Q = [3]  (q = 2, boundary case);  Phi_P = H for {p>=5}
Phi_P(1,1) = sum_i phi_i(1) = 0.33333334300898    prod_{p in {2,3}}(1-1/p) = 0.33333333333333
Phi_P(1,2) = sum_{i<=12} phi_i(1)2^i = 0.12630368680977   [TRUNCATED at i = 12; tail inflated by 2^i; genP_check.py gives 0.12623167]

 k   f_k^P (direct)        reconstruction        residual      residual/2^-k
  6  0.668956988382159  0.6376346197405369  0.031322369  2.0046316
  8  0.6661357242834254  0.6617766712482262  0.004359053  1.1159176
 10  0.6661692081868625  0.6651011414036382  0.0010680668  1.0937004
 12  0.6664239068618863  0.6661202348310362  0.00030367203  1.2438406