  box n=1, entries in [-4,4]: 9 vectors checked
  box n=2, entries in [-4,4]: 81 vectors checked
  box n=3, entries in [-4,4]: 729 vectors checked
  box n=4, entries in [-4,4]: 6561 vectors checked
  box n=5, entries in [-4,4]: 59049 vectors checked
  box n=6, entries in [-3,3]: 117649 vectors checked
  box n=7, entries in [-2,2]: 78125 vectors checked
  box n=8, entries in [-2,2]: 390625 vectors checked
Lemma 3.1: 652828 integer vectors; violations of 'no two consecutive zeros': 0; violations of 'e_(r-1)=e_r=0 => s<=r-2': 0
Lemma 3.1: 4000 structured random rational vectors (n<=12), 978 interior zero coefficients seen, violations: 0
Remark 3.4: r= 4 n= 5 dim=2: e_r vanishes at 60 random rational points: True; max #nonzero coords seen=5; Lemma 3.3 max_J dim(V cap R^J)=1 (dim V - 1 = 1)
Remark 3.4: r= 4 n= 6 dim=2: e_r vanishes at 60 random rational points: True; max #nonzero coords seen=5; Lemma 3.3 max_J dim(V cap R^J)=1 (dim V - 1 = 1)
Remark 3.4: r= 4 n= 7 dim=2: e_r vanishes at 60 random rational points: True; max #nonzero coords seen=5; Lemma 3.3 max_J dim(V cap R^J)=1 (dim V - 1 = 1)
Remark 3.4: r= 6 n= 7 dim=3: e_r vanishes at 60 random rational points: True; max #nonzero coords seen=7; Lemma 3.3 max_J dim(V cap R^J)=2 (dim V - 1 = 2)
Remark 3.4: r= 6 n= 8 dim=3: e_r vanishes at 60 random rational points: True; max #nonzero coords seen=7; Lemma 3.3 max_J dim(V cap R^J)=2 (dim V - 1 = 2)
Remark 3.4: r= 6 n= 9 dim=3: e_r vanishes at 60 random rational points: True; max #nonzero coords seen=7; Lemma 3.3 max_J dim(V cap R^J)=2 (dim V - 1 = 2)
Remark 3.4: r= 8 n= 9 dim=4: e_r vanishes at 60 random rational points: True; max #nonzero coords seen=9; Lemma 3.3 max_J dim(V cap R^J)=3 (dim V - 1 = 3)
Remark 3.4: r= 8 n=10 dim=4: e_r vanishes at 60 random rational points: True; max #nonzero coords seen=9; Lemma 3.3 max_J dim(V cap R^J)=3 (dim V - 1 = 3)
Remark 3.4: r= 8 n=11 dim=4: e_r vanishes at 60 random rational points: True; max #nonzero coords seen=9; Lemma 3.3 max_J dim(V cap R^J)=3 (dim V - 1 = 3)
Remark 3.4: r=10 n=11 dim=5: e_r vanishes at 60 random rational points: True; max #nonzero coords seen=11; Lemma 3.3 max_J dim(V cap R^J)=4 (dim V - 1 = 4)
Remark 3.4: r=10 n=12 dim=5: e_r vanishes at 60 random rational points: True; max #nonzero coords seen=11; Lemma 3.3 max_J dim(V cap R^J)=None (dim V - 1 = 4)
Remark 3.4: r=10 n=13 dim=5: e_r vanishes at 60 random rational points: True; max #nonzero coords seen=11; Lemma 3.3 max_J dim(V cap R^J)=None (dim V - 1 = 4)
Remark 3.4: r=12 n=13 dim=6: e_r vanishes at 60 random rational points: True; max #nonzero coords seen=13; Lemma 3.3 max_J dim(V cap R^J)=None (dim V - 1 = 5)
Remark 3.4: r=12 n=14 dim=6: e_r vanishes at 60 random rational points: True; max #nonzero coords seen=13; Lemma 3.3 max_J dim(V cap R^J)=None (dim V - 1 = 5)
Remark 3.4: r=12 n=15 dim=6: e_r vanishes at 60 random rational points: True; max #nonzero coords seen=13; Lemma 3.3 max_J dim(V cap R^J)=None (dim V - 1 = 5)
Chirvasitu type (b): 40/40 random partition subspaces lie in e_(m-1)^(-1)(0) (30 exact points each)
r=2 example n=3: e_2(1,1,-1/2,0..) = 0
r=2 example n=4: e_2(1,1,-1/2,0..) = 0
r=2 example n=5: e_2(1,1,-1/2,0..) = 0
r=2 example n=6: e_2(1,1,-1/2,0..) = 0
r=2 example n=7: e_2(1,1,-1/2,0..) = 0
search n=3 d=2 r=2: min mean(e_r^2) over V = 7.717e-02 (median random V 1.965e-01; ratio 3.93e-01); best-3 ['7.7e-02', '7.7e-02', '7.7e-02']; coord-residual of best V 3.76e-01; [no subspace (Thm 1.3, r=2)] (1s)
search n=4 d=2 r=2: min mean(e_r^2) over V = 6.837e-02 (median random V 1.990e-01; ratio 3.44e-01); best-3 ['6.8e-02', '6.8e-02', '6.8e-02']; coord-residual of best V 4.85e-01; [no subspace (Thm 1.3, r=2)] (1s)
search n=6 d=2 r=2: min mean(e_r^2) over V = 5.811e-02 (median random V 1.707e-01; ratio 3.40e-01); best-3 ['5.8e-02', '5.8e-02', '5.8e-02']; coord-residual of best V 8.95e-01; [no subspace (Thm 1.3, r=2)] (2s)
search n=5 d=4 r=4: min mean(e_r^2) over V = 1.881e-04 (median random V 1.320e-03; ratio 1.43e-01); best-3 ['1.9e-04', '2.0e-04', '2.0e-04']; coord-residual of best V 1.34e-01; [no subspace (Thm 1.3, n=r+1)] (10s)
search n=6 d=4 r=4: min mean(e_r^2) over V = 2.024e-04 (median random V 2.117e-03; ratio 9.56e-02); best-3 ['2.0e-04', '2.2e-04', '2.2e-04']; coord-residual of best V 1.17e-01; [no subspace (Thm 1.3, new case)] (14s)
search n=7 d=4 r=4: min mean(e_r^2) over V = 1.878e-04 (median random V 3.232e-03; ratio 5.81e-02); best-3 ['1.9e-04', '2.0e-04', '2.2e-04']; coord-residual of best V 7.57e-02; [no subspace (Thm 1.3, new case)] (17s)
search n=8 d=4 r=4: min mean(e_r^2) over V = 2.265e-04 (median random V 3.667e-03; ratio 6.18e-02); best-3 ['2.3e-04', '2.9e-04', '3.5e-04']; coord-residual of best V 8.86e-02; [no subspace (Thm 1.3, new case)] (13s)
search n=7 d=6 r=6: min mean(e_r^2) over V = 4.024e-07 (median random V 3.021e-06; ratio 1.33e-01); best-3 ['4.0e-07', '4.2e-07', '4.3e-07']; coord-residual of best V 9.53e-02; [no subspace (Thm 1.3, n=r+1)] (113s)
search n=8 d=6 r=6: min mean(e_r^2) over V = 4.622e-07 (median random V 7.259e-06; ratio 6.37e-02); best-3 ['4.6e-07', '4.8e-07', '5.0e-07']; coord-residual of best V 1.09e-01; [no subspace (Thm 1.3, new case)] (85s)
search n=6 d=3 r=4: min mean(e_r^2) over V = 7.738e-18 (median random V 1.977e-03; ratio 3.91e-15); best-3 ['7.7e-18', '2.2e-17', '3.4e-17']; coord-residual of best V 2.10e-04; [control: coordinate 3-spaces exist (Cor 1.4); Thm 1.5 says only those] (10s)
search n=7 d=3 r=4: min mean(e_r^2) over V = 3.846e-19 (median random V 3.094e-03; ratio 1.24e-16); best-3 ['3.8e-19', '3.9e-19', '4.1e-17']; coord-residual of best V 8.95e-05; [control: coordinate 3-spaces exist; Thm 1.5 says only those] (13s)
search n=4 d=3 r=3: min mean(e_r^2) over V = 3.546e-03 (median random V 2.118e-02; ratio 1.67e-01); best-3 ['3.5e-03', '3.5e-03', '3.5e-03']; coord-residual of best V 1.47e-01; [odd r=3, n=4: none (Lemma 3.2, irreducible e_3)] (3s)
search n=6 d=3 r=3: min mean(e_r^2) over V = 5.039e-19 (median random V 2.816e-02; ratio 1.79e-17); best-3 ['5.0e-19', '5.7e-19', '6.6e-19']; coord-residual of best V 1.22e+00; [odd r=3, n=6: exists ((a,-a,b,-b,c,-c))] (6s)
search n=5 d=3 r=3: min mean(e_r^2) over V = 3.004e-03 (median random V 2.312e-02; ratio 1.30e-01); best-3 ['3.0e-03', '3.1e-03', '3.1e-03']; coord-residual of best V 1.01e+00; [odd r=3, n=5: (not claimed by paper)] (4s)
total time 293s
python3 ref1_conflitti.py  125.34s user 1.77s system 43% cpu 4:53.71 total
