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 only finitely many Thurston equivalence classes. However, this modular group Hurwitz class contains 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, 0/23, 1/23, 1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 7/1, 8/1, 9/1, 10/1, 11/1 15/1, 16/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.125994) (-0.125369,-0.098825) (-0.097430,-0.096128) (-0.092666,-0.089218) (-0.086228,-0.085207) (-0.081541,-0.080627) (-0.078177,-0.075709) (-0.073545,-0.072800) (-0.070107,-0.069431) (-0.067606,-0.065753) (-0.064114,-0.063548) (-0.061486,-0.060965) (-0.059554,-0.058111) (-0.053216,-0.052060) (-0.048097,-0.047151) (-0.043876,-0.043088) (-0.040336,-0.039669) (-0.037325,-0.036753) (-0.034732,-0.034237) (-0.032477,-0.032043) (-0.030496,-0.030113) (-0.028743,-0.028402) (-0.027180,-0.026876) (-0.025779,-0.025505) (-0.024515,-0.024267) (-0.023369,-0.023144) (-0.022326,-0.022120) (-0.021371,-0.021183) (-0.020495,-0.020322) ( 0.020322,0.020495 ) ( 0.021183,0.021371 ) ( 0.022120,0.022326 ) ( 0.023144,0.023369 ) ( 0.024267,0.024515 ) ( 0.025505,0.025779 ) ( 0.026876,0.027180 ) ( 0.028402,0.028743 ) ( 0.030113,0.030496 ) ( 0.032043,0.032477 ) ( 0.034237,0.034732 ) ( 0.036753,0.037325 ) ( 0.039669,0.040336 ) ( 0.043088,0.043876 ) ( 0.047151,0.048097 ) ( 0.052060,0.053216 ) ( 0.058111,0.059554 ) ( 0.060965,0.061486 ) ( 0.063548,0.064114 ) ( 0.065753,0.067606 ) ( 0.069431,0.070107 ) ( 0.072800,0.073545 ) ( 0.075709,0.078177 ) ( 0.080627,0.081541 ) ( 0.085207,0.086228 ) ( 0.089218,0.092666 ) ( 0.096128,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 (-0.126121,-0.125732) -16/127 HST (-0.138991,-0.111958) -22/175 HST (-0.100112,-0.094527) -4/41 EXTENDED HST -> HST (-0.098076,-0.088511) -3/32 EXTENDED HST -> HST (-0.094004,-0.081295) -3/34 EXTENDED HST -> HST (-0.086991,-0.086922) -2/23 EXTENDED HST (-0.085701,-0.072987) -2/25 EXTENDED HST -> HST (-0.072855,-0.072739) -19/261 HST (-0.072739,-0.072715) -4/55 EXTENDED HST (-0.072720,-0.072644) -33/454 HST (-0.072683,-0.072245) -5/69 HST (-0.076300,-0.068012) -7/97 HST (-0.071475,-0.071382) -1/14 EXTENDED HST (-0.071575,-0.064303) -7/103 HST (-0.067807,-0.067786) -4/59 EXTENDED HST (-0.064343,-0.064098) -7/109 HST (-0.063589,-0.063501) -19/299 HST (-0.063501,-0.063483) -4/63 EXTENDED HST (-0.063486,-0.063428) -33/520 HST (-0.063459,-0.063125) -5/79 HST (-0.066695,-0.059418) -7/111 HST (-0.062535,-0.062465) -1/16 EXTENDED HST (-0.061820,-0.053059) -3/52 HST (-0.057158,-0.057128) -2/35 EXTENDED HST (-0.055584,-0.055528) -1/18 EXTENDED HST (-0.055488,-0.047554) -3/58 HST (-0.051294,-0.051270) -2/39 EXTENDED HST (-0.050023,-0.049977) -1/20 EXTENDED HST (-0.050332,-0.043083) -3/64 HST (-0.046521,-0.046502) -2/43 EXTENDED HST (-0.045473,-0.045436) -1/22 EXTENDED HST (-0.046053,-0.039381) -3/70 HST (-0.042561,-0.042545) -2/47 EXTENDED HST (-0.041682,-0.041651) -1/24 EXTENDED HST (-0.042445,-0.036265) -5/127 HST (-0.039223,-0.039209) -2/51 EXTENDED HST (-0.038475,-0.038448) -1/26 EXTENDED HST (-0.036309,-0.036230) -33/910 HST (-0.036263,-0.036231) -12/331 HST (-0.036236,-0.036054) -3/83 HST (-0.036067,-0.036039) -19/527 HST (-0.036039,-0.036033) -4/111 EXTENDED HST (-0.036034,-0.036016) -33/916 HST (-0.036025,-0.035917) -5/139 HST (-0.037995,-0.033795) -7/195 HST (-0.035726,-0.035703) -1/28 EXTENDED HST (-0.033801,-0.033783) -22/651 HST (-0.033787,-0.033629) -3/89 HST (-0.033641,-0.033616) -19/565 HST (-0.033616,-0.033611) -4/119 EXTENDED HST (-0.033612,-0.033596) -33/982 HST (-0.033604,-0.033510) -5/149 HST (-0.035453,-0.031529) -7/209 HST (-0.033343,-0.033323) -1/30 EXTENDED HST (-0.032733,-0.030306) -11/349 HST (-0.031498,-0.031494) -4/127 EXTENDED HST (-0.031259,-0.031241) -1/32 EXTENDED HST (-0.032316,-0.027546) -3/100 HST (-0.029855,-0.029847) -2/67 EXTENDED HST (-0.029420,-0.029404) -1/34 EXTENDED HST (-0.029568,-0.025072) -2/73 HST (-0.025084,-0.025055) -9/359 HST (-0.025821,-0.024274) -12/479 HST (-0.025006,-0.024994) -1/40 EXTENDED HST (-0.026090,-0.022207) -3/124 HST (-0.024099,-0.024094) -2/83 EXTENDED HST (-0.023815,-0.023804) -1/42 EXTENDED HST (-0.023798,-0.020245) -3/136 HST (-0.021980,-0.021976) -2/91 EXTENDED HST (-0.021743,-0.021735) -1/46 EXTENDED HST (-0.080056,0.095345 ) 0/1 EXTENDED HST ( 0.088240,0.103092 ) 13/136 HST ( 0.095617,0.096165 ) 7/73 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=<1,b,c^-1*b,c^-1*b,c^-1*b,c^-1*b,1,1,1,1,1,1,1,1,1,1,1,1,c,b^-1*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,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,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*b,c^-1*b,c^-1,1,1,1,1,1,1,1,1,1,1,c,c,b^-1*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,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,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,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c>(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,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,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*b,c^-1*b,c^-1,1,1,1,1,1,1,1,1,1,1,c,c,b^-1*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");