These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 25. 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, 0/5, 0/25, 1/25, 1/5, 3/5, 1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 7/1, 8/1, 9/1 10/1, 11/1, 15/1, 17/1, 18/1, 20/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.400564) (-0.398810,-0.223577) (-0.221702,-0.182168) (-0.180412,-0.178571) (-0.178571,-0.174419) (-0.171569,-0.169903) (-0.163551,-0.162037) (-0.159574,-0.156250) (-0.156250,-0.154867) (-0.153597,-0.133521) (-0.131579,-0.129310) (-0.120968,-0.119048) (-0.117501,-0.105380) (-0.104167,-0.102740) (-0.097403,-0.096154) (-0.092593,-0.089286) (-0.086207,-0.085227) (-0.081522,-0.080645) (-0.078125,-0.075758) (-0.073529,-0.072816) (-0.070093,-0.069444) (-0.067568,-0.065789) (-0.064103,-0.063559) (-0.061475,-0.060976) (-0.059524,-0.058140) (-0.053191,-0.052083) (-0.048077,-0.047170) (-0.043860,-0.043103) (-0.040323,-0.039683) (-0.037313,-0.036765) (-0.034722,-0.034247) (-0.032468,-0.032051) (-0.030488,-0.030120) (-0.028736,-0.028409) (-0.027174,-0.026882) (-0.025773,-0.025510) (-0.024510,-0.024272) (-0.023364,-0.023148) (-0.022321,-0.022124) (-0.021368,-0.021186) (-0.020492,-0.020325) ( 0.020325,0.020492 ) ( 0.021186,0.021368 ) ( 0.022124,0.022321 ) ( 0.023148,0.023364 ) ( 0.024272,0.024510 ) ( 0.025510,0.025773 ) ( 0.026882,0.027174 ) ( 0.028409,0.028736 ) ( 0.030120,0.030488 ) ( 0.032051,0.032468 ) ( 0.034247,0.034722 ) ( 0.036765,0.037313 ) ( 0.039683,0.040323 ) ( 0.043103,0.043860 ) ( 0.047170,0.048077 ) ( 0.052083,0.053191 ) ( 0.058140,0.059524 ) ( 0.060976,0.061475 ) ( 0.063559,0.064103 ) ( 0.065789,0.067568 ) ( 0.069444,0.070093 ) ( 0.072816,0.073529 ) ( 0.075758,0.078125 ) ( 0.080645,0.081522 ) ( 0.085227,0.086207 ) ( 0.089286,0.092593 ) ( 0.096154,0.097403 ) ( 0.102740,0.104167 ) ( 0.105380,0.117501 ) ( 0.119048,0.120968 ) ( 0.129310,0.131579 ) ( 0.133521,0.153597 ) ( 0.154867,0.156250 ) ( 0.156250,0.159574 ) ( 0.162037,0.163551 ) ( 0.169903,0.171569 ) ( 0.174419,0.178571 ) ( 0.178571,0.180412 ) ( 0.182168,0.221702 ) ( 0.222689,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 (-0.401436,-0.398574) -2/5 EXTENDED HST (-0.225581,-0.221429) -19/85 HST (-0.222665,-0.221781) -2/9 EXTENDED HST (-0.186317,-0.177584) -125/687 HST (-0.181951,-0.181686) -2/11 EXTENDED HST (-0.177249,-0.169355) -4/23 EXTENDED HST -> HST (-0.174847,-0.163580) -11/65 HST (-0.166889,-0.166445) -1/6 EXTENDED HST (-0.164234,-0.163043) -53/324 HST (-0.164740,-0.154070) -4/25 EXTENDED HST -> HST (-0.155981,-0.152128) -53/344 HST (-0.154058,-0.153635) -2/13 EXTENDED HST (-0.136606,-0.130203) -125/937 HST (-0.133404,-0.133262) -2/15 EXTENDED HST (-0.131890,-0.125498) -4/31 EXTENDED HST -> HST (-0.126707,-0.124238) -32/255 HST (-0.125125,-0.124875) -1/8 EXTENDED HST (-0.125000,-0.116740) -4/33 EXTENDED HST -> HST (-0.107835,-0.102780) -125/1187 HST (-0.105307,-0.105219) -2/19 EXTENDED HST (-0.105016,-0.099684) -4/39 EXTENDED HST -> HST (-0.100080,-0.099920) -1/10 EXTENDED HST (-0.100707,-0.093972) -4/41 EXTENDED HST -> HST (-0.095604,-0.092222) -14/149 HST (-0.093940,-0.091283) -5/54 HST (-0.090538,-0.088068) -5/56 HST (-0.089074,-0.084899) -125/1437 HST (-0.086987,-0.086926) -2/23 EXTENDED HST (-0.086481,-0.082669) -5/59 HST (-0.083389,-0.083278) -1/12 EXTENDED HST (-0.084320,-0.078635) -4/49 EXTENDED HST -> HST (-0.079082,-0.077191) -5/64 HST (-0.076657,-0.074879) -5/66 HST (-0.075874,-0.072318) -125/1687 HST (-0.074096,-0.074052) -2/27 EXTENDED HST (-0.078340,-0.066230) -35/484 HST (-0.072314,-0.072016) -6/83 HST (-0.071469,-0.071388) -1/14 EXTENDED HST (-0.066467,-0.065126) -5/76 HST (-0.066082,-0.062984) -125/1937 HST (-0.064533,-0.064499) -2/31 EXTENDED HST (-0.063025,-0.062849) -9/143 HST (-0.066346,-0.059223) -12/191 HST (-0.062531,-0.062469) -1/16 EXTENDED HST (-0.058668,-0.057621) -5/86 HST (-0.058528,-0.055784) -125/2187 HST (-0.057156,-0.057130) -2/35 EXTENDED HST (-0.058974,-0.052586) -14/251 HST (-0.055580,-0.055531) -1/18 EXTENDED HST (-0.052507,-0.051666) -5/96 HST (-0.052524,-0.050062) -125/2437 HST (-0.051293,-0.051272) -2/39 EXTENDED HST (-0.050073,-0.050049) -41/819 HST (-0.050057,-0.050038) -52/1039 HST (-0.050329,-0.049746) -67/1339 HST (-0.050020,-0.049980) -1/20 EXTENDED HST (-0.051075,-0.047576) -4/81 HST (-0.049342,-0.049020) -3/61 HST (-0.048802,-0.048759) -2/41 EXTENDED HST (-0.047517,-0.046828) -5/106 HST (-0.047637,-0.045404) -125/2687 HST (-0.046520,-0.046503) -2/43 EXTENDED HST (-0.045471,-0.045438) -1/22 EXTENDED HST (-0.046493,-0.043301) -4/89 HST (-0.044910,-0.044643) -3/67 HST (-0.044462,-0.044427) -2/45 EXTENDED HST (-0.043393,-0.042818) -5/116 HST (-0.043582,-0.041539) -125/2937 HST (-0.042560,-0.042546) -2/47 EXTENDED HST (-0.041681,-0.041653) -1/24 EXTENDED HST (-0.042665,-0.039730) -4/97 HST (-0.041209,-0.040984) -3/73 HST (-0.040831,-0.040801) -2/49 EXTENDED HST (-0.039928,-0.039440) -5/126 HST (-0.040163,-0.038281) -125/3187 HST (-0.039222,-0.039210) -2/51 EXTENDED HST (-0.038473,-0.038450) -1/26 EXTENDED HST (-0.039419,-0.036704) -4/105 HST (-0.038071,-0.037879) -3/79 HST (-0.037749,-0.037723) -2/53 EXTENDED HST (-0.036975,-0.036556) -4/109 HST (-0.036616,-0.036378) -3/82 HST (-0.037242,-0.035496) -125/3437 HST (-0.036369,-0.036358) -2/55 EXTENDED HST (-0.035724,-0.035704) -1/28 EXTENDED HST (-0.036632,-0.034106) -4/113 HST (-0.035377,-0.035211) -3/85 HST (-0.035099,-0.035077) -2/57 EXTENDED HST (-0.034117,-0.033910) -3/88 HST (-0.034717,-0.033089) -125/3687 HST (-0.033903,-0.033894) -2/59 EXTENDED HST (-0.033342,-0.033324) -1/30 EXTENDED HST (-0.034214,-0.031851) -4/121 HST (-0.033040,-0.032895) -3/91 HST (-0.032797,-0.032777) -2/61 EXTENDED HST (-0.032512,-0.030988) -125/3937 HST (-0.031750,-0.031742) -2/63 EXTENDED HST (-0.031258,-0.031242) -1/32 EXTENDED HST (-0.030992,-0.030864) -3/97 HST (-0.031545,-0.030160) -5/162 HST (-0.030778,-0.030761) -2/65 EXTENDED HST (-0.030262,-0.029981) -5/166 HST (-0.030571,-0.029138) -125/4187 HST (-0.029854,-0.029847) -2/67 EXTENDED HST (-0.029419,-0.029405) -1/34 EXTENDED HST (-0.029183,-0.029070) -3/103 HST (-0.029713,-0.028405) -5/172 HST (-0.028993,-0.028978) -2/69 EXTENDED HST (-0.028535,-0.028285) -4/141 HST (-0.028320,-0.028177) -3/106 HST (-0.028848,-0.027496) -125/4437 HST (-0.028172,-0.028166) -2/71 EXTENDED HST (-0.027784,-0.027772) -1/36 EXTENDED HST (-0.028083,-0.026843) -5/182 HST (-0.027404,-0.027391) -2/73 EXTENDED HST (-0.027404,-0.026284) -83/3092 HST (-0.026840,-0.026799) -7/261 HST (-0.026802,-0.026674) -3/112 HST (-0.026670,-0.026664) -2/75 EXTENDED HST (-0.026321,-0.026310) -1/38 EXTENDED HST (-0.027066,-0.025190) -4/153 HST (-0.026132,-0.026042) -3/115 HST (-0.025980,-0.025968) -2/77 EXTENDED HST (-0.025889,-0.024400) -4/159 HST (-0.025005,-0.024995) -1/40 EXTENDED HST (-0.024363,-0.024181) -5/206 HST (-0.024677,-0.023520) -125/5187 HST (-0.024099,-0.024094) -2/83 EXTENDED HST (-0.023814,-0.023805) -1/42 EXTENDED HST (-0.023524,-0.023425) -5/213 HST (-0.023449,-0.023280) -5/214 HST (-0.023231,-0.023065) -5/216 HST (-0.023542,-0.022439) -125/5437 HST (-0.022991,-0.022986) -2/87 EXTENDED HST (-0.022731,-0.022723) -1/44 EXTENDED HST (-0.022467,-0.022377) -5/223 HST (-0.022399,-0.022245) -5/224 HST (-0.022200,-0.022048) -5/226 HST (-0.022507,-0.021452) -125/5687 HST (-0.021980,-0.021976) -2/91 EXTENDED HST (-0.021743,-0.021735) -1/46 EXTENDED HST (-0.022196,-0.020687) -8/373 HST (-0.021438,-0.021297) -5/234 HST (-0.021127,-0.020185) -5/242 HST (-0.020622,-0.020615) -2/97 EXTENDED HST (-0.035713,0.038464 ) 0/1 EXTENDED HST ( 0.038433,0.038496 ) 512/13311 HST ( 0.037429,0.040311 ) 4/103 HST ( 0.038860,0.039062 ) 3/77 HST ( 0.039202,0.039229 ) 2/51 EXTENDED HST ( 0.039440,0.039928 ) 5/126 HST ( 0.040072,0.040576 ) 5/124 HST ( 0.040503,0.040799 ) 5/123 HST ( 0.040460,0.041139 ) 49/1201 HST ( 0.040810,0.040823 ) 2/49 EXTENDED HST ( 0.039924,0.042621 ) 4/97 HST ( 0.041653,0.041681 ) 1/24 EXTENDED HST ( 0.042572,0.042899 ) 5/117 HST ( 0.042818,0.043393 ) 5/116 HST ( 0.043564,0.044160 ) 5/114 HST ( 0.044073,0.044424 ) 5/113 HST ( 0.044054,0.044795 ) 49/1103 HST ( 0.044437,0.044452 ) 2/45 EXTENDED HST ( 0.043508,0.046463 ) 4/89 HST ( 0.045438,0.045471 ) 1/22 EXTENDED HST ( 0.046446,0.046483 ) 23/495 HST ( 0.045974,0.046994 ) 39/839 HST ( 0.046492,0.046531 ) 2/43 EXTENDED HST ( 0.046828,0.047517 ) 5/106 HST ( 0.047721,0.048438 ) 5/104 HST ( 0.048334,0.048755 ) 5/103 HST ( 0.048349,0.049164 ) 49/1005 HST ( 0.048771,0.048790 ) 2/41 EXTENDED HST ( 0.049020,0.049342 ) 3/61 HST ( 0.047800,0.051067 ) 4/81 HST ( 0.049980,0.050020 ) 1/20 EXTENDED HST ( 0.051020,0.051170 ) 7/137 HST ( 0.051117,0.051273 ) 13/254 HST ( 0.051259,0.051306 ) 2/39 EXTENDED HST ( 0.050858,0.051760 ) 49/955 HST ( 0.051310,0.051785 ) 5/97 HST ( 0.051666,0.052507 ) 5/96 HST ( 0.052757,0.053633 ) 5/94 HST ( 0.053506,0.054023 ) 5/93 HST ( 0.053571,0.054477 ) 49/907 HST ( 0.054042,0.054066 ) 2/37 EXTENDED HST ( 0.054348,0.054745 ) 3/55 HST ( 0.053030,0.056684 ) 4/73 HST ( 0.055531,0.055580 ) 1/18 EXTENDED HST ( 0.055407,0.058311 ) 5/88 HST ( 0.057114,0.057172 ) 2/35 EXTENDED HST ( 0.057621,0.058668 ) 5/86 HST ( 0.058980,0.060078 ) 5/84 HST ( 0.059918,0.060567 ) 5/83 HST ( 0.060059,0.061078 ) 49/809 HST ( 0.060591,0.060621 ) 2/33 EXTENDED HST ( 0.059546,0.063688 ) 4/65 HST ( 0.062469,0.062531 ) 1/16 EXTENDED HST ( 0.062500,0.065809 ) 5/78 HST ( 0.064479,0.064553 ) 2/31 EXTENDED HST ( 0.065126,0.066467 ) 5/76 HST ( 0.066868,0.068282 ) 5/74 HST ( 0.068076,0.068915 ) 5/73 HST ( 0.068335,0.069499 ) 49/711 HST ( 0.068946,0.068985 ) 2/29 EXTENDED HST ( 0.067888,0.072668 ) 4/57 HST ( 0.071388,0.071469 ) 1/14 EXTENDED HST ( 0.070106,0.075597 ) 4/55 HST ( 0.074879,0.076657 ) 5/66 HST ( 0.077191,0.079082 ) 5/64 HST ( 0.078806,0.079932 ) 5/63 HST ( 0.079256,0.080614 ) 49/613 HST ( 0.079974,0.080026 ) 2/25 EXTENDED HST ( 0.078164,0.083333 ) 5/62 HST ( 0.083278,0.083389 ) 1/12 EXTENDED HST ( 0.082043,0.088509 ) 4/47 EXTENDED HST -> HST ( 0.088068,0.090538 ) 5/56 HST ( 0.091283,0.093940 ) 5/54 HST ( 0.093550,0.095142 ) 5/53 HST ( 0.094332,0.095960 ) 49/515 HST ( 0.095202,0.095274 ) 2/21 EXTENDED HST ( 0.093195,0.099407 ) 5/52 HST ( 0.096963,0.101874 ) 17/171 HST ( 0.099920,0.100080 ) 1/10 EXTENDED HST ( 0.098881,0.106742 ) 4/39 EXTENDED HST -> HST ( 0.116491,0.118522 ) 49/417 HST ( 0.117592,0.117702 ) 2/17 EXTENDED HST ( 0.115385,0.123162 ) 5/42 EXTENDED HST -> HST ( 0.122951,0.123626 ) 9/73 HST ( 0.115094,0.132692 ) 12/97 HST ( 0.124875,0.125125 ) 1/8 EXTENDED HST ( 0.132220,0.133271 ) 15/113 HST ( 0.133175,0.133493 ) 2/15 EXTENDED HST ( 0.132209,0.134825 ) 49/367 HST ( 0.152256,0.154956 ) 49/319 HST ( 0.153752,0.153941 ) 2/13 EXTENDED HST ( 0.151442,0.161836 ) 5/32 EXTENDED HST -> HST ( 0.146121,0.178300 ) 35/216 HST ( 0.173640,0.184322 ) 5/28 EXTENDED HST -> HST ( 0.219711,0.223732 ) 49/221 HST ( 0.222025,0.222420 ) 2/9 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=(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "b=(1,25)(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "c=(1,25)(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "d=<1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c>(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,2)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)", "b=(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "c=<1,c^-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,c>(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "d=<1,d,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c>(1,2)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,24)(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "b=(1,25)(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "c=(1,25)(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "d=(1,24)(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+lambda2: NewSphereMachine( "a=(1,25)(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "b=<1,c^-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,c>(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "c=(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "d=(1,25)(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "a*b*c*d");