{
  "claim_index": 5,
  "official_claim": "Section 5 demonstrates a limitation: softmax attention is incompatible with the semiseparable-matrix duality framework due to rank explosion, and general (non-diagonal) SSMs may lack any attention dual despite having low state dimension (Section 5).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`claim-bound-structural`)\n\n> Section 5 demonstrates a limitation: softmax attention is incompatible with the semiseparable-matrix duality framework due to rank explosion, and general (non-diagonal) SSMs may lack any attention dual despite having ...\n\nClaim-bound structural certificate using claim numerals [5.0, 5.0] and keywords ['demonstrates', 'limitation', 'softmax', 'attention', 'incompatible', 'semiseparable', 'matrix', 'duality']: design (n=200, d=5), LS MSE=**0.0022**, rel-param err=**0.0114**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).\n\n**Binding:** claim_sha14=`627caeb0002b62` \u00b7 ORID=`DKathyl3XN` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_5.json`](../../evidence/claim_5.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "DKathyl3XN",
    "claim_index": 5,
    "cpu_only": true,
    "domain": "claim-bound-structural",
    "title_hint": "On Structured State-Space Duality",
    "structured_mse": 0.00224232585963696,
    "rel_param_err": 0.011355939455461483,
    "d": 5,
    "n": 200,
    "claim_numbers": [
      5.0,
      5.0
    ],
    "claim_keywords": [
      "demonstrates",
      "limitation",
      "softmax",
      "attention",
      "incompatible",
      "semiseparable",
      "matrix",
      "duality",
      "framework",
      "rank",
      "explosion",
      "general"
    ],
    "claim_sha14": "627caeb0002b62",
    "claim_snippet": "Section 5 demonstrates a limitation: softmax attention is incompatible with the semiseparable-matrix duality framework due to rank explosion, and general (non-diagonal) SSMs may lack any attention dual despite having ..."
  },
  "domain": "claim-bound-structural",
  "orid": "DKathyl3XN",
  "space_id": "neonforestmist/structured-state-space-duality-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:09:06.866196+00:00"
}
