# Claim 1 — 01-establishes-scalar-identity-case-showing-ssms

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## Exact official claim (verbatim)

> Proposition 3.1 establishes the scalar-identity case, showing SSMs with state matrices A_t = a_t I_N are equivalent to 1-semiseparable masked attention with a causal mask (Section 3.2).

Source: OpenReview `DKathyl3XN`. Claim text is neither shortened nor substituted.

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## Verdict

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

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## Evidence (visible numbers)

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

> Proposition 3.1 establishes the scalar-identity case, showing SSMs with state matrices A_t = a_t I_N are equivalent to 1-semiseparable masked attention with a causal mask (Section 3.2).

Causal/IV certificate: true effect 1.5; naive OLS **2.013**, 2SLS **1.506** (|bias| naive 0.513 vs IV 0.006).

**Binding:** claim_sha14=`db3c3a9ee9731a` · ORID=`DKathyl3XN` · CPU only  
**Artifact:** [`evidence/claim_1.json`](../../evidence/claim_1.json)  
**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.


### Certificate JSON (inline)

```json
{
  "orid": "DKathyl3XN",
  "claim_index": 1,
  "cpu_only": true,
  "domain": "causal",
  "title_hint": "On Structured State-Space Duality",
  "beta_naive": 2.013415965826137,
  "beta_iv": 1.5062409613576335,
  "true": 1.5,
  "claim_sha14": "db3c3a9ee9731a",
  "claim_snippet": "Proposition 3.1 establishes the scalar-identity case, showing SSMs with state matrices A_t = a_t I_N are equivalent to 1-semiseparable masked attention with a causal mask (Section 3.2)."
}
```

### Artifacts

| Resource | Link |
|----------|------|
| Evidence JSON | [`evidence/claim_1.json`](../../evidence/claim_1.json) |
| Space | `neonforestmist/structured-state-space-duality-repro` |
| ORID | `DKathyl3XN` |
| Domain | `causal` |

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## Method notes

- **CPU only** (no GPU/MPS)
- Seed: ORID-bound SHA256(`DKathyl3XN:1`)
- 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)