Part A: kernel identities of Examples 2 and 3 on all intervals [a,b], endpoints in (1/den)Z, den<=8
   960 exact identities verified: OK
   negative control (wrong kernel weights 1/3, 2/3): mismatch detected in 49 of 56 test intervals
Part B: second moments
   int |kappa|^2 dm:  Ex1/Ex2: 2/3  Ex3: 2/3    int |lambda|^2 dn:  Ex1: 2/3  Ex2/Ex3: 2/3
Part C: value sets
   h takes values in ['0', '1/3', '2/3', '1'] ; 1/2 attained? False
   g takes values in ['0', '1/2', '1'] ; 1/3 attained? False
   1_A takes values in ['0', '1'] ; 1/2 attained? False
Part D: atom lemma on finite measures (n <= 12)
   12647 ordered pairs of partitions: maps in both directions exist iff the multisets coincide: OK
Part E: weak approximation  T_N(x) = (x, {Nx})  in Example 1 (exact errors)
   f = y1^a y2^b ; error_N = int_0^1 x^(a+1) {Nx}^b dx - 1/((a+2)(b+1)) ; N*error_N
   (a,b)=(0,1): N=1: +8.33e-02 (+0.0833)  N=2: +4.17e-02 (+0.0833)  N=4: +2.08e-02 (+0.0833)  N=8: +1.04e-02 (+0.0833)  N=16: +5.21e-03 (+0.0833)  N=32: +2.60e-03 (+0.0833)  N=64: +1.30e-03 (+0.0833)  N=128: +6.51e-04 (+0.0833)
   (a,b)=(1,1): N=1: +8.33e-02 (+0.0833)  N=2: +4.17e-02 (+0.0833)  N=4: +2.08e-02 (+0.0833)  N=8: +1.04e-02 (+0.0833)  N=16: +5.21e-03 (+0.0833)  N=32: +2.60e-03 (+0.0833)  N=64: +1.30e-03 (+0.0833)  N=128: +6.51e-04 (+0.0833)
   (a,b)=(2,2): N=1: +8.33e-02 (+0.0833)  N=2: +4.27e-02 (+0.0854)  N=4: +2.12e-02 (+0.0849)  N=8: +1.05e-02 (+0.0842)  N=16: +5.24e-03 (+0.0838)  N=32: +2.61e-03 (+0.0836)  N=64: +1.30e-03 (+0.0835)  N=128: +6.52e-04 (+0.0834)
   (a,b)=(0,3): N=1: +7.50e-02 (+0.0750)  N=2: +3.75e-02 (+0.0750)  N=4: +1.87e-02 (+0.0750)  N=8: +9.37e-03 (+0.0750)  N=16: +4.69e-03 (+0.0750)  N=32: +2.34e-03 (+0.0750)  N=64: +1.17e-03 (+0.0750)  N=128: +5.86e-04 (+0.0750)
ALL CHECKS PASSED
