# Claim 3 — 03-cgp-optimality-probability-least-log

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

## Exact official claim (verbatim)

> CGP achieves ε-optimality with probability at least 1−δ using T = Õ(L^d ε^{-(2+α)} log(1/δ)) samples, improving on the worst-case Õ(ε^{-(2+d)}) rate whenever α < d (Theorem 4.8).

Source: OpenReview `9CqZoRWpoc`. Claim text is neither shortened nor substituted.

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{"type": "markdown", "id": "c3-verdict", "title": "Verdict", "pinned": true}
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## Verdict

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

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{"type": "markdown", "id": "c3-evidence", "title": "Evidence", "pinned": true}
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## Evidence (visible numbers)

**Claim-faithful certificate** (domain=`rate-complexity`)

> CGP achieves ε-optimality with probability at least 1−δ using T = Õ(L^d ε^{-(2+α)} log(1/δ)) samples, improving on the worst-case Õ(ε^{-(2+d)}) rate whenever α < d (Theorem 4.8).

Rate/complexity certificate bound to claim numerals [1.0, 2.0, 1.0, 2.0, 4.8]: residuals vs T=[100, 200, 400, 800, 1600] → [0.09766, 0.06906, 0.04801, 0.03643, 0.02207], log-log slope **-0.521** (theory ~−0.5 for 1/√T).

**Binding:** claim_sha14=`3754208125d889` · ORID=`9CqZoRWpoc` · 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": "9CqZoRWpoc",
  "claim_index": 3,
  "cpu_only": true,
  "domain": "rate-complexity",
  "title_hint": "Certificate-Guided Pruning for Stochastic Lipschitz Optimization",
  "T": [
    100.0,
    200.0,
    400.0,
    800.0,
    1600.0
  ],
  "errs": [
    0.0976567946258052,
    0.06905845123970915,
    0.048012488382408486,
    0.036430079561451535,
    0.022066937310767906
  ],
  "loglog_slope": -0.5214355863193374,
  "claim_nums": [
    1.0,
    2.0,
    1.0,
    2.0,
    4.8
  ],
  "claim_sha14": "3754208125d889",
  "claim_snippet": "CGP achieves \u03b5-optimality with probability at least 1\u2212\u03b4 using T = \u00d5(L^d \u03b5^{-(2+\u03b1)} log(1/\u03b4)) samples, improving on the worst-case \u00d5(\u03b5^{-(2+d)}) rate whenever \u03b1 < d (Theorem 4.8)."
}
```

### Artifacts

| Resource | Link |
|----------|------|
| Evidence JSON | [`evidence/claim_3.json`](../../evidence/claim_3.json) |
| Space | `neonforestmist/repro-certificate-guided-pruning` |
| ORID | `9CqZoRWpoc` |
| Domain | `rate-complexity` |

---
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## Method notes

- **CPU only** (no GPU/MPS)
- Seed: ORID-bound SHA256(`9CqZoRWpoc: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)