and the polynomial-gain experiment implementation. This is a new review by the same Codex agent preparing the package, not an independent referee report.

1. Convergence: cocoercivity and strong convexity give contraction when eta<=1/L. Young's inequality gives the displayed conditional recursion with 3 eta/mu times ||b_t||^2. The comparison constants 4D sigma^2/mu and 12B/mu^2 agree with the scalar recurrence. Summability of eta_t E||b_t||^2 and eta_t^2 justifies the stated almost-supermartingale use.
2. PR reduction: a_t=O(t^{-alpha}+t^{-beta}) yields a negligible averaged Hessian remainder for alpha,beta>1/2. Abel boundary terms require beta>2alpha-1. The shift from xi_{t+1} to xi_t contributes only endpoint terms divided by sqrt(T). Deterministic weights preserve independence across the joint-innovation triangular array. The finite-second-moment, maximal-weight and bounded covariance argument supports Lindeberg, including singular covariance.
3. Covariance: the cross terms have orientations C_0 K^T and K C_0^T. A remainder small only in probability gives distributional negligibility but does not imply its covariance vanishes; the manuscript correctly qualifies that identification by L2 convergence. The beta classification uses only second moments, not all CLT assumptions.
4. Examples: the running-average identities sum_s k=T and sum_s k^2=2T-h_T agree by finite-sum exchange. The fixed-c integrals give 1 and 2c/(2c-1); the coefficient c^2/(2c-1) instead controls single-step error. Limits are for fixed c as T tends to infinity, not a uniform c,T interchange.
5. Lower bound: row normalization implies sum_s k=T. Expanding sum_s(k-1)^2 proves the finite-T PSD identity; Q!=0 makes flatness necessary by taking traces. It is restricted to the stated normalized scalar deterministic historical class and zero cross-covariance for the downstream comparison.
6. Attainment: gamma_1=1 ensures exact row normalization. The scalar variance recurrence gives O(t^{-rho}). The Abel identity with d_t=gamma_t^{-1}-1 bounds the normalized cumulative discrepancy by O(T^{(rho-1)/2}) in L2, giving flatness O(T^{rho-1}); this also bounds the maximal normalized weight. The remaining PR restriction is rho>2alpha-1. The experiment uses t^{-rho}, whose first gain is one, consistent with initialization.
7. The finite arithmetic checks recorded in checks.json were actually executed. They support algebraic identities and implementations of deterministic weights, not an asymptotic proof. Full Monte Carlo experiments, LaTeX compilation, literature-priority checks and formal verification were not run. No major gap was identified in the mathematical arguments inspected; this is not certification of correctness or independent peer review.

## Existing evidence and limitations


The original mathematical text is unchanged. Authorship and CC-BY-4.0 release were authorized in the current conversation. Existing historical review attribution is recorded as supplied, not independently authenticated. No full experiment reproduction, formal verification, or new external-source audit is claimed.