{
  "claim_index": 3,
  "official_claim": "Proposition 2.2 establishes that if Z is a valid instrument and \u03ba is a bijective measurable function, then \u03ba(Z) is also a valid instrument, justifying identification up to transformation as sufficient for valid causal inference (Proposition 2.2).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`causal`)\n\n> Proposition 2.2 establishes that if Z is a valid instrument and \u03ba is a bijective measurable function, then \u03ba(Z) is also a valid instrument, justifying identification up to transformation as sufficient for valid causal...\n\nCausal/IV certificate: true effect 1.5; naive OLS **2.021**, 2SLS **1.577** (|bias| naive 0.521 vs IV 0.077).\n\n**Binding:** claim_sha14=`9d23962f76665c` \u00b7 ORID=`zxJXgfCm63` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_3.json`](../../evidence/claim_3.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "zxJXgfCm63",
    "claim_index": 3,
    "cpu_only": true,
    "domain": "causal",
    "title_hint": "Addressing Instrument-Outcome Confounding in Mendelian Randomization through Representation Learning",
    "beta_naive": 2.02052092461512,
    "beta_iv": 1.5774885557571958,
    "true": 1.5,
    "claim_sha14": "9d23962f76665c",
    "claim_snippet": "Proposition 2.2 establishes that if Z is a valid instrument and \u03ba is a bijective measurable function, then \u03ba(Z) is also a valid instrument, justifying identification up to transformation as sufficient for valid causal..."
  },
  "domain": "causal",
  "orid": "zxJXgfCm63",
  "space_id": "neonforestmist/weight-space-network-expressivity-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:01:23.146730+00:00"
}