{
  "gaps": [
    430,
    30,
    430
  ],
  "images": [
    "10750/23",
    "750/23",
    "10750/23"
  ],
  "proof": {
    "identity": "D_E,a(u)\u2212D_E,a(v)=E*(u\u2212v), independent of anchor",
    "necessary": "two integral image heads have an integral difference",
    "contradiction": "source gap430 maps to10750/23, not an integer",
    "scope": "no common anchor can make the complete field integral; fractions remain exact"
  }
}