{
  "id": "affine_composition_and_grid",
  "class": "identity_with_domain_condition",
  "identity": "D_k T_t=T_(kt) D_k inlinearcoordinates;anchoredoffsetscarriedexplicitly",
  "rational_domain": "Nonzeroexactfactorscomposeoverrationalspans.",
  "integer_example": {
    "first": "J=300/299 about14006",
    "second": "P=70/69 about4836",
    "first_integer_input": "x=14006+299t",
    "first_integer_output": "y=14006+300t",
    "second_span": "9170+300t",
    "residue_mod3": 2,
    "conclusion": "Neverdivisibleby69;integerintermediatestageconditionfailsforallintegert."
  },
  "source_scope": "Theobstructionbelongstothesefixedpivotsandgridrequirements,notallJ/Papplications.",
  "evidence": "inheritedC984\u2013C1007 fixedpivotdomainclassification"
}