{
  "claim_index": 2,
  "official_claim": "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).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`sequence-memory`)\n\n> 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...\n\nSequence/memory projection certificate: T=200, poly deg=12, recon MSE=**0.0404**.\n\n**Binding:** claim_sha14=`d57372c6fd7c2f` \u00b7 ORID=`DKathyl3XN` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_2.json`](../../evidence/claim_2.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "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..."
  },
  "domain": "sequence-memory",
  "orid": "DKathyl3XN",
  "space_id": "neonforestmist/structured-state-space-duality-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:09:06.862649+00:00"
}