These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 23. 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 0/23, 1/23, 1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 7/1, 8/1, 9/1, 15/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.487382) (-1.484848,-1.452754) (-1.449009,-1.447521) (-1.446889,-1.424046) (-1.420425,-1.418255) (-1.413877,-1.244773) (-1.243902,-1.242424) (-1.241620,-1.241124) (-1.240339,-1.000000) (-1.000000,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 (-1.487911,-1.486737) -235/158 HST (-1.487315,-1.487041) -58/39 HST (-1.486774,-1.486676) -168/113 HST (-1.487746,-1.485516) -223/150 HST (-1.486493,-1.486480) -55/37 EXTENDED HST (-1.485882,-1.485542) -52/35 HST (-1.487060,-1.483385) -101/68 HST (-1.484857,-1.484840) -49/33 EXTENDED HST (-1.457525,-1.446647) -61/42 HST (-1.451641,-1.451585) -45/31 EXTENDED HST (-1.450045,-1.449955) -29/20 EXTENDED HST (-1.425147,-1.422389) -84/59 HST (-1.423131,-1.423023) -37/26 EXTENDED HST (-1.422936,-1.421495) -64/45 HST (-1.421757,-1.421216) -172/121 HST (-1.421297,-1.421109) -469/330 HST (-1.421128,-1.420977) -27/19 EXTENDED HST (-1.421012,-1.420877) -719/506 HST (-1.420945,-1.420584) -287/202 HST (-1.420769,-1.419805) -125/88 HST (-1.419532,-1.416911) -78/55 HST (-1.418053,-1.411352) -17/12 EXTENDED HST -> HST (-1.244786,-1.244724) -178/143 HST (-1.244726,-1.244700) -412/331 HST (-1.244702,-1.244690) -763/613 HST (-1.244773,-1.244605) -1582/1271 HST (-1.244683,-1.244679) -117/94 EXTENDED HST (-1.244963,-1.244192) -173/139 HST (-1.244546,-1.244340) -56/45 HST (-1.244304,-1.244079) -2624/2109 HST (-1.244188,-1.244184) -107/86 EXTENDED HST (-1.244133,-1.244055) -367/295 HST (-1.244201,-1.243909) -994/799 HST (-1.244049,-1.244046) -209/168 EXTENDED HST (-1.243910,-1.243907) -4901/3940 HST (-1.243908,-1.243897) -51/41 EXTENDED HST (-1.242433,-1.242416) -41/33 EXTENDED HST (-1.242563,-1.242177) -692/557 HST (-1.242368,-1.242338) -569/458 HST (-1.242358,-1.242322) -487/392 HST (-1.242343,-1.242299) -364/293 HST (-1.242319,-1.242262) -282/227 HST (-1.242276,-1.242196) -200/161 HST (-1.242190,-1.242185) -159/128 EXTENDED HST (-1.242352,-1.241997) -754/607 HST (-1.242174,-1.242035) -118/95 HST (-1.242002,-1.241963) -349/281 HST (-1.242123,-1.241804) -734/591 HST (-1.241940,-1.241931) -77/62 EXTENDED HST (-1.241811,-1.241771) -303/244 HST (-1.241775,-1.241762) -1207/972 HST (-1.241795,-1.241729) -3580/2883 HST (-1.241762,-1.241755) -113/91 EXTENDED HST (-1.241739,-1.241673) -262/211 HST (-1.241677,-1.241668) -1603/1291 HST (-1.241669,-1.241664) -149/120 EXTENDED HST (-1.241666,-1.241658) -2122/1709 HST (-1.241662,-1.241610) -334/269 HST (-1.241506,-1.240552) -139/112 HST (-1.240968,-1.240960) -103/83 EXTENDED HST (-1.240747,-1.240735) -67/54 EXTENDED HST (-1.240606,-1.240405) -98/79 HST (-1.241031,-1.239603) -129/104 HST (-1.008904,-0.990413) -1/1 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. FUNDAMENTAL GROUP WREATH RECURSIONS When the translation term of the affine map is 0: NewSphereMachine( "a=<1,b,c^-1*b,c^-1*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,b^-1*c,b^-1*c,b^-1*c>(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "b=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "c=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "d=<1,a*b,a*b,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,c,c*d,c*d,c*d,c*d>(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,2)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "b=<1,b,c^-1*b,c^-1*b,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,c,c,c,b^-1*c,b^-1*c,b^-1*c>(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "c=<1,a*b,a*b,a*b,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,c,c,c*d,c*d,c*d,c*d>(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "d=<1,1,a*b,a*b,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,c,c,c*d,c*d,c*d>(1,2)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,22)(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)", "b=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "c=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "d=(1,22)(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "b=<1,a*b,a*b,a*b,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,c,c,c*d,c*d,c*d,c*d>(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "c=<1,b,c^-1*b,c^-1*b,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,c,c,c,b^-1*c,b^-1*c,b^-1*c>(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "d=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "a*b*c*d");