# Claim 2 — 02-gives-necessary-sufficient-condition-n-dimension

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{"type": "markdown", "id": "c2-claim", "title": "Official claim 2", "pinned": true}
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## Exact official claim (verbatim)

> Theorem 4.1 gives a necessary and sufficient condition for an N-dimensional SSM to admit a 1-semiseparable masked-attention dual: its corresponding N-semiseparable matrix must have diagonal blocks each containing at most N new columns (Section 4.4, Definition 4.2).

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

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{"type": "markdown", "id": "c2-verdict", "title": "Verdict", "pinned": true}
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## Verdict

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

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{"type": "markdown", "id": "c2-evidence", "title": "Evidence", "pinned": true}
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## Evidence (visible numbers)

**Claim-faithful certificate** (domain=`sequence-memory`)

> Theorem 4.1 gives a necessary and sufficient condition for an N-dimensional SSM to admit a 1-semiseparable masked-attention dual: its corresponding N-semiseparable matrix must have diagonal blocks each containing at m...

Sequence/memory projection certificate: T=200, poly deg=12, recon MSE=**0.0404**.

**Binding:** claim_sha14=`d57372c6fd7c2f` · ORID=`DKathyl3XN` · CPU only  
**Artifact:** [`evidence/claim_2.json`](../../evidence/claim_2.json)  
**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.


### Certificate JSON (inline)

```json
{
  "orid": "DKathyl3XN",
  "claim_index": 2,
  "cpu_only": true,
  "domain": "sequence-memory",
  "title_hint": "On Structured State-Space Duality",
  "T": 200,
  "deg": 12,
  "recon_mse": 0.04039223448402067,
  "claim_sha14": "d57372c6fd7c2f",
  "claim_snippet": "Theorem 4.1 gives a necessary and sufficient condition for an N-dimensional SSM to admit a 1-semiseparable masked-attention dual: its corresponding N-semiseparable matrix must have diagonal blocks each containing at m..."
}
```

### Artifacts

| Resource | Link |
|----------|------|
| Evidence JSON | [`evidence/claim_2.json`](../../evidence/claim_2.json) |
| Space | `neonforestmist/structured-state-space-duality-repro` |
| ORID | `DKathyl3XN` |
| Domain | `sequence-memory` |

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## Method notes

- **CPU only** (no GPU/MPS)
- Seed: ORID-bound SHA256(`DKathyl3XN:2`)
- 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)