{
  "id": "rounded_residual_coherence",
  "class": "identity",
  "statement": "encode(x+d)=T_d(encode(x));T_eT_d=T_(d+e),whereencode(x)=(Q(x),x\u2212Q(x))",
  "proof": "Bothsidesreconstructtheuniqueexactvaluex+doreventuallyx+d+e,andnearestfiveencodingisunique.",
  "aggregate_statement": "Fororderedrowdataw=y+rho, Uw=Uy+Urho;Urhoisnotrenormalized.",
  "applications": [
    "105ordinaryintertraditionmeasurements",
    "complete25-nodeMosesexactfield"
  ],
  "limits": [
    "Droppingrhoallowsall-inputtranslationonlyford in5Z",
    "ChronologicaladmissionofintermediateTstatesremainsaseparatesourcecondition",
    "BlockroundingQ(Bw)usuallydiffersfromB Q(w)"
  ],
  "evidence": [
    "model/all_ordinary_lifted_translations.json",
    "model/rounded_translation_composition.json",
    "model/Moses_complete_residual_recovery.json"
  ]
}