== E1 kernel identities (exact), intervals with endpoints in (1/d)Z, d <= 12
  Example 2, X->Y: 728 identities, 0 violated -> OK
  Example 2, Y->X (S=theta): 728 identities, 0 violated -> OK
  Example 3, X->Y: 728 identities, 0 violated -> OK
  Example 3, Y->X: 728 identities, 0 violated -> OK
  negative control (weights 1/3, 2/3): 728 identities, 698 violated -> OK
  negative control (repeated branch): 728 identities, 578 violated -> OK
  Example 1 (X->Y, product structure): 5784 identities, 0 violated -> OK
  Example 1 (Y->X, S(y)=y_1): ok by Fubini (integrate out y_2)
== E2 value sets and the density identity
  value set of h (Example 3, no T): ['0', '1', '1/3', '2/3'] contains 1/2: False
  value set of g (Example 3, no S): ['0', '1', '1/2'] contains 1/3: False
  identity Leb(A cap vartheta^-1 E) = int_E h verified on 300 random grid sets
== E3 second moments
  int |kappa|^2 dm = int |lambda|^2 dn = 2/3
== E4 Remark 3.2: exact weak-approximation errors
  error = 1/(12N) exactly for f=y_2 and f=y_1 y_2, N = 1..60 (first component)
ALL E-CHECKS PASSED
