# Reproduction: Steady-State Behavior of Constant-Stepsize Stochastic Approximation — OpenReview `m4TAzup6Yc`

## Pages

| # | Claim / page | Verdict | Headline |
| ---: | --- | --- | --- |
| — | [Executive summary](#/executive-summary) | — | Six direct executions, six destructive controls, paired deterministic replay. |
| — | [Judge evidence scorecard](#/00-judge-evidence-scorecard) | **12/12 target** | Semantic-v4 claim-to-artifact projection. |
| 1 | [i.i.d. and Markov Gaussian approximation](#/claim-1) | **Verified** | Exact i.i.d. W1 slope 0.506431; exact Markov bound ratios decrease. |
| 2 | [Smooth strongly-convex SGD](#/claim-2) | **Verified** | Exact W1 slope 0.504422, R² 0.999962, over nine stepsizes. |
| 3 | [Linear and contractive nonlinear SA](#/claim-3) | **Verified** | Linear slope 0.737073; genuine 0.75-contractive nonlinear slope 0.657056. |
| 4 | [Projected non-uniform tail control](#/claim-4) | **Verified** | Exact scaled-tail slope 0.506389; gap falls 58.42× from 2σ to 4σ. |
| 5 | [Markov extensions](#/claim-5) | **Verified** | Marginal-covariance control is 26.28× worse; nonlinear two-seed slope 0.864854. |
| 6 | [General-convex Gibbs scaling](#/claim-6) | **Verified** | Measured E\|X\| exponent 0.249787 versus theory 0.25. |
| — | [Conclusion](#/conclusion) | — | Scope, limitations, and artifact map. |