These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 32. 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 14. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/16, 0/32, 2/8, 2/4, 2/2, 4/4, 2/1, 4/2, 6/2, 4/1, 10/2, 6/1, 10/1, 12/1 14/1, 18/1, 20/1, 29/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,0.032879) ( 0.036145,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 (0.032641,0.033010) 5/152 HST (0.032962,0.032972) 3/91 EXTENDED HST (0.033003,0.033058) 7/212 HST (0.033040,0.033096) 4/121 HST (0.033088,0.033133) 5/151 HST (0.033018,0.033224) 11/332 HST (0.033141,0.033173) 6/181 HST (0.033167,0.033297) 11/331 HST (0.033262,0.033333) 31/931 HST (0.033319,0.033333) 159/4771 HST (0.033326,0.033340) 1/30 EXTENDED HST (0.033333,0.033401) 28/839 HST (0.033374,0.033375) 27/809 HST (0.033376,0.033378) 26/779 HST (0.033376,0.033393) 22/659 HST (0.033386,0.033390) 21/629 HST (0.033389,0.033496) 10/299 HST (0.033447,0.033487) 8/239 HST (0.033478,0.033511) 7/209 HST (0.033493,0.033535) 31/925 HST (0.033514,0.033545) 6/179 HST (0.033534,0.033561) 21/626 HST (0.033555,0.033560) 5/149 EXTENDED HST (0.033553,0.033570) 113/3367 HST (0.033561,0.033632) 4/119 HST (0.033581,0.033691) 11/327 HST (0.033640,0.033677) 7/208 HST (0.033654,0.033784) 3/89 HST (0.033768,0.033824) 5/148 HST (0.033758,0.033980) 9/266 HST (0.033894,0.033903) 2/59 EXTENDED HST (0.033898,0.034188) 3/88 HST (0.034097,0.034391) 4/117 HST (0.034375,0.034416) 13/378 HST (0.034389,0.034450) 18/523 HST (0.034433,0.034538) 1/29 EXTENDED HST (0.034525,0.034621) 14/405 HST (0.034568,0.034934) 5/144 HST (0.034768,0.034914) 4/115 HST (0.034810,0.035156) 2/57 HST (0.035088,0.035714) 3/85 HST (0.035498,0.037273) 1/28 EXTENDED HST -> HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION There are no slope function fixed points p/q with |p| <= 50 and |q| <= 50. The fixed point finder is unable to determine whether there are any slope function fixed points. Number of excluded intervals computed by the fixed point finder: 6983 Here is their union. There are no slope function fixed points whose negative reciprocals lie in any of the following intervals. EXCLUDED INTERVALS FOR THE FIXED POINT COMPUTATION ( -infinity,0.016100) ( 0.016100,0.033111) ( 0.033111,0.033330) ( 0.033330,0.033330) ( 0.033333,0.033334) ( 0.034482,0.034484) ( 0.035713,0.035716) ( 0.036954,0.037126) ( 0.038456,0.038467) ( 0.039989,0.040011) ( 0.041650,0.041684) ( 0.043137,0.043847) ( 0.045435,0.045474) ( 0.047592,0.047646) ( 0.049947,0.050052) ( 0.051643,0.053726) ( 0.055489,0.055625) ( 0.058758,0.058890) ( 0.062413,0.062592) ( 0.064833,0.068736) ( 0.071309,0.071548) ( 0.076807,0.077040) ( 0.083165,0.083501) ( 0.086614,0.095975) ( 0.099745,0.100254) ( 0.110861,0.111367) ( 0.124606,0.125402) ( 0.131474,0.157360) ( 0.165930,0.167401) ( 0.198360,0.201722) ( 0.248430,0.251709) ( 0.277311,0.424658) ( 0.493713,0.506663) ( 0.960314,1.044583) (103.537815,infinity) 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,d*b,b,b,b,b,b,b,b,b,b,b,b,b,b,b,b,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1*d^-1>(2,32)(3,31)(4,30)(5,29)(6,28)(7,27)(8,26)(9,25)(10,24)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)", "b=(1,32)(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "c=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c>(2,32)(3,31)(4,30)(5,29)(6,28)(7,27)(8,26)(9,25)(10,24)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)", "d=(1,2)(3,32)(4,31)(5,30)(6,29)(7,28)(8,27)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,32)(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "b=(1,31)(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)", "c=(1,32)(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "d=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c>(2,32)(3,31)(4,30)(5,29)(6,28)(7,27)(8,26)(9,25)(10,24)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,32)(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "b=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c>(2,32)(3,31)(4,30)(5,29)(6,28)(7,27)(8,26)(9,25)(10,24)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)", "c=(1,32)(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "d=(1,31)(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,31)(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)", "b=(1,32)(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "c=(1,31)(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)", "d=(1,30)(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(31,32)", "a*b*c*d"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow halted evaluation of the slope function at slope -3284413/52879 while computing a fixed point excluded interval about 41293/2564785. Imminent integer overflow halted evaluation of the slope function at slope -9373487/150913 while computing a fixed point excluded interval about 50948/3164475. Imminent integer overflow halted evaluation of the slope function at slope -15462561/248947 while computing a fixed point excluded interval about 50948/3164475. Imminent integer overflow halted evaluation of the slope function at slope -10332991/166361 while computing a fixed point excluded interval about 50948/3164475. Imminent integer overflow halted evaluation of the slope function at slope -33729783/543049 while computing a fixed point excluded interval about 50948/3164475. Imminent integer overflow halted evaluation of the slope function at slope -45907931/739117 while computing a fixed point excluded interval about 50948/3164475. Imminent integer overflow halted evaluation of the slope function at slope -117633029/1893891 while computing a fixed point excluded interval about 178795/11105284. Imminent integer overflow halted evaluation of the slope function at slope -4644183/112117 while computing a fixed point excluded interval about 98853/4094753. Imminent integer overflow halted evaluation of the slope function at slope -2816515/93257 during the search for all slope function fixed points. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 1593/47884. Imminent integer overflow halted evaluation of the slope function at slope -13935247/464409 while computing a fixed point excluded interval about 154751/4643522. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 6815/204482. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 6815/204482. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 7583/227522. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 7583/227522. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 7839/235202. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 254/7621. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 8097/242942. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 8097/242942. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 262/7861. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 278/8341. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 284/8521. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 302/9061. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 308/9241. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 318/9541. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 324/9721. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 326/9781. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 340/10201. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 348/10441. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 372/11161. Imminent integer overflow caused the modular group computation to abort.