== T1  Lemma 2.1 (M = B D B^{-1}) on random / adversarial instances
   instances: Z 10849, Z[i] 15258; failures: {'Z': 0, 'Z[i]': 0, 'Z simplified': 0, 'Z[i] simplified': 0}
== T2  Theorem 1.1(i): M.c(y) = c(y)^p for all admissible y (schoolbook re-check)
   fields: 63 (p<=97, q<=8192); admissible y: 47698; failures: 0; 53.9s
   max |entry| of the Lemma 2.1 matrix per q (sample): q=4:13, q=8:57, q=16:1201, q=128:867679, q=256:6768633, q=1024:474267301, q=2187:3996407539, q=4096:33166193409, q=8192:262458882205
== T3  log-free orbits of SL_2(Z) = <S,T> and GL_2(Z) on (F_q^*)^2
   q=    4: orbits SL2=2 GL2=2, divisors(q-1)=2; c(y)^p outside orbit: 0/2; negative control separated 2/2
   q=    8: orbits SL2=2 GL2=2, divisors(q-1)=2; c(y)^p outside orbit: 0/6; negative control separated 6/6
   q=   16: orbits SL2=4 GL2=4, divisors(q-1)=4; c(y)^p outside orbit: 0/14; negative control separated 40/40
   q=   32: orbits SL2=2 GL2=2, divisors(q-1)=2; c(y)^p outside orbit: 0/30; negative control separated 30/30
   q=   64: orbits SL2=6 GL2=6, divisors(q-1)=6; c(y)^p outside orbit: 0/62; negative control separated 172/172
   q=  128: orbits SL2=2 GL2=2, divisors(q-1)=2; c(y)^p outside orbit: 0/126; negative control separated 126/126
   q=  256: orbits SL2=8 GL2=8, divisors(q-1)=8; c(y)^p outside orbit: 0/254; negative control separated 736/736
   q=  512: orbits SL2=4 GL2=4, divisors(q-1)=4; c(y)^p outside orbit: 0/510; negative control separated 1506/1506
   q=    3: orbits SL2=2 GL2=2, divisors(q-1)=2; c(y)^p outside orbit: 0/0; negative control separated 0/0
   q=    9: orbits SL2=4 GL2=4, divisors(q-1)=4; c(y)^p outside orbit: 0/6; negative control separated 18/18
   q=   27: orbits SL2=4 GL2=4, divisors(q-1)=4; c(y)^p outside orbit: 0/24; negative control separated 66/66
   q=   81: orbits SL2=10 GL2=10, divisors(q-1)=10; c(y)^p outside orbit: 0/78; negative control separated 228/228
   q=  243: orbits SL2=6 GL2=6, divisors(q-1)=6; c(y)^p outside orbit: 0/240; negative control separated 660/660
   q=    5: orbits SL2=3 GL2=3, divisors(q-1)=3; c(y)^p outside orbit: 0/2; negative control separated 4/4
   q=   25: orbits SL2=8 GL2=8, divisors(q-1)=8; c(y)^p outside orbit: 0/22; negative control separated 64/64
   q=  125: orbits SL2=6 GL2=6, divisors(q-1)=6; c(y)^p outside orbit: 0/122; negative control separated 352/352
   q=    7: orbits SL2=4 GL2=4, divisors(q-1)=4; c(y)^p outside orbit: 0/4; negative control separated 12/12
   q=   49: orbits SL2=10 GL2=10, divisors(q-1)=10; c(y)^p outside orbit: 0/46; negative control separated 132/132
   q=  343: orbits SL2=12 GL2=12, divisors(q-1)=12; c(y)^p outside orbit: 0/340; negative control separated 930/930
   q=   11: orbits SL2=4 GL2=4, divisors(q-1)=4; c(y)^p outside orbit: 0/8; negative control separated 22/22
   q=  121: orbits SL2=16 GL2=16, divisors(q-1)=16; c(y)^p outside orbit: 0/118; negative control separated 336/336
   q=   13: orbits SL2=6 GL2=6, divisors(q-1)=6; c(y)^p outside orbit: 0/10; negative control separated 30/30
   q=  169: orbits SL2=16 GL2=16, divisors(q-1)=16; c(y)^p outside orbit: 0/166; negative control separated 480/480
   q=   17: orbits SL2=5 GL2=5, divisors(q-1)=5; c(y)^p outside orbit: 0/14; negative control separated 42/42
   q=  289: orbits SL2=18 GL2=18, divisors(q-1)=18; c(y)^p outside orbit: 0/286; negative control separated 844/844
   q=   19: orbits SL2=6 GL2=6, divisors(q-1)=6; c(y)^p outside orbit: 0/16; negative control separated 44/44
   q=   23: orbits SL2=4 GL2=4, divisors(q-1)=4; c(y)^p outside orbit: 0/20; negative control separated 56/56
   q=   29: orbits SL2=6 GL2=6, divisors(q-1)=6; c(y)^p outside orbit: 0/26; negative control separated 74/74
   q=   31: orbits SL2=8 GL2=8, divisors(q-1)=8; c(y)^p outside orbit: 0/28; negative control separated 74/74
   total admissible y: 2580; all OK: True
== T4  Remark 4.1: fixed M serves at most min_rows(|alpha|+|beta|) closed points
   8752 (M, eps, field) triples (|entries|<=4 for q<=128, <=3 above); max(count - bound) = 0; OK: True
   F_128: 17768 matrices of GL_2(Z) with |entries|<=30 tested against 126 y and both signs; matches: 0 (paper: none, since |tr M| >= 61 is forced)
   min |tr M| with det(M -+ 2I) = 0 mod 127: 61 (paper: 61)
== T5  Jacobian rank of S and T at all F_q-points of the fibres (small q); zero set of I_phi
   q=4: 236 points checked, rank<2 at 0, zero set != {1,c(y)} for 0 fibres
   q=8: 5652 points checked, rank<2 at 0, zero set != {1,c(y)} for 0 fibres
   q=3: 0 points checked, rank<2 at 0, zero set != {1,c(y)} for 0 fibres
   q=9: 8088 points checked, rank<2 at 0, zero set != {1,c(y)} for 0 fibres
   q=5: 456 points checked, rank<2 at 0, zero set != {1,c(y)} for 0 fibres
   q=7: 2512 points checked, rank<2 at 0, zero set != {1,c(y)} for 0 fibres
== SUMMARY {'T1': True, 'T2': True, 'T3': True, 'T4': True, 'T5': True} total 71.2s
