[C1] Rote's wheel formula: sign, identity (1), f', conventions; residual formula
  ok    n=3 convex ccw rim, hub inside: all brackets of the printed formula positive
  ok    n=3 convex: printed formula (no minus sign) is NOT a self-stress
  ok    n=3 convex: residual of the printed formula = -2 det(u,w)(p_0-p_i)/(product)
  ok    n=3 convex: with the minus sign it is a self-stress
  ok    n=3 convex: sum w f(a,b) = 1 identically in a, b (det convention)
  ok    n=3 convex: sum w f' = 1 (det convention)
  ok    n=3 convex: area convention: w_area = 4 w_det, sum w f_area = 1, sum w f' = 4
  ok    n=3 convex: N computed at base point p_0 is sum_i D(p0,pi,pi+1)/D_rim = 1
  ok    n=3 random0: printed formula (no minus sign) is NOT a self-stress
  ok    n=3 random0: residual of the printed formula = -2 det(u,w)(p_0-p_i)/(product)
  ok    n=3 random0: with the minus sign it is a self-stress
  ok    n=3 random0: sum w f(a,b) = 1 identically in a, b (det convention)
  ok    n=3 random0: sum w f' = 1 (det convention)
  ok    n=3 random0: area convention: w_area = 4 w_det, sum w f_area = 1, sum w f' = 4
  ok    n=3 random0: N computed at base point p_0 is sum_i D(p0,pi,pi+1)/D_rim = 1
  ok    n=3 random1: printed formula (no minus sign) is NOT a self-stress
  ok    n=3 random1: residual of the printed formula = -2 det(u,w)(p_0-p_i)/(product)
  ok    n=3 random1: with the minus sign it is a self-stress
  ok    n=3 random1: sum w f(a,b) = 1 identically in a, b (det convention)
  ok    n=3 random1: sum w f' = 1 (det convention)
  ok    n=3 random1: area convention: w_area = 4 w_det, sum w f_area = 1, sum w f' = 4
  ok    n=3 random1: N computed at base point p_0 is sum_i D(p0,pi,pi+1)/D_rim = 1
  ok    n=3 random2: printed formula (no minus sign) is NOT a self-stress
  ok    n=3 random2: residual of the printed formula = -2 det(u,w)(p_0-p_i)/(product)
  ok    n=3 random2: with the minus sign it is a self-stress
  ok    n=3 random2: sum w f(a,b) = 1 identically in a, b (det convention)
  ok    n=3 random2: sum w f' = 1 (det convention)
  ok    n=3 random2: area convention: w_area = 4 w_det, sum w f_area = 1, sum w f' = 4
  ok    n=3 random2: N computed at base point p_0 is sum_i D(p0,pi,pi+1)/D_rim = 1
  ok    n=4 convex ccw rim, hub inside: all brackets of the printed formula positive
  ok    n=4 convex: printed formula (no minus sign) is NOT a self-stress
  ok    n=4 convex: residual of the printed formula = -2 det(u,w)(p_0-p_i)/(product)
  ok    n=4 convex: with the minus sign it is a self-stress
  ok    n=4 convex: sum w f(a,b) = 1 identically in a, b (det convention)
  ok    n=4 convex: sum w f' = 1 (det convention)
  ok    n=4 convex: area convention: w_area = 4 w_det, sum w f_area = 1, sum w f' = 4
  ok    n=4 convex: N computed at base point p_0 is sum_i D(p0,pi,pi+1)/D_rim = 1
  ok    n=4 random0: printed formula (no minus sign) is NOT a self-stress
  ok    n=4 random0: residual of the printed formula = -2 det(u,w)(p_0-p_i)/(product)
  ok    n=4 random0: with the minus sign it is a self-stress
  ok    n=4 random0: sum w f(a,b) = 1 identically in a, b (det convention)
  ok    n=4 random0: sum w f' = 1 (det convention)
  ok    n=4 random0: area convention: w_area = 4 w_det, sum w f_area = 1, sum w f' = 4
  ok    n=4 random0: N computed at base point p_0 is sum_i D(p0,pi,pi+1)/D_rim = 1
  ok    n=4 random1: printed formula (no minus sign) is NOT a self-stress
  ok    n=4 random1: residual of the printed formula = -2 det(u,w)(p_0-p_i)/(product)
  ok    n=4 random1: with the minus sign it is a self-stress
  ok    n=4 random1: sum w f(a,b) = 1 identically in a, b (det convention)
  ok    n=4 random1: sum w f' = 1 (det convention)
  ok    n=4 random1: area convention: w_area = 4 w_det, sum w f_area = 1, sum w f' = 4
  ok    n=4 random1: N computed at base point p_0 is sum_i D(p0,pi,pi+1)/D_rim = 1
  ok    n=4 random2: printed formula (no minus sign) is NOT a self-stress
  ok    n=4 random2: residual of the printed formula = -2 det(u,w)(p_0-p_i)/(product)
  ok    n=4 random2: with the minus sign it is a self-stress
  ok    n=4 random2: sum w f(a,b) = 1 identically in a, b (det convention)
  ok    n=4 random2: sum w f' = 1 (det convention)
  ok    n=4 random2: area convention: w_area = 4 w_det, sum w f_area = 1, sum w f' = 4
  ok    n=4 random2: N computed at base point p_0 is sum_i D(p0,pi,pi+1)/D_rim = 1
  ok    n=5 convex ccw rim, hub inside: all brackets of the printed formula positive
  ok    n=5 convex: printed formula (no minus sign) is NOT a self-stress
  ok    n=5 convex: residual of the printed formula = -2 det(u,w)(p_0-p_i)/(product)
  ok    n=5 convex: with the minus sign it is a self-stress
  ok    n=5 convex: sum w f(a,b) = 1 identically in a, b (det convention)
  ok    n=5 convex: sum w f' = 1 (det convention)
  ok    n=5 convex: area convention: w_area = 4 w_det, sum w f_area = 1, sum w f' = 4
  ok    n=5 convex: N computed at base point p_0 is sum_i D(p0,pi,pi+1)/D_rim = 1
  ok    n=5 random0: printed formula (no minus sign) is NOT a self-stress
  ok    n=5 random0: residual of the printed formula = -2 det(u,w)(p_0-p_i)/(product)
  ok    n=5 random0: with the minus sign it is a self-stress
  ok    n=5 random0: sum w f(a,b) = 1 identically in a, b (det convention)
  ok    n=5 random0: sum w f' = 1 (det convention)
  ok    n=5 random0: area convention: w_area = 4 w_det, sum w f_area = 1, sum w f' = 4
  ok    n=5 random0: N computed at base point p_0 is sum_i D(p0,pi,pi+1)/D_rim = 1
  ok    n=5 random1: printed formula (no minus sign) is NOT a self-stress
  ok    n=5 random1: residual of the printed formula = -2 det(u,w)(p_0-p_i)/(product)
  ok    n=5 random1: with the minus sign it is a self-stress
  ok    n=5 random1: sum w f(a,b) = 1 identically in a, b (det convention)
  ok    n=5 random1: sum w f' = 1 (det convention)
  ok    n=5 random1: area convention: w_area = 4 w_det, sum w f_area = 1, sum w f' = 4
  ok    n=5 random1: N computed at base point p_0 is sum_i D(p0,pi,pi+1)/D_rim = 1
  ok    n=5 random2: printed formula (no minus sign) is NOT a self-stress
  ok    n=5 random2: residual of the printed formula = -2 det(u,w)(p_0-p_i)/(product)
  ok    n=5 random2: with the minus sign it is a self-stress
  ok    n=5 random2: sum w f(a,b) = 1 identically in a, b (det convention)
  ok    n=5 random2: sum w f' = 1 (det convention)
  ok    n=5 random2: area convention: w_area = 4 w_det, sum w f_area = 1, sum w f' = 4
  ok    n=5 random2: N computed at base point p_0 is sum_i D(p0,pi,pi+1)/D_rim = 1
  ok    n=6 convex ccw rim, hub inside: all brackets of the printed formula positive
  ok    n=6 convex: printed formula (no minus sign) is NOT a self-stress
  ok    n=6 convex: residual of the printed formula = -2 det(u,w)(p_0-p_i)/(product)
  ok    n=6 convex: with the minus sign it is a self-stress
  ok    n=6 convex: sum w f(a,b) = 1 identically in a, b (det convention)
  ok    n=6 convex: sum w f' = 1 (det convention)
  ok    n=6 convex: area convention: w_area = 4 w_det, sum w f_area = 1, sum w f' = 4
  ok    n=6 convex: N computed at base point p_0 is sum_i D(p0,pi,pi+1)/D_rim = 1
  ok    n=6 random0: printed formula (no minus sign) is NOT a self-stress
  ok    n=6 random0: residual of the printed formula = -2 det(u,w)(p_0-p_i)/(product)
  ok    n=6 random0: with the minus sign it is a self-stress
  ok    n=6 random0: sum w f(a,b) = 1 identically in a, b (det convention)
  ok    n=6 random0: sum w f' = 1 (det convention)
  ok    n=6 random0: area convention: w_area = 4 w_det, sum w f_area = 1, sum w f' = 4
  ok    n=6 random0: N computed at base point p_0 is sum_i D(p0,pi,pi+1)/D_rim = 1
  ok    n=6 random1: printed formula (no minus sign) is NOT a self-stress
  ok    n=6 random1: residual of the printed formula = -2 det(u,w)(p_0-p_i)/(product)
  ok    n=6 random1: with the minus sign it is a self-stress
  ok    n=6 random1: sum w f(a,b) = 1 identically in a, b (det convention)
  ok    n=6 random1: sum w f' = 1 (det convention)
  ok    n=6 random1: area convention: w_area = 4 w_det, sum w f_area = 1, sum w f' = 4
  ok    n=6 random1: N computed at base point p_0 is sum_i D(p0,pi,pi+1)/D_rim = 1
  ok    n=6 random2: printed formula (no minus sign) is NOT a self-stress
  ok    n=6 random2: residual of the printed formula = -2 det(u,w)(p_0-p_i)/(product)
  ok    n=6 random2: with the minus sign it is a self-stress
  ok    n=6 random2: sum w f(a,b) = 1 identically in a, b (det convention)
  ok    n=6 random2: sum w f' = 1 (det convention)
  ok    n=6 random2: area convention: w_area = 4 w_det, sum w f_area = 1, sum w f' = 4
  ok    n=6 random2: N computed at base point p_0 is sum_i D(p0,pi,pi+1)/D_rim = 1
  ok    n=7 convex ccw rim, hub inside: all brackets of the printed formula positive
  ok    n=7 convex: printed formula (no minus sign) is NOT a self-stress
  ok    n=7 convex: residual of the printed formula = -2 det(u,w)(p_0-p_i)/(product)
  ok    n=7 convex: with the minus sign it is a self-stress
  ok    n=7 convex: sum w f(a,b) = 1 identically in a, b (det convention)
  ok    n=7 convex: sum w f' = 1 (det convention)
  ok    n=7 convex: area convention: w_area = 4 w_det, sum w f_area = 1, sum w f' = 4
  ok    n=7 convex: N computed at base point p_0 is sum_i D(p0,pi,pi+1)/D_rim = 1
  ok    n=7 random0: printed formula (no minus sign) is NOT a self-stress
  ok    n=7 random0: residual of the printed formula = -2 det(u,w)(p_0-p_i)/(product)
  ok    n=7 random0: with the minus sign it is a self-stress
  ok    n=7 random0: sum w f(a,b) = 1 identically in a, b (det convention)
  ok    n=7 random0: sum w f' = 1 (det convention)
  ok    n=7 random0: area convention: w_area = 4 w_det, sum w f_area = 1, sum w f' = 4
  ok    n=7 random0: N computed at base point p_0 is sum_i D(p0,pi,pi+1)/D_rim = 1
  ok    n=7 random1: printed formula (no minus sign) is NOT a self-stress
  ok    n=7 random1: residual of the printed formula = -2 det(u,w)(p_0-p_i)/(product)
  ok    n=7 random1: with the minus sign it is a self-stress
  ok    n=7 random1: sum w f(a,b) = 1 identically in a, b (det convention)
  ok    n=7 random1: sum w f' = 1 (det convention)
  ok    n=7 random1: area convention: w_area = 4 w_det, sum w f_area = 1, sum w f' = 4
  ok    n=7 random1: N computed at base point p_0 is sum_i D(p0,pi,pi+1)/D_rim = 1
  ok    n=7 random2: printed formula (no minus sign) is NOT a self-stress
  ok    n=7 random2: residual of the printed formula = -2 det(u,w)(p_0-p_i)/(product)
  ok    n=7 random2: with the minus sign it is a self-stress
  ok    n=7 random2: sum w f(a,b) = 1 identically in a, b (det convention)
  ok    n=7 random2: sum w f' = 1 (det convention)
  ok    n=7 random2: area convention: w_area = 4 w_det, sum w f_area = 1, sum w f' = 4
  ok    n=7 random2: N computed at base point p_0 is sum_i D(p0,pi,pi+1)/D_rim = 1
  ok    n=8 convex ccw rim, hub inside: all brackets of the printed formula positive
  ok    n=8 convex: printed formula (no minus sign) is NOT a self-stress
  ok    n=8 convex: residual of the printed formula = -2 det(u,w)(p_0-p_i)/(product)
  ok    n=8 convex: with the minus sign it is a self-stress
  ok    n=8 convex: sum w f(a,b) = 1 identically in a, b (det convention)
  ok    n=8 convex: sum w f' = 1 (det convention)
  ok    n=8 convex: area convention: w_area = 4 w_det, sum w f_area = 1, sum w f' = 4
  ok    n=8 convex: N computed at base point p_0 is sum_i D(p0,pi,pi+1)/D_rim = 1
  ok    n=8 random0: printed formula (no minus sign) is NOT a self-stress
  ok    n=8 random0: residual of the printed formula = -2 det(u,w)(p_0-p_i)/(product)
  ok    n=8 random0: with the minus sign it is a self-stress
  ok    n=8 random0: sum w f(a,b) = 1 identically in a, b (det convention)
  ok    n=8 random0: sum w f' = 1 (det convention)
  ok    n=8 random0: area convention: w_area = 4 w_det, sum w f_area = 1, sum w f' = 4
  ok    n=8 random0: N computed at base point p_0 is sum_i D(p0,pi,pi+1)/D_rim = 1
  ok    n=8 random1: printed formula (no minus sign) is NOT a self-stress
  ok    n=8 random1: residual of the printed formula = -2 det(u,w)(p_0-p_i)/(product)
  ok    n=8 random1: with the minus sign it is a self-stress
  ok    n=8 random1: sum w f(a,b) = 1 identically in a, b (det convention)
  ok    n=8 random1: sum w f' = 1 (det convention)
  ok    n=8 random1: area convention: w_area = 4 w_det, sum w f_area = 1, sum w f' = 4
  ok    n=8 random1: N computed at base point p_0 is sum_i D(p0,pi,pi+1)/D_rim = 1
  ok    n=8 random2: printed formula (no minus sign) is NOT a self-stress
  ok    n=8 random2: residual of the printed formula = -2 det(u,w)(p_0-p_i)/(product)
  ok    n=8 random2: with the minus sign it is a self-stress
  ok    n=8 random2: sum w f(a,b) = 1 identically in a, b (det convention)
  ok    n=8 random2: sum w f' = 1 (det convention)
  ok    n=8 random2: area convention: w_area = 4 w_det, sum w f_area = 1, sum w f' = 4
  ok    n=8 random2: N computed at base point p_0 is sum_i D(p0,pi,pi+1)/D_rim = 1
[C2] identities (I1), (I2) and the three-vector identity, as polynomial identities
  ok    (I1) D(a,p,q)D(b,p,q) - det(p,q)^2 = <q-p, U(q)-U(p)>
  ok    (I2) f'(p,q) - det(p,q)^2 = <q-p, V(q)-V(p)>, V(x) = |x|^2 x/2
  ok    D(a,p,q) = det(p,q) - det(a,q-p)
  ok    det(w,z)u + det(z,u)w + det(u,w)z = 0
  ok    int over [p,q] of |x|^2 ds / |q-p| = (|p|^2+|q|^2+<p,q>)/3
[C3] Theorem A and A' and sum w f' = N on random frameworks (degenerate positions included)
  ok    48 frameworks, 175 basis stresses: F(a,b) = N, sum w L L^T = N e3 e3^T, sum w f' = N, base point independent
  ok    negative control: a perturbed stress violates A'
[C4] exact certificates for prism + edge 04 and K33 + edge 01
  ok    prism+04: all 6 one-edge extensions of the base graph are isomorphic
  ok    prism+04: no three points collinear
  ok    prism+04: rank R = 9 = 2n-3, stress space of dimension 1
  ok    prism+04: stress nonzero on all 10 edges
  ok    prism+04: every 9-edge subgraph has rank 9 (rigidity circuit)
  ok    prism+04: normalised stress equals the printed table
  ok    prism+04: printed values form a self-stress
  ok    prism+04: F(a,b) = 1 identically in a, b
  ok    prism+04: sum w f' = 1
  ok    K33+01: all 6 one-edge extensions of the base graph are isomorphic
  ok    K33+01: no three points collinear
  ok    K33+01: rank R = 9 = 2n-3, stress space of dimension 1
  ok    K33+01: stress nonzero on all 10 edges
  ok    K33+01: every 9-edge subgraph has rank 9 (rigidity circuit)
  ok    K33+01: normalised stress equals the printed table
  ok    K33+01: printed values form a self-stress
  ok    K33+01: F(a,b) = 1 identically in a, b
  ok    K33+01: sum w f' = 1
  ok    prism+04 drawing is non-crossing
        K33+01 drawing: 4 crossing pairs [((0, 3), (1, 4)), ((0, 3), (2, 5)), ((1, 4), (2, 5)), ((2, 5), (0, 1))]
[C5] Theorem B: Maxwell-Cremona liftings and volumes (exact)
  ok    prism+04: bounded faces 014, 034, 1245, 0235, 345
  ok    prism+04: lifting consistent on every edge (jump rule and continuity)
  ok    prism+04: z = 0 at p0,p1,p2; z(p3) = 77/23550, z(p4) = 187/23550, z(p5) = 119/23550
  ok    prism+04: volume = 1/6
  ok    K33+01: 4 crossing points, drawing in general position
  ok    K33+01 planarised: self-stress, N unchanged (= 1)
  ok    K33+01 planarised: lifting consistent, 6 * volume = 1
  ok    K4 (RSS Lemma 2.6 stress): self-stress, sum w f(a,b) = 1 identically (RSS Lemma 3.10)
  ok    K4 convex planarised at the diagonal crossing = Rote's wheel stress W4 (edge by edge)
  ok    K4 convex planarised: lifting consistent, volume 1/6
  ok    wheel convex n=5 (star-shaped from the hub): pyramid, z(p0) = 1/D_rim, z = 0 on the rim, volume 1/6
  ok    wheel star-shaped n=6 (star-shaped from the hub): pyramid, z(p0) = 1/D_rim, z = 0 on the rim, volume 1/6
[C6] exceptional positions: no three collinear, unique stress, N = 0
  ok    wheel W4 at (0,0),(4,1),(-3,2),(-1,-5),(5,58/5): rim area 0, no three collinear, rank 7, stress space dim 1, nonzero on all edges, N = 0
  ok    wheel W4 there: rescaled Rote stress sigma is a self-stress with N(sigma) = 0
  ok    wheel W4 there: for h = x1 + 2 x2 + 30, sum sigma L L^T/(h_i h_j) = C l l^T with C != 0 (Lemma D)
  ok    prism+04 exceptional point: no three collinear, rank 9, dim 1, nonzero on all edges, N = 0
  ok    K33+01 exceptional point: no three collinear, rank 9, dim 1, nonzero on all edges, N = 0
[C7] Theorem A_h and the transfer C_h = det(S)^2 N(mu; p') on random frameworks
  ok    71 (framework, stress, h) triples: proportional to l l^T, mu is a stress of p', C_h = det(S)^2 N(mu;p')
  ok    collinear subdivision (stresses w/t, w/(1-t)) keeps the stress property and N
[C8] Proposition E: generic stresses on the slice p0=(0,0), p1=(1,0), p2=(0,1) (polynomial identities)
  ok    on the slice D012 = 1 and every triangle area has degree <= 2
  ok    prism+04: the polynomial w of Table 2 is a self-stress on the slice
  ok    prism+04: N(w) = -D014 D034 D345 Q_P, Q_P with 13 terms
  ok    prism+04: Q_P = D025 - D014 D025 + D024 D035 + D025^2 - D025 D035 - D025 D045 + D035 D045
  ok    prism+04: Q_P = x3 y5 D245 + x5 C_P and D245 = x4(y5-1) - x5(y4-1)
  ok    prism+04 witness: y5 does not divide x5 C_P (value at a point with y5 = 0 is nonzero)
  ok    prism+04 witness: D245 does not divide C_P (D245 = 0, C_P != 0 at a point)
  ok    K33+01: the polynomial w of Table 2 is a self-stress on the slice
  ok    K33+01: N(w) = -D013 D014 D015 Q_K, Q_K with 24 terms
  ok    K33+01: Q_K = A y3 + B with A = x3 D245 + x4 x5 E, E = x4 - x5 + y4 - y5, and B as printed
  ok    K33+01: A = y4 x5 (x4 - x3) + R with R free of y4
  ok    K33+01 witness: x5 does not divide R
  ok    K33+01 witness: x4 - x3 does not divide R
  ok    K33+01 witness: A does not divide B (A = 0, B != 0 at a point)
  ok    prism+04: at the exceptional point Q = 0 and w_e != 0 for all ten edges
  ok    K33+01: at the exceptional point Q = 0 and w_e != 0 for all ten edges
  ok    prism+04: the slice stress at the affine image of the certificate is proportional to it
  ok    K33+01: the slice stress at the affine image of the certificate is proportional to it

ALL CHECKS PASSED
