C1   vectors tested 137256; with an interior zero coefficient 17784; with two consecutive zeros 0; violations of [e_(r-1)=e_r=0 => |supp|<=r-2] 0
C1   key lemma on all of {-3..3}^n, n<=6: PASS
C2a  r=2: e_r vanishes on a coordinate (r-1)-space of R^4: PASS
C2a  r=4: e_r vanishes on a coordinate (r-1)-space of R^6: PASS
C2a  r=6: e_r vanishes on a coordinate (r-1)-space of R^8: PASS
C2b  odd r=3: e_r vanishes on the 3-space (a1,-a1,...,a3,-a3) of R^6: PASS
C2b  odd r=3: e_r vanishes on the 5-space (a1,-a1,...,a5,-a5) of R^10: PASS
C2b  odd r=5: e_r vanishes on the 5-space (a1,-a1,...,a5,-a5) of R^10: PASS
C2c  even r=2: e_r is NOT identically zero on (a1,-a1,...) (control): PASS
C2c  even r=4: e_r is NOT identically zero on (a1,-a1,...) (control): PASS
C3   r=4: eps=2^-0, F_r has 5 distinct real roots (Sturm), F_r(0)=eps!=0; even coefficients e_2..e_4 of y vanish: True; dim V_r = 2; y has 5 nonzero coordinates; e_r|V_r == 0: True; e_(r-1)|V_r == 0: False (expected False)
C3   r=4: counterexample to the heuristic certified: PASS
C3   r=4: numeric check with 70-digit roots: max |e_r| on V_r samples = 1.296e-70, max |e_(r-1)| = 8.126e+00
C3   r=4: numeric cross-check: PASS
C3   r=6: eps=2^-0, F_r has 7 distinct real roots (Sturm), F_r(0)=eps!=0; even coefficients e_2..e_6 of y vanish: True; dim V_r = 3; y has 7 nonzero coordinates; e_r|V_r == 0: True; e_(r-1)|V_r == 0: False (expected False)
C3   r=6: counterexample to the heuristic certified: PASS
C3   r=6: numeric check with 70-digit roots: max |e_r| on V_r samples = 4.431e-69, max |e_(r-1)| = 5.728e+02
C3   r=6: numeric cross-check: PASS
C3   r=8: eps=2^-0, F_r has 9 distinct real roots (Sturm), F_r(0)=eps!=0; even coefficients e_2..e_8 of y vanish: True; dim V_r = 4; y has 9 nonzero coordinates; e_r|V_r == 0: True; e_(r-1)|V_r == 0: False (expected False)
C3   r=8: counterexample to the heuristic certified: PASS
C3   r=8: numeric check with 70-digit roots: max |e_r| on V_r samples = 1.656e-65, max |e_(r-1)| = 3.038e+05
C3   r=8: numeric cross-check: PASS
C4   n=4, dim=2, r=2: min over 12 starts of max|e_r| on the unit sphere of V = 4.996e-01
C4   n=4, dim=2, r=2: no r-dim subspace found numerically: PASS
C4   n=5, dim=2, r=2: min over 12 starts of max|e_r| on the unit sphere of V = 4.998e-01
C4   n=5, dim=2, r=2: no r-dim subspace found numerically: PASS
C4   n=5, dim=4, r=4: min over 12 starts of max|e_r| on the unit sphere of V = 5.174e-02
C4   n=5, dim=4, r=4: no r-dim subspace found numerically: PASS
C4   n=6, dim=4, r=4: min over 12 starts of max|e_r| on the unit sphere of V = 5.118e-02
C4   n=6, dim=4, r=4: no r-dim subspace found numerically: PASS
C4   n=5, dim=3, r=4: 13/20 starts reach e_r|V=0; of these 13 are coordinate subspaces (n-d zero rows); residuals of the others: [0.034529925833, 0.034920972631, 0.036196366473, 0.036480547251, 0.037098510564]
C4   n=5, dim=3, r=4: every numerically found 3-space in e_4=0 is a coordinate space: PASS
C4   n=6, dim=3, r=4: 9/20 starts reach e_r|V=0; of these 9 are coordinate subspaces (n-d zero rows); residuals of the others: [0.030350818783, 0.030657203418, 0.031365909812, 0.031431071939, 0.031992426006]
C4   n=6, dim=3, r=4: every numerically found 3-space in e_4=0 is a coordinate space: PASS
C4   n=7, dim=5, r=6: 11/12 starts reach e_r|V=0; of these 11 are coordinate subspaces
C4   n=7, dim=5, r=6: every numerically found 5-space in e_6=0 is a coordinate space: PASS
C4   n=7, dim=2, r=4: 20/20 starts reach e_4|V=0; non-coordinate among them: 20 (numbers of zero rows: [0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4])
ALL CONFLITTI CHECKS PASS
