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  "official_claim": "Proposition 4.1 proves the equivalence between N-semiseparable matrices and N-SSS (sequentially semiseparable) representable matrices (Section 4.4).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`claim-bound-structural`)\n\n> Proposition 4.1 proves the equivalence between N-semiseparable matrices and N-SSS (sequentially semiseparable) representable matrices (Section 4.4).\n\nClaim-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).\n\n**Binding:** claim_sha14=`2404a3e87e9a5a` \u00b7 ORID=`DKathyl3XN` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_4.json`](../../evidence/claim_4.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
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    "claim_index": 4,
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    "domain": "claim-bound-structural",
    "title_hint": "On Structured State-Space Duality",
    "structured_mse": 0.0024999715838720463,
    "rel_param_err": 0.007411671561079411,
    "d": 4,
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    "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)."
  },
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  "orid": "DKathyl3XN",
  "space_id": "neonforestmist/structured-state-space-duality-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:09:06.865142+00:00"
}