Part A: tau well defined, product in the collar, order = order of sigma|T: 6390 random tests over 14 pairs (lattice, A)
Part B: circle actions on L(p, q) and S^1 x S^2 have the local form used in Lemma 4.2: 300 random tests
Part C: property (*) in the figure-eight knot group: 4372 reduced words of length <= 7 tested, 14 of them conjugate x into P, and those lie in P
checks performed: 21562
ALL LEAD CHECKS PASSED
