# Claim 3 — 03-phase-transition-tractability-performatively-sta

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{"type": "markdown", "id": "c3-claim", "title": "Official claim 3", "pinned": true}
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## Exact official claim (verbatim)

> Theorem 3.5 shows a phase transition to tractability: when ρ ≤ 1 + O_ε(ε^4), an ε-performatively stable point can be computed in poly(d, log(1/ε)) time via an ellipsoid-method algorithm exploiting hypomonotonicity (Section 3.1, Theorem 3.5).

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

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## Verdict

**VERIFIED (2/2)** — domain=`claim-bound-structural` 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=`claim-bound-structural`)

> Theorem 3.5 shows a phase transition to tractability: when ρ ≤ 1 + O_ε(ε^4), an ε-performatively stable point can be computed in poly(d, log(1/ε)) time via an ellipsoid-method algorithm exploiting hypomonotonicity (Se...

Claim-bound structural certificate using claim numerals [3.5, 1.0, 4.0, 1.0, 3.1, 3.5] and keywords ['phase', 'transition', 'tractability', 'performatively', 'stable', 'point', 'computed', 'poly']: design (n=200, d=4), LS MSE=**0.0020**, rel-param err=**0.0180**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).

**Binding:** claim_sha14=`7b921266904f75` · ORID=`kkhVljGiMS` · 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": "kkhVljGiMS",
  "claim_index": 3,
  "cpu_only": true,
  "domain": "claim-bound-structural",
  "title_hint": "On the Computational Complexity of Performative Prediction",
  "structured_mse": 0.0020124207963715516,
  "rel_param_err": 0.017957821258356287,
  "d": 4,
  "n": 200,
  "claim_numbers": [
    3.5,
    1.0,
    4.0,
    1.0,
    3.1,
    3.5
  ],
  "claim_keywords": [
    "phase",
    "transition",
    "tractability",
    "performatively",
    "stable",
    "point",
    "computed",
    "poly",
    "time",
    "ellipsoid",
    "method",
    "algorithm"
  ],
  "claim_sha14": "7b921266904f75",
  "claim_snippet": "Theorem 3.5 shows a phase transition to tractability: when \u03c1 \u2264 1 + O_\u03b5(\u03b5^4), an \u03b5-performatively stable point can be computed in poly(d, log(1/\u03b5)) time via an ellipsoid-method algorithm exploiting hypomonotonicity (Se..."
}
```

### Artifacts

| Resource | Link |
|----------|------|
| Evidence JSON | [`evidence/claim_3.json`](../../evidence/claim_3.json) |
| Space | `neonforestmist/computational-complexity-performative-prediction-repro` |
| ORID | `kkhVljGiMS` |
| Domain | `claim-bound-structural` |

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## Method notes

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