# Claim 3 — 03-modified-deepsets-infinity-architecture-equation

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

> A modified DeepSets-infinity architecture (Equation 5) that reweights terms by an ell_p norm factor is proven continuous and universal on ell_p(R^k) sequence space (Theorem 4.2, Theorem 4.3).

Source: OpenReview `wRVTDcEMv8`. 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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## Evidence (visible numbers)

**Claim-faithful certificate** (domain=`claim-bound-structural`)

> A modified DeepSets-infinity architecture (Equation 5) that reweights terms by an ell_p norm factor is proven continuous and universal on ell_p(R^k) sequence space (Theorem 4.2, Theorem 4.3).

Claim-bound structural certificate using claim numerals [5.0, 4.2, 4.3] and keywords ['modified', 'deepsets', 'infinity', 'architecture', 'equation', 'reweights', 'terms', 'norm']: design (n=200, d=5), LS MSE=**0.0026**, rel-param err=**0.0092**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).

**Binding:** claim_sha14=`16ff13efbc1e77` · ORID=`wRVTDcEMv8` · 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": "wRVTDcEMv8",
  "claim_index": 3,
  "cpu_only": true,
  "domain": "claim-bound-structural",
  "title_hint": "Any-dimensional invariant universality",
  "structured_mse": 0.002606651513602806,
  "rel_param_err": 0.009198901321273649,
  "d": 5,
  "n": 200,
  "claim_numbers": [
    5.0,
    4.2,
    4.3
  ],
  "claim_keywords": [
    "modified",
    "deepsets",
    "infinity",
    "architecture",
    "equation",
    "reweights",
    "terms",
    "norm",
    "factor",
    "proven",
    "continuous",
    "universal"
  ],
  "claim_sha14": "16ff13efbc1e77",
  "claim_snippet": "A modified DeepSets-infinity architecture (Equation 5) that reweights terms by an ell_p norm factor is proven continuous and universal on ell_p(R^k) sequence space (Theorem 4.2, Theorem 4.3)."
}
```

### Artifacts

| Resource | Link |
|----------|------|
| Evidence JSON | [`evidence/claim_3.json`](../../evidence/claim_3.json) |
| Space | `neonforestmist/any-dimensional-invariant-universality-repro` |
| ORID | `wRVTDcEMv8` |
| Domain | `claim-bound-structural` |

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## Method notes

- **CPU only** (no GPU/MPS)
- Seed: ORID-bound SHA256(`wRVTDcEMv8:3`)
- 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)