(A) multi-affinity, degrees, exact certificate Q - T*P - sum(t_i-1)^2 == 0
  m= 1 n= 3 degP=2 degQ=3 MA=True resid_terms=0 -> True
  m= 2 n= 5 degP=2 degQ=4 MA=True resid_terms=0 -> True
  m= 3 n= 7 degP=2 degQ=4 MA=True resid_terms=0 -> True
  m= 4 n= 9 degP=2 degQ=4 MA=True resid_terms=0 -> True
  m= 5 n=11 degP=2 degQ=4 MA=True resid_terms=0 -> True
  m= 6 n=13 degP=2 degQ=4 MA=True resid_terms=0 -> True
  m= 7 n=15 degP=2 degQ=4 MA=True resid_terms=0 -> True
  m= 8 n=17 degP=2 degQ=4 MA=True resid_terms=0 -> True
  m= 9 n=19 degP=2 degQ=4 MA=True resid_terms=0 -> True
  m=10 n=21 degP=2 degQ=4 MA=True resid_terms=0 -> True
(B) Schwartz-Zippel exact integer evaluation of the certificate, m up to 40
  m=11: 200 random integer points, mismatches=0
  m=15: 200 random integer points, mismatches=0
  m=20: 200 random integer points, mismatches=0
  m=25: 200 random integer points, mismatches=0
  m=30: 200 random integer points, mismatches=0
  m=40: 200 random integer points, mismatches=0
(C) block lemma: f_j = prod(d vars) - 1, P = x0 - S, Q = x0*S - 2 sum_{j<l} f_j f_l
  d=2 k=5 n=11 degP=2 degQ=4 MA=True resid=0 -> True
  d=3 k=5 n=16 degP=3 degQ=6 MA=True resid=0 -> True
  d=4 k=5 n=21 degP=4 degQ=8 MA=True resid=0 -> True
  d=5 k=5 n=26 degP=5 degQ=10 MA=True resid=0 -> True
(D) components of prod(z_1..z_d)=1 in R^d: count sign classes with even # of minus signs
  d=2: 2 == 2^(d-1)=2
  d=3: 4 == 2^(d-1)=4
  d=4: 8 == 2^(d-1)=8
  d=5: 16 == 2^(d-1)=16
  d=6: 32 == 2^(d-1)=32
(E) refutation attempt: minimise P^2+Q^2 numerically from random starts (m=2,3,4); any near-zero must have all x_i*y_i ~ 1, x0 ~ m; record sign patterns seen
  m=2: converged 400/400, max deviation from (x_i y_i=1, x0=m) = 6.64e-07, sign patterns seen = 4 (2^m=4)
  m=3: converged 319/400, max deviation from (x_i y_i=1, x0=m) = 7.43e-07, sign patterns seen = 8 (2^m=8)
  m=4: converged 290/400, max deviation from (x_i y_i=1, x0=m) = 1.66e-05, sign patterns seen = 16 (2^m=16)
OVERALL: PASS
