A1. Lemma 6.2(a): every element of Z/d is a sum of two units, odd d = 5..301             OK 
A2. the count N(s) of the proof equals the product formula, and N(s) >= 3                OK 
A3. Lemma 6.2(b), construction of the proof, odd d = 5..151, m = 5..200 (14504 pairs)    OK 
A4. m = 5, d = 5, all w_j = 1 (Theorem 1.3): sum 0, consecutive sums 2 are units         OK 
A5. Theorem 8.7: units with w_tI + w_tO = -3 exist; s_j = 2, -3 are non-zero; b_j <= d/3; genus (d-b_j)/2 >= 2 OK 
    for d = 5: all five exponents 1, b_j = 1, genus 2, genus of the cover 6              OK 
B1. Lemma 6.1: genus (d-1)(|P|-2)/2 from chi = 2d - |P|(d-1)                             OK 
B2. Lemma 6.3(1): xi = (-3 chi - b)/2 >= d - 3 >= 2 for chi = d - k(d-1), k >= 2, b <= d, d >= 5 OK 
B3. Proposition 6.5: b_j a proper divisor of odd d gives b_j <= d/3 and genus (d-b_j)/2 >= d/3 > 1 OK 
B4. Proposition 8.5: chi(U_q), the two lower bounds for -chi, and genus > 1 (m <= 15, odd d <= 59) OK 
C. Lemma 3.1 for all labelled graphs with <= 5 vertices and all non-empty sets (32767 pairs) OK 
D. Lemma 6.4 for m = 4..12: the minimal sets are the m sets V - {j, j+1}; the partition statement OK 
E1. hexagon: 39 sets are not contained in a join; the minimal ones are {j,j+3} and the two triangles OK 
    in the prism (complement of the hexagon) j is adjacent to j+2, j+3, j+4              OK 
E2. Figure 1: for Lambda = P_4 the only minimal set not contained in a join of Gamma is {2,3} OK 
F. Proposition 8.5, 292 pairs (m, I) with 5 <= m <= 10: neighbours of i, cliques through q OK 
   connected dominating sets of Lambda_I (m <= 8): with q they contain i-1 or i+1 for all i in I; without q they are c.d. in C_m OK 
G. joins of the path b-a'-b'-a lie in {b,a',b'} or {a',b',a}; none contains both end vertices OK (joins: [[0, 1], [0, 1, 2], [1, 2], [1, 2, 3], [2, 3]])
RESULT: ALL CHECKS PASSED
