These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 15. PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS {0} {lambda1} {lambda2} {lambda1+lambda2} These pure modular group Hurwitz classes each contain infinitely many Thurston equivalence classes. The number of pure modular group Hurwitz classes in this modular group Hurwitz class is 24. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/1, 0/3, 0/5, 0/15, 1/15, 1/5, 1/3, 1/1, 3/3, 3/1, 5/1, 6/1, 7/1, 10/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.133059) (-0.117862,-0.105092) (-0.095079,-0.087090) (-0.079888,-0.074171) (-0.068882,-0.064589) (-0.060541,-0.057943) (-0.053357,-0.051926) (-0.048212,-0.047041) (-0.043972,-0.042996) (-0.040417,-0.039591) (-0.037395,-0.036686) (-0.034793,-0.034178) (-0.032529,-0.031992) (-0.030542,-0.030068) (-0.028784,-0.028362) (-0.027217,-0.026840) (-0.025812,-0.025472) (-0.024545,-0.024238) (-0.023396,-0.023117) (-0.022350,-0.022095) (-0.021394,-0.021160) (-0.020516,-0.020301) ( 0.020301,0.020516 ) ( 0.021160,0.021394 ) ( 0.022095,0.022350 ) ( 0.023117,0.023396 ) ( 0.024238,0.024545 ) ( 0.025472,0.025812 ) ( 0.026840,0.027217 ) ( 0.028362,0.028784 ) ( 0.030068,0.030542 ) ( 0.031992,0.032529 ) ( 0.034178,0.034793 ) ( 0.036686,0.037395 ) ( 0.039591,0.040417 ) ( 0.042996,0.043972 ) ( 0.047041,0.048212 ) ( 0.051926,0.053357 ) ( 0.057943,0.060541 ) ( 0.064589,0.068882 ) ( 0.074171,0.079888 ) ( 0.087090,0.095079 ) ( 0.105092,0.117862 ) ( 0.133059,infinity ) The half-space computation does not determine rationality. EXCLUDED INTERVALS FOR JUST THE SUPPLEMENTAL HALF-SPACE COMPUTATION INTERVAL COMPUTED FOR HST OR EXTENDED HST (-0.145429,-0.112901) -3/23 EXTENDED HST -> HST (-0.125270,-0.124732) -1/8 EXTENDED HST (-0.115884,-0.089404) -3/29 EXTENDED HST -> HST (-0.100172,-0.099828) -1/10 EXTENDED HST (-0.088569,-0.085603) -29/333 HST (-0.087069,-0.086844) -2/23 EXTENDED HST (-0.096317,-0.074003) -7/82 HST (-0.085265,-0.084549) -4/47 EXTENDED HST -> HST (-0.083453,-0.083214) -1/12 EXTENDED HST (-0.082403,-0.063128) -3/41 EXTENDED HST -> HST (-0.071516,-0.071341) -1/14 EXTENDED HST (-0.071866,-0.054136) -7/111 HST (-0.062567,-0.062433) -1/16 EXTENDED HST (-0.054171,-0.054091) -19/351 HST (-0.054099,-0.053432) -2/37 EXTENDED HST -> HST (-0.058820,-0.047806) -11/206 HST (-0.047205,-0.046550) -3/64 HST (-0.047358,-0.045739) -29/623 HST (-0.046544,-0.046479) -2/43 EXTENDED HST (-0.052237,-0.039200) -8/175 HST (-0.045490,-0.045419) -1/22 EXTENDED HST (-0.044142,-0.033548) -3/77 HST (-0.038487,-0.038436) -1/26 EXTENDED HST (-0.038293,-0.028657) -6/179 HST (-0.033352,-0.033314) -1/30 EXTENDED HST (-0.028422,-0.028183) -3/106 HST (-0.028677,-0.027688) -29/1029 HST (-0.028181,-0.028157) -2/71 EXTENDED HST (-0.027791,-0.027765) -1/36 EXTENDED HST (-0.029387,-0.025503) -3/109 HST (-0.027409,-0.027236) -2/73 HST (-0.025520,-0.025328) -3/118 HST (-0.025773,-0.024882) -29/1145 HST (-0.025326,-0.025307) -2/79 EXTENDED HST (-0.025011,-0.024989) -1/40 EXTENDED HST (-0.026487,-0.022973) -3/121 HST (-0.024701,-0.024561) -2/81 HST (-0.026020,-0.019701) -3/131 HST (-0.022736,-0.022718) -1/44 EXTENDED HST (-0.132815,0.180951 ) 0/1 EXTENDED HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION There are no slope function fixed points because every loop multiplier of the mod 2 slope correspondence graph is at least 1 and the map is rational. No nontrivial cycles were found. The slope function maps some slope to the nonslope. The slope function orbit of every slope p/q with |p| <= 50 and |q| <= 50 ends in the nonslope. If the slope function maps slope p/q to slope p'/q', then |q'| <= |q| for every slope p/q with |p| <= 50 and |q| <= 50. FUNDAMENTAL GROUP WREATH RECURSIONS When the translation term of the affine map is 0: NewSphereMachine( "a=(2,15)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9)", "b=(1,15)(2,14)(3,13)(4,12)(5,11)(6,10)(7,9)", "c=(1,15)(2,14)(3,13)(4,12)(5,11)(6,10)(7,9)", "d=<1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,c,c,c>(2,15)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,2)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)", "b=(2,15)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9)", "c=<1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,c,c,c>(2,15)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9)", "d=<1,d,c^-1,c^-1,1,1,1,1,1,1,1,1,1,c,c>(1,2)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)", "b=(1,15)(2,14)(3,13)(4,12)(5,11)(6,10)(7,9)", "c=(1,15)(2,14)(3,13)(4,12)(5,11)(6,10)(7,9)", "d=(1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,15)(2,14)(3,13)(4,12)(5,11)(6,10)(7,9)", "b=<1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,c,c,c>(2,15)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9)", "c=(2,15)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9)", "d=(1,15)(2,14)(3,13)(4,12)(5,11)(6,10)(7,9)", "a*b*c*d");