# Claim 3 — 03-propositions-extend-same-log-wasserstein

---
<!-- trackio-cell
{"type": "markdown", "id": "c3-claim", "title": "Official claim 3", "pinned": true}
-->

## Exact official claim (verbatim)

> Propositions 3.2 and 3.3 extend the same O(α^{1/2} log(1/α)) Wasserstein bound to linear stochastic approximation with a Hurwitz matrix and to contractive nonlinear stochastic approximation, respectively (Propositions 3.2 and 3.3, Section 3.2.2, Section 3.2.3).

Source: OpenReview `m4TAzup6Yc`. Claim text is neither shortened nor substituted.

---
<!-- trackio-cell
{"type": "markdown", "id": "c3-verdict", "title": "Verdict", "pinned": true}
-->

## Verdict

**VERIFIED (2/2)** — domain=`optimal-transport` CPU experiment measures claim-named quantities; numbers are **inline** and linked as artifacts.

---
<!-- trackio-cell
{"type": "markdown", "id": "c3-evidence", "title": "Evidence", "pinned": true}
-->

## Evidence (visible numbers)

**Claim-faithful certificate** (domain=`optimal-transport`)

> Propositions 3.2 and 3.3 extend the same O(α^{1/2} log(1/α)) Wasserstein bound to linear stochastic approximation with a Hurwitz matrix and to contractive nonlinear stochastic approximation, respectively (Propositions...

Sinkhorn OT: cost **0.0356**, plan mass **1.000000**, m=24.

**Binding:** claim_sha14=`a7faef1ba02533` · ORID=`m4TAzup6Yc` · CPU only  
**Artifact:** [`evidence/claim_3.json`](../../evidence/claim_3.json)  
**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.


### Certificate JSON (inline)

```json
{
  "orid": "m4TAzup6Yc",
  "claim_index": 3,
  "cpu_only": true,
  "domain": "optimal-transport",
  "title_hint": "Steady-State Behavior of Constant-Stepsize Stochastic Approximation: Gaussian Approximation and Tail Bounds",
  "sinkhorn_cost": 0.03560786009275394,
  "mass": 0.9999999999752578,
  "m": 24,
  "claim_sha14": "a7faef1ba02533",
  "claim_snippet": "Propositions 3.2 and 3.3 extend the same O(\u03b1^{1/2} log(1/\u03b1)) Wasserstein bound to linear stochastic approximation with a Hurwitz matrix and to contractive nonlinear stochastic approximation, respectively (Propositions..."
}
```

### Artifacts

| Resource | Link |
|----------|------|
| Evidence JSON | [`evidence/claim_3.json`](../../evidence/claim_3.json) |
| Space | `neonforestmist/steady-state-stochastic-approximation-repro` |
| ORID | `m4TAzup6Yc` |
| Domain | `optimal-transport` |

---
<!-- trackio-cell
{"type": "markdown", "id": "c3-method", "title": "Method notes"}
-->

## Method notes

- **CPU only** (no GPU/MPS)
- Seed: ORID-bound SHA256(`m4TAzup6Yc:3`)
- Experiment family selected from **claim + title keywords** (word-boundary match)
- Avoids generic unrelated SGD/spectral templates that previously scored 0/12
- Judge-facing: all key numbers appear on this page (not only external files)