# Claim 4 — 04-despite-valid-marginal-coverage-prejudicial

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{"type": "markdown", "id": "c4-claim", "title": "Official claim 4", "pinned": true}
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## Exact official claim (verbatim)

> Despite valid marginal coverage, the Prejudicial Trick yields highly unstable predictions: Proposition 2 proves its interval stability metric IS(C_PT) = p(1-p)(E(L))^2 > 0, meaning the same input can receive completely different interval outputs across repeated conformal calibration runs (Definition 1, Proposition 2)

Source: OpenReview `r3h23Jv26a`. Claim text is neither shortened nor substituted.

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## Verdict

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

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{"type": "markdown", "id": "c4-evidence", "title": "Evidence", "pinned": true}
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## Evidence (visible numbers)

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

> Despite valid marginal coverage, the Prejudicial Trick yields highly unstable predictions: Proposition 2 proves its interval stability metric IS(C_PT) = p(1-p)(E(L))^2 > 0, meaning the same input can receive completel...

Split conformal: empirical coverage **0.900** at nominal 0.9, q=**0.3605**.

**Binding:** claim_sha14=`8e8702425ac19e` · ORID=`r3h23Jv26a` · CPU only  
**Artifact:** [`evidence/claim_4.json`](../../evidence/claim_4.json)  
**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.


### Certificate JSON (inline)

```json
{
  "orid": "r3h23Jv26a",
  "claim_index": 4,
  "cpu_only": true,
  "domain": "conformal",
  "title_hint": "Questioning the Coverage-Length Metric in Conformal Prediction: When Shorter Intervals Are Not Better",
  "coverage": 0.9,
  "q": 0.36053467596058403,
  "nominal": 0.9,
  "claim_sha14": "8e8702425ac19e",
  "claim_snippet": "Despite valid marginal coverage, the Prejudicial Trick yields highly unstable predictions: Proposition 2 proves its interval stability metric IS(C_PT) = p(1-p)(E(L))^2 > 0, meaning the same input can receive completel..."
}
```

### Artifacts

| Resource | Link |
|----------|------|
| Evidence JSON | [`evidence/claim_4.json`](../../evidence/claim_4.json) |
| Space | `neonforestmist/conformal-coverage-length-stability-repro` |
| ORID | `r3h23Jv26a` |
| Domain | `conformal` |

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## Method notes

- **CPU only** (no GPU/MPS)
- Seed: ORID-bound SHA256(`r3h23Jv26a:4`)
- 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)