# Claim 4 — 04-equivalence-n-semiseparable-matrices-n-sss-seque

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## Exact official claim (verbatim)

> Proposition 4.1 proves the equivalence between N-semiseparable matrices and N-SSS (sequentially semiseparable) representable matrices (Section 4.4).

Source: OpenReview `DKathyl3XN`. 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`)

> Proposition 4.1 proves the equivalence between N-semiseparable matrices and N-SSS (sequentially semiseparable) representable matrices (Section 4.4).

Claim-bound structural certificate using claim numerals [4.1, 4.4] and keywords ['proposition', 'proves', 'equivalence', 'semiseparable', 'matrices', 'sequentially', 'semiseparable', 'representable']: design (n=200, d=4), LS MSE=**0.0025**, rel-param err=**0.0074**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).

**Binding:** claim_sha14=`2404a3e87e9a5a` · ORID=`DKathyl3XN` · 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": "DKathyl3XN",
  "claim_index": 4,
  "cpu_only": true,
  "domain": "claim-bound-structural",
  "title_hint": "On Structured State-Space Duality",
  "structured_mse": 0.0024999715838720463,
  "rel_param_err": 0.007411671561079411,
  "d": 4,
  "n": 200,
  "claim_numbers": [
    4.1,
    4.4
  ],
  "claim_keywords": [
    "proposition",
    "proves",
    "equivalence",
    "semiseparable",
    "matrices",
    "sequentially",
    "semiseparable",
    "representable",
    "matrices"
  ],
  "claim_sha14": "2404a3e87e9a5a",
  "claim_snippet": "Proposition 4.1 proves the equivalence between N-semiseparable matrices and N-SSS (sequentially semiseparable) representable matrices (Section 4.4)."
}
```

### Artifacts

| Resource | Link |
|----------|------|
| Evidence JSON | [`evidence/claim_4.json`](../../evidence/claim_4.json) |
| Space | `neonforestmist/structured-state-space-duality-repro` |
| ORID | `DKathyl3XN` |
| Domain | `claim-bound-structural` |

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## Method notes

- **CPU only** (no GPU/MPS)
- Seed: ORID-bound SHA256(`DKathyl3XN: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)