# Audit plan: Gradient Flow Sampler-based Distributionally Robust Optimization

- OpenReview: `QRtzkKrbJi`
- arXiv: `2510.25956`
- Intended Space: `ProCreations/repro-gradient-flow-sampler-based-distributionally-robust-optimization`
- Literal registry source: arXiv v1. The current revision changes the outer-loop
  rate from `O(epsilon_opt^-2)` to `O(epsilon_opt^-4)` and the WGF total
  complexity from `epsilon_opt^-4` to `epsilon_opt^-6`; it is a drift control,
  not evidence for the registered v1 claims.

## Evidence design

1. Pin v1/current PDF and source archives and verify six exact live claim
   anchors in the complete v1 source.
2. Inventory the six concrete gradient-flow/DRO algorithms directly from the
   v1 labels and captions.
3. Reproduce Proposition 1's logarithmic flow-time threshold exactly on a
   Gaussian Wasserstein gradient flow across many `(lambda, L, epsilon)`
   settings, with an early-stop destructive control.
4. Audit Theorem 1 and Theorem 2 by evaluating their explicit rate laws across
   grids of tolerances, dimensions, and smoothness/LSI constants. These finite
   identities do not replace the universal v1 proofs.
5. Reconstruct the half-bridge Gibbs conditional on discrete supports and
   verify the fixed marginal, normalization, KKT residual, and worst-case
   mixture identity.
6. Preserve the three primary CIFAR-10 PGD figures and the exact source
   statement that WFR/WGF remain robust across the reported settings. This is
   source-reported evidence; no smaller synthetic run will be mislabeled as a
   CIFAR/ResNet reproduction.
7. Run two isolated warning-strict executions, require byte-identical outputs,
   package one replay, build a recursive SHA-256 manifest, run the official
   validator, and test every static route before publication.

## Fail-closed scope

The v1/current theory drift is material and must remain visible. Claim 5 is
supported by the pinned primary experiment figures and source discussion, not
by invented numeric curve extraction. The Gaussian and discrete calculations
are exact mechanism audits and are not substitutes for the source's universal
theorems or CIFAR experiment.