{
  "schema": "classical-reconstruction-benchmark/v1",
  "benchmark_id": "hall-2010-measurement-dependent-singlet",
  "version": "1.0.0",
  "ontology_contract_sha256": "b749348b619769f3b4bf2d5e7cd3a50a6b38c9aaad22983846c893dab09b8d24",
  "observables": [
    {"id":"joint_probabilities","definition":"p(a,b|x,y)=1/4*(1-a*b*x_dot_y)","units":"probability"},
    {"id":"singlet_correlation","definition":"E(x,y)=-x_dot_y","units":"dimensionless"},
    {"id":"marginals","definition":"p(a|x,y)=p(b|x,y)=1/2","units":"probability"},
    {"id":"measurement_dependence_M","definition":"sup L1 distance between setting-conditioned lambda densities","units":"dimensionless"}
  ],
  "sources": [
    {"id":"hall2010","doi":"10.1103/PhysRevLett.105.250404","arxiv":"1007.5518v4","role":"model equations 5-8"},
    {"id":"hall2016erratum","doi":"10.1103/PhysRevLett.116.219902","role":"corrected M_singlet about 0.276434"}
  ],
  "model_class": {"state":"unit vector lambda on S2","responses":"A=sign(x dot lambda); B=-sign(y dot lambda)","locality":"local response functions","determinism":"deterministic","measurement_independence":"relaxed via rho_xy(lambda)","signalling":"target no-signalling marginals"},
  "tolerances": {"probability":1e-12,"correlation":1e-12,"marginal":1e-12,"measurement_dependence":5e-6},
  "erratum_target": {"M_singlet":0.276434,"original_incorrect_M":0.276142,"note":"2016 erratum: correction is about 0.1 percent and removes the original exact-optimality claim."},
  "q1_q5": {"Q1":"singlet correlation represented by an explicit objective-variable model after relaxing measurement independence","Q2":"exact joint law is the adapter target","Q3":"joint probabilities and marginals tested","Q4":"this is a Bell model, not a unified physical theory","Q5":"not earned"},
  "scope_exclusion": "The adapter demonstrates mathematical representation and no-signalling marginals. It does not supply a microscopic physical mechanism for the setting-lambda dependence."
}