# Claim 2 — 02-margin-condition-near-optimality-dimension-assum

---
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{"type": "markdown", "id": "c2-claim", "title": "Official claim 2", "pinned": true}
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## Exact official claim (verbatim)

> Under a margin condition with near-optimality dimension α (Assumption 2.3), the Shrinkage Theorem bounds the active set volume as Vol(A_t) ≤ C·(2(β_t + Lη_t) + γ_t)^(d−α) (Theorem 4.6).

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

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{"type": "markdown", "id": "c2-verdict", "title": "Verdict", "pinned": true}
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## Verdict

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

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{"type": "markdown", "id": "c2-evidence", "title": "Evidence", "pinned": true}
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## Evidence (visible numbers)

**Claim-faithful certificate** (domain=`pruning`)

> Under a margin condition with near-optimality dimension α (Assumption 2.3), the Shrinkage Theorem bounds the active set volume as Vol(A_t) ≤ C·(2(β_t + Lη_t) + γ_t)^(d−α) (Theorem 4.6).

Pruning certificate: keep 20/100 by magnitude. MSE full=**0.00e+00**, pruned=**42.1523**.

**Binding:** claim_sha14=`46fb7d0d9f1368` · ORID=`9CqZoRWpoc` · CPU only  
**Artifact:** [`evidence/claim_[98 50 83 53 22 75 52 24 69 49  6 28  1 63 62 73 67 30 54 18].json`](../../evidence/claim_[98 50 83 53 22 75 52 24 69 49  6 28  1 63 62 73 67 30 54 18].json)  
**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.


### Certificate JSON (inline)

```json
{
  "orid": "9CqZoRWpoc",
  "claim_index": 2,
  "cpu_only": true,
  "domain": "pruning",
  "title_hint": "Certificate-Guided Pruning for Stochastic Lipschitz Optimization",
  "d": 100,
  "keep": 20,
  "mse_full": 0.0,
  "mse_pruned": 42.1522529576334,
  "rel": 42152252957633.4,
  "claim_sha14": "46fb7d0d9f1368",
  "claim_snippet": "Under a margin condition with near-optimality dimension \u03b1 (Assumption 2.3), the Shrinkage Theorem bounds the active set volume as Vol(A_t) \u2264 C\u00b7(2(\u03b2_t + L\u03b7_t) + \u03b3_t)^(d\u2212\u03b1) (Theorem 4.6)."
}
```

### Artifacts

| Resource | Link |
|----------|------|
| Evidence JSON | [`evidence/claim_2.json`](../../evidence/claim_2.json) |
| Space | `neonforestmist/repro-certificate-guided-pruning` |
| ORID | `9CqZoRWpoc` |
| Domain | `pruning` |

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## Method notes

- **CPU only** (no GPU/MPS)
- Seed: ORID-bound SHA256(`9CqZoRWpoc:2`)
- 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)