(1) geometric intersection count of core curves  /  (2) algebraic (H2)-(H4) => (H5):
   odd n = 5..61: geometric count equals [i+j in {m,m+1}] for all i,j: True ; algebraic (H5) with eps_0=+1 (value -1 on i+j in {m,m+1}, 0 otherwise; <c,c>=<c',c'>=0): True
(3) T_1 T = -R_{2pi/n}:
   n = 3..59: True
(4) (H8) against the honest billiard, words in tau = tau_0 and tau' = tau_1:
   n=9: 40 words tested; factor tuple equals n/gcd(n, alpha*j) with (alpha,beta) from (H8): eps=+1 -> 28, eps=-1 -> 40 ; gcd(alpha,n) values met (eps=-1): [1, 3]  (0.8s)
   n=15: 40 words tested; factor tuple equals n/gcd(n, alpha*j) with (alpha,beta) from (H8): eps=+1 -> 19, eps=-1 -> 40 ; gcd(alpha,n) values met (eps=-1): [1, 3, 5]  (3.0s)
   n=21: 40 words tested; factor tuple equals n/gcd(n, alpha*j) with (alpha,beta) from (H8): eps=+1 -> 18, eps=-1 -> 40 ; gcd(alpha,n) values met (eps=-1): [1, 3, 7]  (6.4s)
   n=25: 40 words tested; factor tuple equals n/gcd(n, alpha*j) with (alpha,beta) from (H8): eps=+1 -> 32, eps=-1 -> 40 ; gcd(alpha,n) values met (eps=-1): [1, 5, 25]  (16.5s)
   n=27: 40 words tested; factor tuple equals n/gcd(n, alpha*j) with (alpha,beta) from (H8): eps=+1 -> 25, eps=-1 -> 40 ; gcd(alpha,n) values met (eps=-1): [1, 3, 9, 27]  (18.1s)
   n=33: 16 words tested; factor tuple equals n/gcd(n, alpha*j) with (alpha,beta) from (H8): eps=+1 -> 7, eps=-1 -> 16 ; gcd(alpha,n) values met (eps=-1): [1, 3, 11]  (11.1s)
   n=35: 16 words tested; factor tuple equals n/gcd(n, alpha*j) with (alpha,beta) from (H8): eps=+1 -> 9, eps=-1 -> 16 ; gcd(alpha,n) values met (eps=-1): [1, 5, 7]  (12.3s)
   n=45: 16 words tested; factor tuple equals n/gcd(n, alpha*j) with (alpha,beta) from (H8): eps=+1 -> 8, eps=-1 -> 16 ; gcd(alpha,n) values met (eps=-1): [1, 3, 5]  (31.2s)
