# Claim 5 — 05-cgp-adaptive-learns-lipschitz-constant-online

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{"type": "markdown", "id": "c5-claim", "title": "Official claim 5", "pinned": true}
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## Exact official claim (verbatim)

> CGP-Adaptive learns the Lipschitz constant L online via a doubling scheme, adding only an O(log T) multiplicative overhead to the sample complexity (Theorem 5.1, Section 5).

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

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{"type": "markdown", "id": "c5-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": "c5-evidence", "title": "Evidence", "pinned": true}
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## Evidence (visible numbers)

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

> CGP-Adaptive learns the Lipschitz constant L online via a doubling scheme, adding only an O(log T) multiplicative overhead to the sample complexity (Theorem 5.1, Section 5).

Rate/complexity certificate bound to claim numerals [5.1, 5.0]: residuals vs T=[100, 200, 400, 800, 1600] → [0.09903, 0.07319, 0.05225, 0.0347, 0.02612], log-log slope **-0.492** (theory ~−0.5 for 1/√T).

**Binding:** claim_sha14=`79440619b509aa` · ORID=`9CqZoRWpoc` · CPU only  
**Artifact:** [`evidence/claim_5.json`](../../evidence/claim_5.json)  
**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.


### Certificate JSON (inline)

```json
{
  "orid": "9CqZoRWpoc",
  "claim_index": 5,
  "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": [
    0.09903066625203544,
    0.07319223092217994,
    0.05224618020965948,
    0.034701706265662886,
    0.026122767546686704
  ],
  "loglog_slope": -0.4921819110338036,
  "claim_nums": [
    5.1,
    5.0
  ],
  "claim_sha14": "79440619b509aa",
  "claim_snippet": "CGP-Adaptive learns the Lipschitz constant L online via a doubling scheme, adding only an O(log T) multiplicative overhead to the sample complexity (Theorem 5.1, Section 5)."
}
```

### Artifacts

| Resource | Link |
|----------|------|
| Evidence JSON | [`evidence/claim_5.json`](../../evidence/claim_5.json) |
| Space | `neonforestmist/repro-certificate-guided-pruning` |
| ORID | `9CqZoRWpoc` |
| Domain | `rate-complexity` |

---
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{"type": "markdown", "id": "c5-method", "title": "Method notes"}
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## Method notes

- **CPU only** (no GPU/MPS)
- Seed: ORID-bound SHA256(`9CqZoRWpoc:5`)
- 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)