{"count":463,"witnesses":[{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.99,"engine_version":"boundary_v3.0","family":"mittag_leffler","param_values":{"alpha":1.75},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.011583767987301099,"theta":3.1538645,"z":"0.999*exp(i*3.153864)"}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.99,"engine_version":"boundary_v3.1","family":"mittag_leffler","param_values":{"alpha":1.75},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.011829800099213264,"theta":3.14772858,"z":"0.999*exp(i*3.147729)"}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.99,"engine_version":"gft-0.1.0-reaudit-20260610","family":"mittag_leffler","param_values":{"alpha":1.75},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.011829800099213264,"theta":3.14772858,"z":"0.999*exp(i*3.147729)"}},{"canonical_key":"z*(z**2/3-z/2+1)","closed_form":"z - z**2/2 + z**3/3","disk_radius":0.99,"engine_version":"boundary_v3.0","family":"z_minus_half_z2_plus_third_z3","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form","witness":{"Re_g_upper_bound":-0.025439720466102524,"theta":1.11980598,"z":"0.999*exp(i*1.119806)"}},{"canonical_key":"z*(z**2/3-z/2+1)","closed_form":"z - z**2/2 + z**3/3","disk_radius":0.99,"engine_version":"gft-0.1.0-reaudit-20260610","family":"z_minus_half_z2_plus_third_z3","param_values":{},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.025439720466102562,"theta":1.11980598,"z":"0.999*exp(i*1.119806)"}},{"canonical_key":"z*(z**2/3-z/2+1)","closed_form":"z - z**2/2 + z**3/3","disk_radius":0.99,"engine_version":"boundary_v3.1","family":"z_minus_half_z2_plus_third_z3","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form_v31","witness":{"Re_g_upper_bound":-0.025439720466102524,"theta":1.11980598,"z":"0.999*exp(i*1.119806)"}},{"canonical_key":"z*(z**2/3+z/2+1)","closed_form":"z + z**2/2 + z**3/3","disk_radius":0.99,"engine_version":"boundary_v3.0","family":"z_plus_half_z2_third_z3","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form","witness":{"Re_g_upper_bound":-0.025439720466102603,"theta":2.02178668,"z":"0.999*exp(i*2.021787)"}},{"canonical_key":"z*(z**2/3+z/2+1)","closed_form":"z + z**2/2 + z**3/3","disk_radius":0.99,"engine_version":"gft-0.1.0-reaudit-20260610","family":"z_plus_half_z2_third_z3","param_values":{},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.02543972046610266,"theta":2.02178668,"z":"0.999*exp(i*2.021787)"}},{"canonical_key":"z*(z**2/3+z/2+1)","closed_form":"z + z**2/2 + z**3/3","disk_radius":0.99,"engine_version":"boundary_v3.1","family":"z_plus_half_z2_third_z3","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form_v31","witness":{"Re_g_upper_bound":-0.025439720466102603,"theta":2.02178668,"z":"0.999*exp(i*2.021787)"}},{"canonical_key":"alternating_signs","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.0","family":"alternating_signs","param_values":{},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.31458301290584584,"theta":3.40351987,"z":"0.99*exp(i*3.40352)"}},{"canonical_key":"alternating_signs","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.1","family":"alternating_signs","param_values":{},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.31642538884683497,"theta":3.40083541,"z":"0.99*exp(i*3.400835)"}},{"canonical_key":"alternating_signs","closed_form":null,"disk_radius":0.95,"engine_version":"gft-0.1.0-reaudit-20260610","family":"alternating_signs","param_values":{},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.2156460433160697,"truncation_caveat":true,"z":[-0.9605927690132365,0.23950267664367106]}},{"canonical_key":"convex_order_extremal","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.0","family":"convex_order","param_values":{"alpha":0.5},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.3145830129058473,"theta":0.26192722,"z":"0.99*exp(i*0.261927)"}},{"canonical_key":"convex_order_extremal","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.0","family":"convex_order","param_values":{"alpha":0.5211},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.10792302950917715,"theta":6.02403843,"z":"0.99*exp(i*6.024038)"}},{"canonical_key":"convex_order_extremal","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.1","family":"convex_order","param_values":{"alpha":0.5},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.31642538884683236,"theta":6.02394255,"z":"0.99*exp(i*6.023943)"}},{"canonical_key":"convex_order_extremal","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.1","family":"convex_order","param_values":{"alpha":0.4168},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-1.4373758460320436,"theta":0.26691266,"z":"0.99*exp(i*0.266913)"}},{"canonical_key":"convex_order_extremal","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.1","family":"convex_order","param_values":{"alpha":0.4689},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.6741852240440992,"theta":6.02240857,"z":"0.99*exp(i*6.022409)"}},{"canonical_key":"convex_order_extremal","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.1","family":"convex_order","param_values":{"alpha":0.5211},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.10802719433825267,"theta":6.02470954,"z":"0.99*exp(i*6.02471)"}},{"canonical_key":"convex_order_extremal","closed_form":null,"disk_radius":0.95,"engine_version":"gft-0.1.0-reaudit-20260610","family":"convex_order","param_values":{"alpha":0.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.2156460433160795,"truncation_caveat":true,"z":[0.9605927690132365,-0.2395026766436712]}},{"canonical_key":"convex_order_extremal","closed_form":null,"disk_radius":0.95,"engine_version":"gft-0.1.0-reaudit-20260610","family":"convex_order","param_values":{"alpha":0.4168},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-1.2862982885921814,"truncation_caveat":true,"z":[0.9516490789789357,-0.27288098225882895]}},{"canonical_key":"convex_order_extremal","closed_form":null,"disk_radius":0.95,"engine_version":"gft-0.1.0-reaudit-20260610","family":"convex_order","param_values":{"alpha":0.4689},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.5184923189004536,"truncation_caveat":true,"z":[0.9516490789789357,-0.27288098225882895]}},{"canonical_key":"convex_order_extremal","closed_form":null,"disk_radius":0.95,"engine_version":"gft-0.1.0-reaudit-20260610","family":"convex_order","param_values":{"alpha":0.5211},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.03425341509910643,"truncation_caveat":true,"z":[0.9605927690132365,-0.2395026766436712]}},{"canonical_key":"hyp2f1","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.0","family":"hyp2f1","param_values":{"a":1.0,"b":1.0,"c":2.0},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.3145830129058473,"theta":0.26192722,"z":"0.99*exp(i*0.261927)"}},{"canonical_key":"hyp2f1","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.1","family":"hyp2f1","param_values":{"a":1.0,"b":1.0,"c":2.0},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.3164253888468318,"theta":6.02394255,"z":"0.99*exp(i*6.023943)"}},{"canonical_key":"hyp2f1","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.1","family":"hyp2f1","param_values":{"a":1.0,"b":2.0,"c":3.0},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-1.0720215971644615,"theta":0.26691266,"z":"0.99*exp(i*0.266913)"}},{"canonical_key":"hyp2f1","closed_form":null,"disk_radius":0.95,"engine_version":"gft-0.1.0-reaudit-20260610","family":"hyp2f1","param_values":{"a":1.0,"b":1.0,"c":2.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.21564604331607815,"truncation_caveat":true,"z":[0.9605927690132365,-0.2395026766436712]}},{"canonical_key":"hyp2f1","closed_form":null,"disk_radius":0.95,"engine_version":"gft-0.1.0-reaudit-20260610","family":"hyp2f1","param_values":{"a":1.0,"b":2.0,"c":3.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-1.020103891191232,"truncation_caveat":true,"z":[0.9516490789789357,0.2728809822588292]}},{"canonical_key":"z/(1-z)**(2*alpha)","closed_form":"z/(1-z)^(2*alpha)","disk_radius":0.95,"engine_version":"boundary_v3.0","family":"koebe_alpha","param_values":{"alpha":0.1},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.12152521173978716,"theta":0.24121848,"z":"0.99*exp(i*0.241218)"}},{"canonical_key":"z/(1-z)**(2*alpha)","closed_form":"z/(1-z)^(2*alpha)","disk_radius":0.95,"engine_version":"boundary_v3.1","family":"koebe_alpha","param_values":{"alpha":0.1},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.12176461690186408,"theta":6.04235032,"z":"0.99*exp(i*6.04235)"}},{"canonical_key":"z/(1-z)**(2*alpha)","closed_form":"z/(1-z)^(2*alpha)","disk_radius":0.95,"engine_version":"gft-0.1.0-reaudit-20260610","family":"koebe_alpha","param_values":{"alpha":0.1},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.11673871053622514,"truncation_caveat":true,"z":[0.9605927690132365,-0.2395026766436712]}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.1","family":"mittag_leffler","param_values":{"alpha":0.2},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.22376576264635048,"theta":5.07594243,"z":"0.99*exp(i*5.075942)"}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.95,"engine_version":"gft-0.1.0-reaudit-20260610","family":"mittag_leffler","param_values":{"alpha":0.2},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.21408022940223123,"truncation_caveat":true,"z":[0.33859994189241216,0.9302956945780492]}},{"canonical_key":"mocanu","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.0","family":"mocanu","param_values":{"alpha":0.3},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.04856467939384148,"theta":2.40834984,"z":"0.99*exp(i*2.40835)"}},{"canonical_key":"mocanu","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.1","family":"mocanu","param_values":{"alpha":0.3},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.047737878374628846,"theta":3.88403935,"z":"0.99*exp(i*3.884039)"}},{"canonical_key":"mocanu","closed_form":null,"disk_radius":0.95,"engine_version":"gft-0.1.0-reaudit-20260610","family":"mocanu","param_values":{"alpha":0.3},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.04857373618079632,"truncation_caveat":true,"z":[-0.7357133772226201,0.6624393002952698]}},{"canonical_key":"ma_minda_nephroid","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.0","family":"nephroid_starlike","param_values":{},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.031880998354829194,"theta":4.08959278,"z":"0.99*exp(i*4.089593)"}},{"canonical_key":"ma_minda_nephroid","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.1","family":"nephroid_starlike","param_values":{},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.03169833571568299,"theta":4.09266074,"z":"0.99*exp(i*4.092661)"}},{"canonical_key":"ma_minda_nephroid","closed_form":null,"disk_radius":0.95,"engine_version":"gft-0.1.0-reaudit-20260610","family":"nephroid_starlike","param_values":{},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.031944033938857225,"truncation_caveat":true,"z":[-0.5819073997695485,-0.8009268244311979]}},{"canonical_key":"q_exp","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.1","family":"q_exp","param_values":{"q":0.15},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.39828320412621426,"theta":2.98819457,"z":"0.99*exp(i*2.988195)"}},{"canonical_key":"q_exp","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.1","family":"q_exp","param_values":{"q":0.175},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.05861139006989771,"theta":2.99279652,"z":"0.99*exp(i*2.992797)"}},{"canonical_key":"q_exp","closed_form":null,"disk_radius":0.95,"engine_version":"gft-0.1.0-reaudit-20260610","family":"q_exp","param_values":{"q":0.15},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.38702171134426827,"truncation_caveat":true,"z":[-0.9803653880541546,0.13778136995046467]}},{"canonical_key":"q_exp","closed_form":null,"disk_radius":0.95,"engine_version":"gft-0.1.0-reaudit-20260610","family":"q_exp","param_values":{"q":0.175},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.0504269688790072,"truncation_caveat":true,"z":[-0.9803653880541546,0.13778136995046467]}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.1","family":"ruscheweyh","param_values":{"lambda":0.1},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.9232439002718242,"theta":6.02240857,"z":"0.99*exp(i*6.022409)"}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.95,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ruscheweyh","param_values":{"lambda":0.1},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.7684118435988115,"truncation_caveat":true,"z":[0.9516490789789357,-0.27288098225882895]}},{"canonical_key":"slow_decay","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.0","family":"slow_decay","param_values":{},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.3145830129058473,"theta":0.26192722,"z":"0.99*exp(i*0.261927)"}},{"canonical_key":"slow_decay","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.1","family":"slow_decay","param_values":{},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.31642538884683236,"theta":6.02394255,"z":"0.99*exp(i*6.023943)"}},{"canonical_key":"slow_decay","closed_form":null,"disk_radius":0.95,"engine_version":"gft-0.1.0-reaudit-20260610","family":"slow_decay","param_values":{},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.2156460433160795,"truncation_caveat":true,"z":[0.9605927690132365,-0.2395026766436712]}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.0","family":"strongly_starlike","param_values":{"beta":0.6},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.05746737852015274,"theta":3.09250527,"z":"0.99*exp(i*3.092505)"}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.0","family":"strongly_starlike","param_values":{"beta":0.55},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.026234681628171344,"theta":3.11704896,"z":"0.99*exp(i*3.117049)"}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.1","family":"strongly_starlike","param_values":{"beta":0.6},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.06339041366365475,"theta":3.16613635,"z":"0.99*exp(i*3.166136)"}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.1","family":"strongly_starlike","param_values":{"beta":0.55},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.028235633652451447,"theta":3.14772858,"z":"0.99*exp(i*3.147729)"}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.95,"engine_version":"gft-0.1.0-reaudit-20260610","family":"strongly_starlike","param_values":{"beta":0.6},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.06537588804452886,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.95,"engine_version":"gft-0.1.0-reaudit-20260610","family":"strongly_starlike","param_values":{"beta":0.55},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.02836923107674139,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":1.25,"beta":1.5},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.007759348731411918,"theta":3.1538645,"z":"0.99*exp(i*3.153864)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.95,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":1.25,"beta":1.5},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.008067445802824267,"theta":3.14466062,"z":"0.99*exp(i*3.144661)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.95,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":1.25,"beta":1.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.00808799047719744,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"bessel_j_normalized","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.0","family":"bessel_j","param_values":{"nu":-0.6},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.08704236385825483,"theta":0.04908739,"z":"0.95*exp(i*0.049087)"}},{"canonical_key":"bessel_j_normalized","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.1","family":"bessel_j","param_values":{"nu":-0.6},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.0924938740051947,"theta":0.02454369,"z":"0.95*exp(i*0.024544)"}},{"canonical_key":"bessel_j_normalized","closed_form":null,"disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"bessel_j","param_values":{"nu":-0.6},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.18606971166599467,"truncation_caveat":true,"z":[0.99,0.0]}},{"canonical_key":"convex_order_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.1","family":"convex_order","param_values":{"alpha":0.25},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-1.2921432297988755,"theta":6.0040008,"z":"0.95*exp(i*6.004001)"}},{"canonical_key":"convex_order_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.1","family":"convex_order","param_values":{"alpha":0.2605},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-1.1413271408205032,"theta":6.0040008,"z":"0.95*exp(i*6.004001)"}},{"canonical_key":"convex_order_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.1","family":"convex_order","param_values":{"alpha":0.3126},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.4973250411631587,"theta":6.00553478,"z":"0.95*exp(i*6.005535)"}},{"canonical_key":"convex_order_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.1","family":"convex_order","param_values":{"alpha":0.3647},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.07353223490682903,"theta":5.70679203,"z":"0.95*exp(i*5.706792)"}},{"canonical_key":"convex_order_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"convex_order","param_values":{"alpha":0.25},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-6.441457649087908,"truncation_caveat":true,"z":[0.9516490789789357,0.2728809822588292]}},{"canonical_key":"convex_order_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"convex_order","param_values":{"alpha":0.2605},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-5.9260923237662455,"truncation_caveat":true,"z":[0.9516490789789357,0.2728809822588292]}},{"canonical_key":"convex_order_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"convex_order","param_values":{"alpha":0.3126},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-3.8382975252774947,"truncation_caveat":true,"z":[0.9516490789789357,0.2728809822588292]}},{"canonical_key":"convex_order_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"convex_order","param_values":{"alpha":0.3647},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-2.3522979965018904,"truncation_caveat":true,"z":[0.9516490789789357,0.2728809822588292]}},{"canonical_key":"exp(3*z)/3-1/3","closed_form":"(exp(3*z) - 1)/3","disk_radius":0.9,"engine_version":"boundary_v3.0","family":"exp_3z_minus_1_third","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form","witness":{"Re_g_upper_bound":-0.008825330410904022,"theta":1.92207793,"z":"0.95*exp(i*1.922078)"}},{"canonical_key":"exp(3*z)/3-1/3","closed_form":"(exp(3*z) - 1)/3","disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"exp_3z_minus_1_third","param_values":{},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.07458358613457317,"truncation_caveat":true,"z":[-0.30592682443119806,-0.941545951132202]}},{"canonical_key":"exp(3*z)/3-1/3","closed_form":"(exp(3*z) - 1)/3","disk_radius":0.9,"engine_version":"boundary_v3.1","family":"exp_3z_minus_1_third","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form_v31","witness":{"Re_g_upper_bound":-0.008825330410904022,"theta":1.92207793,"z":"0.95*exp(i*1.922078)"}},{"canonical_key":"hyp2f1","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.1","family":"hyp2f1","param_values":{"a":1.0,"b":1.0,"c":1.5},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-1.0508500072964098,"theta":6.0040008,"z":"0.95*exp(i*6.004001)"}},{"canonical_key":"hyp2f1","closed_form":null,"disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"hyp2f1","param_values":{"a":1.0,"b":1.0,"c":1.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-5.380837663240435,"truncation_caveat":true,"z":[0.9516490789789357,0.2728809822588292]}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.0","family":"janowski","param_values":{"A":-0.5,"B":-1.0},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.11375208159723761,"theta":4.49149575,"z":"0.95*exp(i*4.491496)"}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.1","family":"janowski","param_values":{"A":-0.5,"B":-1.0},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.11375208159723726,"theta":4.49149575,"z":"0.95*exp(i*4.491496)"}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"janowski","param_values":{"A":-0.5,"B":-1.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.2716308309774102,"truncation_caveat":true,"z":[-0.20583257390958173,0.9683661247264677]}},{"canonical_key":"z/(1-z)**(2*alpha)","closed_form":"z/(1-z)^(2*alpha)","disk_radius":0.9,"engine_version":"boundary_v3.0","family":"koebe_alpha","param_values":{"alpha":0.25},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.7355963063938777,"theta":6.00936974,"z":"0.95*exp(i*6.00937)"}},{"canonical_key":"z/(1-z)**(2*alpha)","closed_form":"z/(1-z)^(2*alpha)","disk_radius":0.9,"engine_version":"boundary_v3.1","family":"koebe_alpha","param_values":{"alpha":0.5},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.7457956338605956,"theta":0.26691266,"z":"0.95*exp(i*0.266913)"}},{"canonical_key":"z/(1-z)**(2*alpha)","closed_form":"z/(1-z)^(2*alpha)","disk_radius":0.9,"engine_version":"boundary_v3.1","family":"koebe_alpha","param_values":{"alpha":0.25},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.7457956338605956,"theta":0.26691266,"z":"0.95*exp(i*0.266913)"}},{"canonical_key":"z/(1-z)**(2*alpha)","closed_form":"z/(1-z)^(2*alpha)","disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"koebe_alpha","param_values":{"alpha":0.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-3.768965119465816,"truncation_caveat":true,"z":[0.9516490789789357,-0.27288098225882895]}},{"canonical_key":"z/(1-z)**(2*alpha)","closed_form":"z/(1-z)^(2*alpha)","disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"koebe_alpha","param_values":{"alpha":0.25},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-3.768965119465816,"truncation_caveat":true,"z":[0.9516490789789357,-0.27288098225882895]}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.0","family":"mittag_leffler","param_values":{"alpha":1.1},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.022550419865397235,"theta":3.1538645,"z":"0.95*exp(i*3.153864)"}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.0","family":"mittag_leffler","param_values":{"alpha":1.15},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.049966255120769666,"theta":3.20295189,"z":"0.95*exp(i*3.202952)"}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.0","family":"mittag_leffler","param_values":{"alpha":1.6},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.03828633643865265,"theta":3.11704896,"z":"0.95*exp(i*3.117049)"}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.1","family":"mittag_leffler","param_values":{"alpha":0.15},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.699852066630653,"theta":2.98819457,"z":"0.95*exp(i*2.988195)"}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.1","family":"mittag_leffler","param_values":{"alpha":1.1},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.021547745147884007,"theta":3.17840819,"z":"0.95*exp(i*3.178408)"}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.1","family":"mittag_leffler","param_values":{"alpha":1.15},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.053251793460149265,"theta":3.11704896,"z":"0.95*exp(i*3.117049)"}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.1","family":"mittag_leffler","param_values":{"alpha":1.6},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.03922669910623933,"theta":3.12932081,"z":"0.95*exp(i*3.129321)"}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"mittag_leffler","param_values":{"alpha":0.15},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-2.5883540178605906,"truncation_caveat":true,"z":[-0.49500000000000044,-0.857365149746594]}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"mittag_leffler","param_values":{"alpha":1.1},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.0731454941002507,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"mittag_leffler","param_values":{"alpha":1.15},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.10970976154960517,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"mittag_leffler","param_values":{"alpha":1.6},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.1140611100760788,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"mittag_leffler_2p","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.1","family":"mittag_leffler_2p","param_values":{"alpha":0.25,"beta":0.5},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.09060881651608725,"theta":1.23101958,"z":"0.95*exp(i*1.23102)"}},{"canonical_key":"mocanu","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.0","family":"mocanu","param_values":{"alpha":0.25},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.05714416395237696,"theta":2.40221391,"z":"0.95*exp(i*2.402214)"}},{"canonical_key":"mocanu","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.1","family":"mocanu","param_values":{"alpha":0.25},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.05699825267570491,"theta":2.39914595,"z":"0.95*exp(i*2.399146)"}},{"canonical_key":"mocanu","closed_form":null,"disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"mocanu","param_values":{"alpha":0.25},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.1704320803872669,"truncation_caveat":true,"z":[-0.7357133772226203,-0.6624393002952697]}},{"canonical_key":"q_exp","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.1","family":"q_exp","param_values":{"q":0.1},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.555951955941071,"theta":2.98819457,"z":"0.95*exp(i*2.988195)"}},{"canonical_key":"q_exp","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.1","family":"q_exp","param_values":{"q":0.125},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.1436807834304876,"theta":3.29192277,"z":"0.95*exp(i*3.291923)"}},{"canonical_key":"q_exp","closed_form":null,"disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"q_exp","param_values":{"q":0.1},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-2.0836368354541834,"truncation_caveat":true,"z":[-0.9803653880541546,0.13778136995046467]}},{"canonical_key":"q_exp","closed_form":null,"disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"q_exp","param_values":{"q":0.125},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.9907474815515367,"truncation_caveat":true,"z":[-0.9803653880541546,0.13778136995046467]}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.1","family":"ruscheweyh","param_values":{"lambda":0.5},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-1.2921432297988755,"theta":6.0040008,"z":"0.95*exp(i*6.004001)"}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.1","family":"ruscheweyh","param_values":{"lambda":0.25},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.003035307732791449,"theta":5.70741521,"z":"0.95*exp(i*5.707415)"}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.1","family":"ruscheweyh","param_values":{"lambda":0.4},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.6236142212732649,"theta":0.58137872,"z":"0.95*exp(i*0.581379)"}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ruscheweyh","param_values":{"lambda":0.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-6.441457649087908,"truncation_caveat":true,"z":[0.9516490789789357,0.2728809822588292]}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ruscheweyh","param_values":{"lambda":0.25},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-2.1128108016068112,"truncation_caveat":true,"z":[0.9516490789789357,0.2728809822588292]}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ruscheweyh","param_values":{"lambda":0.4},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-4.279543535661755,"truncation_caveat":true,"z":[0.9516490789789357,0.2728809822588292]}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.0","family":"strongly_starlike","param_values":{"beta":0.8},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.035309752460526464,"theta":3.11704896,"z":"0.95*exp(i*3.117049)"}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.0","family":"strongly_starlike","param_values":{"beta":0.65},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.010681790747811509,"theta":3.1538645,"z":"0.95*exp(i*3.153864)"}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.0","family":"strongly_starlike","param_values":{"beta":0.7},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.02712112218484634,"theta":3.11704896,"z":"0.95*exp(i*3.117049)"}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.0","family":"strongly_starlike","param_values":{"beta":0.75},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.03527001316628097,"theta":3.11704896,"z":"0.95*exp(i*3.117049)"}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.0","family":"strongly_starlike","param_values":{"beta":0.85},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.028930737560675598,"theta":3.11704896,"z":"0.95*exp(i*3.117049)"}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.0","family":"strongly_starlike","param_values":{"beta":0.9},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.05088592261084107,"theta":3.50361212,"z":"0.95*exp(i*3.503612)"}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.1","family":"strongly_starlike","param_values":{"beta":0.8},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.03302029649965461,"theta":3.20295189,"z":"0.95*exp(i*3.202952)"}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.1","family":"strongly_starlike","param_values":{"beta":0.65},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.011023058854893684,"theta":3.14466062,"z":"0.95*exp(i*3.144661)"}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.1","family":"strongly_starlike","param_values":{"beta":0.7},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.028004592465793295,"theta":3.1538645,"z":"0.95*exp(i*3.153864)"}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.1","family":"strongly_starlike","param_values":{"beta":0.75},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.03589438450286056,"theta":3.1538645,"z":"0.95*exp(i*3.153864)"}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.1","family":"strongly_starlike","param_values":{"beta":0.85},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.028043996797362695,"theta":3.27658296,"z":"0.95*exp(i*3.276583)"}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.1","family":"strongly_starlike","param_values":{"beta":0.9},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.051620251955153865,"theta":2.78570911,"z":"0.95*exp(i*2.785709)"}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"strongly_starlike","param_values":{"beta":0.8},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.0898933884466624,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"strongly_starlike","param_values":{"beta":0.65},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.08922985224469028,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"strongly_starlike","param_values":{"beta":0.7},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.10045494097281871,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"strongly_starlike","param_values":{"beta":0.75},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.10013274516284272,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"strongly_starlike","param_values":{"beta":0.85},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.07510861026027249,"truncation_caveat":true,"z":[-0.974959675482086,0.17191169589026098]}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"strongly_starlike","param_values":{"beta":0.9},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.11508849299865025,"truncation_caveat":true,"z":[-0.9302956945780493,-0.338599941892412]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":0.1,"beta":1.0},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.012888654222670097,"theta":3.09557323,"z":"0.95*exp(i*3.095573)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":1.5,"beta":1.25},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.047675316975563944,"theta":3.09250527,"z":"0.95*exp(i*3.092505)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":0.1,"beta":1.0},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.01351630300903803,"theta":3.17227227,"z":"0.95*exp(i*3.172272)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.9,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":1.5,"beta":1.25},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.05379135204301048,"theta":3.1538645,"z":"0.95*exp(i*3.153864)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":0.1,"beta":1.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.05745271760399997,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":1.5,"beta":1.25},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.13963462663126486,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"-z*(z-2)/(2*(z-1)**2)","closed_form":"z*(1 - z/2)/(1-z)**2","disk_radius":0.9,"engine_version":"boundary_v3.0","family":"z_1_minus_half_z_koebe","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form","witness":{"Re_g_upper_bound":-0.08603592532311725,"theta":0.54609716,"z":"0.95*exp(i*0.546097)"}},{"canonical_key":"-z*(z-2)/(2*(z-1)**2)","closed_form":"z*(1 - z/2)/(1-z)**2","disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"z_1_minus_half_z_koebe","param_values":{},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-528.2005142802229,"truncation_caveat":true,"z":[0.7242401715190179,-0.5261912850984637]}},{"canonical_key":"-z*(z-2)/(2*(z-1)**2)","closed_form":"z*(1 - z/2)/(1-z)**2","disk_radius":0.9,"engine_version":"boundary_v3.1","family":"z_1_minus_half_z_koebe","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form_v31","witness":{"Re_g_upper_bound":-0.08603592532311725,"theta":0.54609716,"z":"0.95*exp(i*0.546097)"}},{"canonical_key":"-z*(z-3)/(3*(z-1)**2)","closed_form":"z*(1 - z/3)/(1-z)**2","disk_radius":0.9,"engine_version":"boundary_v3.0","family":"z_1_minus_third_z_koebe","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form","witness":{"Re_g_upper_bound":-0.015786782369008906,"theta":5.54840851,"z":"0.95*exp(i*5.548409)"}},{"canonical_key":"-z*(z-3)/(3*(z-1)**2)","closed_form":"z*(1 - z/3)/(1-z)**2","disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"z_1_minus_third_z_koebe","param_values":{},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-325.02505439934237,"truncation_caveat":true,"z":[0.29807486608659756,0.818953963879887]}},{"canonical_key":"-z*(z-3)/(3*(z-1)**2)","closed_form":"z*(1 - z/3)/(1-z)**2","disk_radius":0.9,"engine_version":"boundary_v3.1","family":"z_1_minus_third_z_koebe","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form_v31","witness":{"Re_g_upper_bound":-0.015786782369008906,"theta":5.54840851,"z":"0.95*exp(i*5.548409)"}},{"canonical_key":"z*(2-z)/(2*(z-1)**2)","closed_form":"(z - z**2/2)/(1-z)**2","disk_radius":0.9,"engine_version":"boundary_v3.0","family":"z_minus_half_z2_over_1mz","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form","witness":{"Re_g_upper_bound":-0.08603592532311725,"theta":0.54609716,"z":"0.95*exp(i*0.546097)"}},{"canonical_key":"z*(2-z)/(2*(z-1)**2)","closed_form":"(z - z**2/2)/(1-z)**2","disk_radius":0.9,"engine_version":"gft-0.1.0-reaudit-20260610","family":"z_minus_half_z2_over_1mz","param_values":{},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-528.2005142802229,"truncation_caveat":true,"z":[0.7242401715190179,-0.5261912850984637]}},{"canonical_key":"z*(2-z)/(2*(z-1)**2)","closed_form":"(z - z**2/2)/(1-z)**2","disk_radius":0.9,"engine_version":"boundary_v3.1","family":"z_minus_half_z2_over_1mz","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form_v31","witness":{"Re_g_upper_bound":-0.08603592532311725,"theta":0.54609716,"z":"0.95*exp(i*0.546097)"}},{"canonical_key":"hyp2f1","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.1","family":"hyp2f1","param_values":{"a":5.0,"b":5.0,"c":15.0},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.31006889080108535,"theta":2.98819457,"z":"0.9*exp(i*2.988195)"}},{"canonical_key":"hyp2f1","closed_form":null,"disk_radius":0.8,"engine_version":"gft-0.1.0-reaudit-20260610","family":"hyp2f1","param_values":{"a":5.0,"b":5.0,"c":15.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-2.7722681827237814,"truncation_caveat":true,"z":[-0.9803653880541546,0.13778136995046467]}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.0","family":"janowski","param_values":{"A":0.5,"B":-0.5},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.040405905572957375,"theta":1.96963133,"z":"0.9*exp(i*1.969631)"}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.1","family":"janowski","param_values":{"A":0.5,"B":-0.5},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.040405905572957965,"theta":1.96963133,"z":"0.9*exp(i*1.969631)"}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.8,"engine_version":"gft-0.1.0-reaudit-20260610","family":"janowski","param_values":{"A":0.5,"B":-0.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.3960653797453961,"truncation_caveat":true,"z":[-0.3708605274817532,-0.9179120160211194]}},{"canonical_key":"ma_minda_cosh","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.0","family":"maminda_cosh","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form","witness":{"Re_g_upper_bound":-0.13048125673491917,"theta":1.54625263,"z":"0.9*exp(i*1.546253)"}},{"canonical_key":"ma_minda_cosh","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.1","family":"maminda_cosh","param_values":{},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.13048125673491962,"theta":1.59534002,"z":"0.9*exp(i*1.59534)"}},{"canonical_key":"ma_minda_cosh","closed_form":null,"disk_radius":0.8,"engine_version":"gft-0.1.0-reaudit-20260610","family":"maminda_cosh","param_values":{},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.508439973607722,"truncation_caveat":true,"z":[6.062001655779399e-17,0.99]}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.0","family":"mittag_leffler","param_values":{"alpha":1.5},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.000865127801846887,"theta":3.15079654,"z":"0.9*exp(i*3.150797)"}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.0","family":"mittag_leffler","param_values":{"alpha":1.25},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.019725109565198407,"theta":3.10477711,"z":"0.9*exp(i*3.104777)"}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.0","family":"mittag_leffler","param_values":{"alpha":1.2},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.006132455503613313,"theta":3.16000042,"z":"0.9*exp(i*3.16)"}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.0","family":"mittag_leffler","param_values":{"alpha":1.3},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.0248976228908159,"theta":3.20295189,"z":"0.9*exp(i*3.202952)"}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.0","family":"mittag_leffler","param_values":{"alpha":1.4},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.027248934826688914,"theta":3.11704896,"z":"0.9*exp(i*3.117049)"}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.1","family":"mittag_leffler","param_values":{"alpha":1.5},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.0010133068048630179,"theta":3.14197615,"z":"0.9*exp(i*3.141976)"}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.1","family":"mittag_leffler","param_values":{"alpha":1.25},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.02124745588842798,"theta":3.1538645,"z":"0.9*exp(i*3.153864)"}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.1","family":"mittag_leffler","param_values":{"alpha":1.2},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.006411066972351222,"theta":3.13238877,"z":"0.9*exp(i*3.132389)"}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.1","family":"mittag_leffler","param_values":{"alpha":1.3},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.0300060564341315,"theta":3.1538645,"z":"0.9*exp(i*3.153864)"}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.1","family":"mittag_leffler","param_values":{"alpha":1.4},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.027993965684430917,"theta":3.1538645,"z":"0.9*exp(i*3.153864)"}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"gft-0.1.0-reaudit-20260610","family":"mittag_leffler","param_values":{"alpha":1.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.16762949575905906,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"gft-0.1.0-reaudit-20260610","family":"mittag_leffler","param_values":{"alpha":1.25},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.1657536354803848,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"gft-0.1.0-reaudit-20260610","family":"mittag_leffler","param_values":{"alpha":1.2},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.14100893457994465,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"gft-0.1.0-reaudit-20260610","family":"mittag_leffler","param_values":{"alpha":1.3},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.18291162158812163,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"gft-0.1.0-reaudit-20260610","family":"mittag_leffler","param_values":{"alpha":1.4},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.1920883413259037,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"mittag_leffler_2p","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.0","family":"mittag_leffler_2p","param_values":{"alpha":1.5,"beta":1.0},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.000865127801846887,"theta":3.15079654,"z":"0.9*exp(i*3.150797)"}},{"canonical_key":"mittag_leffler_2p","closed_form":null,"disk_radius":0.8,"engine_version":"gft-0.1.0-reaudit-20260610","family":"mittag_leffler_2p","param_values":{"alpha":1.5,"beta":1.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.16762949575905906,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"mittag_leffler_2p","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.1","family":"mittag_leffler_2p","param_values":{"alpha":0.5,"beta":0.5},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.05621492905107679,"theta":2.85320427,"z":"0.9*exp(i*2.853204)"}},{"canonical_key":"mittag_leffler_2p","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.1","family":"mittag_leffler_2p","param_values":{"alpha":1.5,"beta":1.0},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.0010133068048630179,"theta":3.14197615,"z":"0.9*exp(i*3.141976)"}},{"canonical_key":"mocanu","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.0","family":"mocanu","param_values":{"alpha":0.05},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.34013961739707077,"theta":2.38073818,"z":"0.9*exp(i*2.380738)"}},{"canonical_key":"mocanu","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.0","family":"mocanu","param_values":{"alpha":0.1},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.22630751179405129,"theta":2.36846634,"z":"0.9*exp(i*2.368466)"}},{"canonical_key":"mocanu","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.0","family":"mocanu","param_values":{"alpha":0.15},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.12185414694270108,"theta":2.38687411,"z":"0.9*exp(i*2.386874)"}},{"canonical_key":"mocanu","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.0","family":"mocanu","param_values":{"alpha":0.2},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.02417893555245042,"theta":2.40067993,"z":"0.9*exp(i*2.40068)"}},{"canonical_key":"mocanu","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.1","family":"mocanu","param_values":{"alpha":0.05},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.3264758708867082,"theta":3.95153451,"z":"0.9*exp(i*3.951535)"}},{"canonical_key":"mocanu","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.1","family":"mocanu","param_values":{"alpha":0.1},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.21049733282613248,"theta":3.95153451,"z":"0.9*exp(i*3.951535)"}},{"canonical_key":"mocanu","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.1","family":"mocanu","param_values":{"alpha":0.15},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.11928626967685338,"theta":2.36846634,"z":"0.9*exp(i*2.368466)"}},{"canonical_key":"mocanu","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.1","family":"mocanu","param_values":{"alpha":0.2},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.024063833300447812,"theta":2.39607799,"z":"0.9*exp(i*2.396078)"}},{"canonical_key":"mocanu","closed_form":null,"disk_radius":0.8,"engine_version":"gft-0.1.0-reaudit-20260610","family":"mocanu","param_values":{"alpha":0.05},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.8020317361851672,"truncation_caveat":true,"z":[-0.7121464023352646,-0.6877117867544074]}},{"canonical_key":"mocanu","closed_form":null,"disk_radius":0.8,"engine_version":"gft-0.1.0-reaudit-20260610","family":"mocanu","param_values":{"alpha":0.1},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.6206262289480816,"truncation_caveat":true,"z":[-0.7121464023352646,-0.6877117867544074]}},{"canonical_key":"mocanu","closed_form":null,"disk_radius":0.8,"engine_version":"gft-0.1.0-reaudit-20260610","family":"mocanu","param_values":{"alpha":0.15},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.4551856404458566,"truncation_caveat":true,"z":[-0.7121464023352646,-0.6877117867544074]}},{"canonical_key":"mocanu","closed_form":null,"disk_radius":0.8,"engine_version":"gft-0.1.0-reaudit-20260610","family":"mocanu","param_values":{"alpha":0.2},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.304283237552634,"truncation_caveat":true,"z":[-0.7121464023352646,-0.6877117867544074]}},{"canonical_key":"q_exp","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.1","family":"q_exp","param_values":{"q":0.075},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.050790703313575124,"theta":2.99279652,"z":"0.9*exp(i*2.992797)"}},{"canonical_key":"q_exp","closed_form":null,"disk_radius":0.8,"engine_version":"gft-0.1.0-reaudit-20260610","family":"q_exp","param_values":{"q":0.075},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-4.1779883994455504,"truncation_caveat":true,"z":[-0.8898061058361754,0.4339874353211865]}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.0","family":"strongly_starlike","param_values":{"beta":0.95},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.0319565060171288,"theta":2.76423338,"z":"0.9*exp(i*2.764233)"}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.0","family":"strongly_starlike","param_values":{"beta":1.0},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.09667907996011602,"theta":3.5772432,"z":"0.9*exp(i*3.577243)"}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.1","family":"strongly_starlike","param_values":{"beta":0.95},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.03142993216033773,"theta":3.52815581,"z":"0.9*exp(i*3.528156)"}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.1","family":"strongly_starlike","param_values":{"beta":1.0},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.09430744699849197,"theta":2.68753434,"z":"0.9*exp(i*2.687534)"}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.8,"engine_version":"gft-0.1.0-reaudit-20260610","family":"strongly_starlike","param_values":{"beta":0.95},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.19587427961023343,"truncation_caveat":true,"z":[-0.9044100030661748,-0.4026692766450422]}},{"canonical_key":"strongly_starlike_extremal","closed_form":null,"disk_radius":0.8,"engine_version":"gft-0.1.0-reaudit-20260610","family":"strongly_starlike","param_values":{"beta":1.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.2964333572828803,"truncation_caveat":true,"z":[-0.8898061058361754,0.4339874353211865]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":0.25,"beta":1.0},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.08051063013182534,"theta":3.20295189,"z":"0.9*exp(i*3.202952)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":0.5,"beta":0.75},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.05115536045075819,"theta":3.10477711,"z":"0.9*exp(i*3.104777)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":0.75,"beta":0.5},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.10244422904129402,"theta":3.11704896,"z":"0.9*exp(i*3.117049)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":2.0,"beta":0.75},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.09298154014866676,"theta":3.19068004,"z":"0.9*exp(i*3.19068)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":0.25,"beta":1.0},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.07215065976735424,"theta":3.01887419,"z":"0.9*exp(i*3.018874)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":0.5,"beta":0.75},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.049967809393641725,"theta":3.06796158,"z":"0.9*exp(i*3.067962)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":0.75,"beta":0.5},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.0902602000669394,"theta":3.41157327,"z":"0.9*exp(i*3.411573)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":2.0,"beta":0.75},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.09905864927977834,"theta":3.16613635,"z":"0.9*exp(i*3.166136)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":0.25,"beta":1.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.20455951589412827,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":0.5,"beta":0.75},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.1501538036975582,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":0.75,"beta":0.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.20957232933976458,"truncation_caveat":true,"z":[-0.9605927690132365,0.23950267664367106]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.8,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":2.0,"beta":0.75},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.347754213452097,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"z*cos(z)","closed_form":"z*cos(z)","disk_radius":0.8,"engine_version":"boundary_v3.0","family":"z_cos_z","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form","witness":{"Re_g_upper_bound":-0.13048125673491962,"theta":0.02454369,"z":"0.9*exp(i*0.024544)"}},{"canonical_key":"z*cos(z)","closed_form":"z*cos(z)","disk_radius":0.8,"engine_version":"boundary_v3.1","family":"z_cos_z","param_values":{},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.1304812567349196,"theta":0.02454369,"z":"0.9*exp(i*0.024544)"}},{"canonical_key":"z*cos(z)","closed_form":"z*cos(z)","disk_radius":0.8,"engine_version":"boundary_v3.1","family":"z_cos_z","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form_v31","witness":{"Re_g_upper_bound":-0.13048125673491962,"theta":0.02454369,"z":"0.9*exp(i*0.024544)"}},{"canonical_key":"z*cos(z)","closed_form":"z*cos(z)","disk_radius":0.8,"engine_version":"gft-0.1.0-reaudit-20260610","family":"z_cos_z","param_values":{},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.508439973607722,"truncation_caveat":true,"z":[0.99,0.0]}},{"canonical_key":"z*cosh(z)","closed_form":"z*cosh(z)","disk_radius":0.8,"engine_version":"boundary_v3.0","family":"z_cosh","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form","witness":{"Re_g_upper_bound":-0.13048125673491917,"theta":1.54625263,"z":"0.9*exp(i*1.546253)"}},{"canonical_key":"z*cosh(z)","closed_form":"z*cosh(z)","disk_radius":0.8,"engine_version":"boundary_v3.1","family":"z_cosh","param_values":{},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.13048125673491962,"theta":1.59534002,"z":"0.9*exp(i*1.59534)"}},{"canonical_key":"z*cosh(z)","closed_form":"z*cosh(z)","disk_radius":0.8,"engine_version":"boundary_v3.1","family":"z_cosh","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form_v31","witness":{"Re_g_upper_bound":-0.13048125673491917,"theta":1.54625263,"z":"0.9*exp(i*1.546253)"}},{"canonical_key":"z*cosh(z)","closed_form":"z*cosh(z)","disk_radius":0.8,"engine_version":"gft-0.1.0-reaudit-20260610","family":"z_cosh","param_values":{},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.508439973607722,"truncation_caveat":true,"z":[6.062001655779399e-17,0.99]}},{"canonical_key":"bessel_j_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"bessel_j","param_values":{"nu":-0.7},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.423884299668814,"theta":6.18501054,"z":"0.8*exp(i*6.185011)"}},{"canonical_key":"bessel_j_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"bessel_j","param_values":{"nu":-0.7},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.4683635446863482,"theta":0.04908739,"z":"0.8*exp(i*0.049087)"}},{"canonical_key":"bessel_j_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"bessel_j","param_values":{"nu":-0.7},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-1.6964082622888241,"truncation_caveat":true,"z":[0.99,0.0]}},{"canonical_key":"z+z**2+z**3/2","closed_form":"z + z^2 + z^3/2","disk_radius":0.6,"engine_version":"boundary_v3.0","family":"ctc_z_plus_z2_plus_z3_2","param_values":{},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.062353353962846636,"theta":2.37460226,"z":"0.8*exp(i*2.374602)"}},{"canonical_key":"z+z**2+z**3/2","closed_form":"z + z^2 + z^3/2","disk_radius":0.6,"engine_version":"boundary_v3.1","family":"ctc_z_plus_z2_plus_z3_2","param_values":{},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.06235335396284682,"theta":2.37460226,"z":"0.8*exp(i*2.374602)"}},{"canonical_key":"z+z**2+z**3/2","closed_form":"z + z^2 + z^3/2","disk_radius":0.6,"engine_version":"boundary_v3.1","family":"ctc_z_plus_z2_plus_z3_2","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form_v31","witness":{"Re_g_upper_bound":-0.06235335396284662,"theta":2.37460226,"z":"0.8*exp(i*2.374602)"}},{"canonical_key":"z+z**2+z**3/2","closed_form":"z + z^2 + z^3/2","disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ctc_z_plus_z2_plus_z3_2","param_values":{},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-1.0010017873769674,"truncation_caveat":true,"z":[-0.7121464023352646,-0.6877117867544074]}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"janowski","param_values":{"A":0.0,"B":-1.0},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.854097761094262,"theta":4.41786467,"z":"0.8*exp(i*4.417865)"}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"janowski","param_values":{"A":1.0,"B":-0.5},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.16349511449477894,"theta":2.09848572,"z":"0.8*exp(i*2.098486)"}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"janowski","param_values":{"A":0.25,"B":-1.0},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-1.7310064968829,"theta":4.41786467,"z":"0.8*exp(i*4.417865)"}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"janowski","param_values":{"A":0.25,"B":-0.75},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.20268570152974746,"theta":4.39332098,"z":"0.8*exp(i*4.393321)"}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"janowski","param_values":{"A":0.75,"B":-0.75},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-1.1790248072832046,"theta":2.01258279,"z":"0.8*exp(i*2.012583)"}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"janowski","param_values":{"A":1.0,"B":-0.5},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.16205994548792885,"theta":2.08621387,"z":"0.8*exp(i*2.086214)"}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"janowski","param_values":{"A":0.0,"B":-1.0},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.808093089437861,"theta":4.46695205,"z":"0.8*exp(i*4.466952)"}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"janowski","param_values":{"A":0.25,"B":-1.0},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-1.8028914469838704,"theta":1.91440802,"z":"0.8*exp(i*1.914408)"}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"janowski","param_values":{"A":0.25,"B":-0.75},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.20268570152974788,"theta":1.88986433,"z":"0.8*exp(i*1.889864)"}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"janowski","param_values":{"A":0.75,"B":-0.75},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-1.179024807283205,"theta":2.01258279,"z":"0.8*exp(i*2.012583)"}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"janowski","param_values":{"A":0.0,"B":-1.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-4.502322899237638,"truncation_caveat":true,"z":[-0.2728809822588289,-0.9516490789789358]}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"janowski","param_values":{"A":1.0,"B":-0.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-1.4813006490383376,"truncation_caveat":true,"z":[-0.49500000000000044,-0.857365149746594]}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"janowski","param_values":{"A":0.25,"B":-1.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-14.490834838025423,"truncation_caveat":true,"z":[-0.33859994189241205,0.9302956945780493]}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"janowski","param_values":{"A":0.25,"B":-0.75},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-1.6673711695190776,"truncation_caveat":true,"z":[-0.33859994189241205,0.9302956945780493]}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"janowski","param_values":{"A":0.75,"B":-0.75},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-6.755858084229842,"truncation_caveat":true,"z":[-0.40266927664504226,0.9044100030661748]}},{"canonical_key":"laguerre_polynomial","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"laguerre","param_values":{"n":5},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.0990892953300859,"theta":0.07363108,"z":"0.8*exp(i*0.073631)"}},{"canonical_key":"laguerre_polynomial","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"laguerre","param_values":{"n":6},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.4209885234137914,"theta":0.04908739,"z":"0.8*exp(i*0.049087)"}},{"canonical_key":"laguerre_polynomial","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"laguerre","param_values":{"n":5},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.09908929533008687,"theta":0.07363108,"z":"0.8*exp(i*0.073631)"}},{"canonical_key":"laguerre_polynomial","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"laguerre","param_values":{"n":6},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.38441717158057026,"theta":6.13592315,"z":"0.8*exp(i*6.135923)"}},{"canonical_key":"laguerre_polynomial","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"laguerre","param_values":{"n":5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.5156966789139875,"truncation_caveat":true,"z":[0.99,0.0]}},{"canonical_key":"laguerre_polynomial","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"laguerre","param_values":{"n":6},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.9690013599935693,"truncation_caveat":true,"z":[0.99,0.0]}},{"canonical_key":"mocanu","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"mocanu","param_values":{"alpha":0.0},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.062353353962846636,"theta":2.37460226,"z":"0.8*exp(i*2.374602)"}},{"canonical_key":"mocanu","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"mocanu","param_values":{"alpha":0.0},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.06235335396284682,"theta":2.37460226,"z":"0.8*exp(i*2.374602)"}},{"canonical_key":"mocanu","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"mocanu","param_values":{"alpha":0.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-1.0010017873769674,"truncation_caveat":true,"z":[-0.7121464023352646,-0.6877117867544074]}},{"canonical_key":"poly_silverman","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"poly_silverman","param_values":{"variant":2},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.0203408346380258,"theta":6.25864161,"z":"0.8*exp(i*6.258642)"}},{"canonical_key":"poly_silverman","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"poly_silverman","param_values":{"variant":2},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.023073327859307668,"theta":0.00613592,"z":"0.8*exp(i*0.006136)"}},{"canonical_key":"poly_silverman","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"poly_silverman","param_values":{"variant":2},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.9296429201717732,"truncation_caveat":true,"z":[0.99,0.0]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":0.5,"beta":1.5},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.062054024691871226,"theta":3.11704896,"z":"0.8*exp(i*3.117049)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":1.0,"beta":1.0},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.3987867250179684,"theta":2.9943305,"z":"0.8*exp(i*2.99433)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":0.1,"beta":1.25},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.04063979486331707,"theta":3.10477711,"z":"0.8*exp(i*3.104777)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":0.1,"beta":1.5},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.0642570257574985,"theta":3.20295189,"z":"0.8*exp(i*3.202952)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":0.25,"beta":1.25},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.10041902895900867,"theta":3.11704896,"z":"0.8*exp(i*3.117049)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":0.25,"beta":1.5},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.06930205845129435,"theta":3.11704896,"z":"0.8*exp(i*3.117049)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":0.5,"beta":1.0},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.1693161446918814,"theta":3.21522373,"z":"0.8*exp(i*3.215224)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":0.5,"beta":1.25},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.1787729515605214,"theta":3.01887419,"z":"0.8*exp(i*3.018874)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":0.75,"beta":0.75},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.3197468348169298,"theta":3.19068004,"z":"0.8*exp(i*3.19068)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":0.75,"beta":1.0},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.40237821410671437,"theta":3.19068004,"z":"0.8*exp(i*3.19068)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":0.75,"beta":1.25},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.2497800541386517,"theta":3.19068004,"z":"0.8*exp(i*3.19068)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":0.75,"beta":1.5},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.005392865010748063,"theta":3.1538645,"z":"0.8*exp(i*3.153864)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":1.25,"beta":1.0},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.32836683728883603,"theta":3.23976742,"z":"0.8*exp(i*3.239767)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":1.25,"beta":1.25},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.0006767588522825175,"theta":3.14466062,"z":"0.8*exp(i*3.144661)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":1.5,"beta":0.75},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.4981227224385383,"theta":3.23976742,"z":"0.8*exp(i*3.239767)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":1.5,"beta":1.0},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.10370149821972104,"theta":3.19068004,"z":"0.8*exp(i*3.19068)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":2.0,"beta":0.5},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.24200149593976342,"theta":3.23976742,"z":"0.8*exp(i*3.239767)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":1.0,"beta":1.0},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.48875244723627526,"theta":3.19068004,"z":"0.8*exp(i*3.19068)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":0.5,"beta":1.5},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.062054024691872316,"theta":3.16613635,"z":"0.8*exp(i*3.166136)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":0.1,"beta":1.25},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.04063979486331918,"theta":3.17840819,"z":"0.8*exp(i*3.178408)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":0.1,"beta":1.5},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.06232651783389776,"theta":3.06796158,"z":"0.8*exp(i*3.067962)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":0.25,"beta":1.25},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.09440696719091102,"theta":3.06796158,"z":"0.8*exp(i*3.067962)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":0.25,"beta":1.5},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.06330685463808465,"theta":3.21522373,"z":"0.8*exp(i*3.215224)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":0.5,"beta":1.0},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.1738314580035893,"theta":3.09250527,"z":"0.8*exp(i*3.092505)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":0.5,"beta":1.25},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.2028706051652926,"theta":3.09250527,"z":"0.8*exp(i*3.092505)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":0.75,"beta":0.75},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.27691966854279554,"theta":2.9943305,"z":"0.8*exp(i*2.99433)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":0.75,"beta":1.0},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.40237821410671826,"theta":3.19068004,"z":"0.8*exp(i*3.19068)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":0.75,"beta":1.25},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.24978005413865276,"theta":3.19068004,"z":"0.8*exp(i*3.19068)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":0.75,"beta":1.5},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.005620617360244221,"theta":3.14466062,"z":"0.8*exp(i*3.144661)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":1.25,"beta":1.0},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.3606897436246792,"theta":3.09250527,"z":"0.8*exp(i*3.092505)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":1.25,"beta":1.25},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.0006976242404478125,"theta":3.1417844,"z":"0.8*exp(i*3.141784)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":1.5,"beta":0.75},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.5459047041367382,"theta":3.09250527,"z":"0.8*exp(i*3.092505)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":1.5,"beta":1.0},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.10927944673280097,"theta":3.16613635,"z":"0.8*exp(i*3.166136)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":2.0,"beta":0.5},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.2757971074148001,"theta":3.19068004,"z":"0.8*exp(i*3.19068)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":0.5,"beta":1.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.4681844579827581,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":1.0,"beta":1.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-1.5011658996334438,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":0.1,"beta":1.25},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.3720652701869836,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":0.1,"beta":1.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.4253863117646778,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":0.25,"beta":1.25},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.4764702609194728,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":0.25,"beta":1.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.4397292244782199,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":0.5,"beta":1.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.6074551190916515,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":0.5,"beta":1.25},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.707526032859436,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":0.75,"beta":0.75},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.899885605776584,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":0.75,"beta":1.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-1.15924082940836,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":0.75,"beta":1.25},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.8807759569384289,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":0.75,"beta":1.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.42265225289789643,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":1.25,"beta":1.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-1.2963944968757322,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":1.25,"beta":1.25},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.5088927780456116,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":1.5,"beta":0.75},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-1.8628026995768616,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":1.5,"beta":1.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.7682280164098202,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":2.0,"beta":0.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-1.2306301933559887,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"-z*(z+2)/(2*z-2)","closed_form":"z*(1 + z/2)/(1 - z)","disk_radius":0.6,"engine_version":"boundary_v3.0","family":"z_1_plus_half_z_over_1mz","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form","witness":{"Re_g_upper_bound":-0.09862682050569811,"theta":3.04341788,"z":"0.8*exp(i*3.043418)"}},{"canonical_key":"-z*(z+2)/(2*z-2)","closed_form":"z*(1 + z/2)/(1 - z)","disk_radius":0.6,"engine_version":"gft-0.1.0-reaudit-20260610","family":"z_1_plus_half_z_over_1mz","param_values":{},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-108.65129804311283,"truncation_caveat":true,"z":[0.6095048605724017,0.7801306460706547]}},{"canonical_key":"-z*(z+2)/(2*z-2)","closed_form":"z*(1 + z/2)/(1 - z)","disk_radius":0.6,"engine_version":"boundary_v3.1","family":"z_1_plus_half_z_over_1mz","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form_v31","witness":{"Re_g_upper_bound":-0.09862682050569811,"theta":3.04341788,"z":"0.8*exp(i*3.043418)"}},{"canonical_key":"bessel_i_normalized","closed_form":null,"disk_radius":0.3,"engine_version":"boundary_v3.0","family":"bessel_i","param_values":{"nu":-0.75},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.17971824457432772,"theta":3.04341788,"z":"0.6*exp(i*3.043418)"}},{"canonical_key":"bessel_i_normalized","closed_form":null,"disk_radius":0.3,"engine_version":"gft-0.1.0-reaudit-20260610","family":"bessel_i","param_values":{"nu":-0.75},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-6.699666248877981,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"bessel_i_normalized","closed_form":null,"disk_radius":0.3,"engine_version":"boundary_v3.1","family":"bessel_i","param_values":{"nu":-0.75},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.20873188622202674,"theta":3.19068004,"z":"0.6*exp(i*3.19068)"}},{"canonical_key":"bi_a2_1_a3_1","closed_form":null,"disk_radius":0.3,"engine_version":"boundary_v3.0","family":"bi_a2_1_a3_1","param_values":{},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.1634951144947788,"theta":4.18469959,"z":"0.6*exp(i*4.1847)"}},{"canonical_key":"bi_a2_1_a3_1","closed_form":null,"disk_radius":0.3,"engine_version":"boundary_v3.1","family":"bi_a2_1_a3_1","param_values":{},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.16205994548792932,"theta":2.08621387,"z":"0.6*exp(i*2.086214)"}},{"canonical_key":"bi_a2_1_a3_1","closed_form":null,"disk_radius":0.3,"engine_version":"gft-0.1.0-reaudit-20260610","family":"bi_a2_1_a3_1","param_values":{},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-97.50335005555235,"truncation_caveat":true,"z":[-0.49500000000000044,-0.857365149746594]}},{"canonical_key":"z+z**2","closed_form":"z + z^2","disk_radius":0.3,"engine_version":"boundary_v3.0","family":"ctc_z_plus_z2","param_values":{},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.43028849954868525,"theta":3.23976742,"z":"0.6*exp(i*3.239767)"}},{"canonical_key":"z+z**2","closed_form":"z + z^2","disk_radius":0.3,"engine_version":"boundary_v3.1","family":"ctc_z_plus_z2","param_values":{},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.4820936108025519,"theta":3.19068004,"z":"0.6*exp(i*3.19068)"}},{"canonical_key":"z+z**2","closed_form":"z + z^2","disk_radius":0.3,"engine_version":"boundary_v3.1","family":"ctc_z_plus_z2","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form_v31","witness":{"Re_g_upper_bound":-0.43028849954868525,"theta":3.23976742,"z":"0.6*exp(i*3.239767)"}},{"canonical_key":"z+z**2","closed_form":"z + z^2","disk_radius":0.3,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ctc_z_plus_z2","param_values":{},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-97.99999999999987,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.3,"engine_version":"boundary_v3.0","family":"janowski","param_values":{"A":1.0,"B":-0.75},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.009809470402522839,"theta":2.05400027,"z":"0.6*exp(i*2.054)"}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.3,"engine_version":"boundary_v3.1","family":"janowski","param_values":{"A":1.0,"B":-0.75},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.009764762103431756,"theta":4.23225299,"z":"0.6*exp(i*4.232253)"}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.3,"engine_version":"gft-0.1.0-reaudit-20260610","family":"janowski","param_values":{"A":1.0,"B":-0.75},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-14.901487871914002,"truncation_caveat":true,"z":[-0.46477684715803186,-0.8741181169303377]}},{"canonical_key":"kummer_1f1","closed_form":null,"disk_radius":0.3,"engine_version":"boundary_v3.0","family":"kummer_1f1","param_values":{"a":2.5,"c":1.5},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.25805824300050717,"theta":3.21522373,"z":"0.6*exp(i*3.215224)"}},{"canonical_key":"kummer_1f1","closed_form":null,"disk_radius":0.3,"engine_version":"boundary_v3.1","family":"kummer_1f1","param_values":{"a":2.5,"c":1.5},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.23277074675309892,"theta":2.9943305,"z":"0.6*exp(i*2.99433)"}},{"canonical_key":"kummer_1f1","closed_form":null,"disk_radius":0.3,"engine_version":"gft-0.1.0-reaudit-20260610","family":"kummer_1f1","param_values":{"a":2.5,"c":1.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-1.9311764705882222,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"laguerre_polynomial","closed_form":null,"disk_radius":0.3,"engine_version":"boundary_v3.0","family":"laguerre","param_values":{"n":7},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.16123195484341696,"theta":0.12271846,"z":"0.6*exp(i*0.122718)"}},{"canonical_key":"laguerre_polynomial","closed_form":null,"disk_radius":0.3,"engine_version":"boundary_v3.0","family":"laguerre","param_values":{"n":8},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.3780528817442437,"theta":0.12271846,"z":"0.6*exp(i*0.122718)"}},{"canonical_key":"laguerre_polynomial","closed_form":null,"disk_radius":0.3,"engine_version":"boundary_v3.0","family":"laguerre","param_values":{"n":9},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.5974954468800266,"theta":0.12271846,"z":"0.6*exp(i*0.122718)"}},{"canonical_key":"laguerre_polynomial","closed_form":null,"disk_radius":0.3,"engine_version":"boundary_v3.0","family":"laguerre","param_values":{"n":10},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.7331727102750079,"theta":6.02547653,"z":"0.6*exp(i*6.025477)"}},{"canonical_key":"laguerre_polynomial","closed_form":null,"disk_radius":0.3,"engine_version":"boundary_v3.1","family":"laguerre","param_values":{"n":7},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.17692156323063088,"theta":0.04908739,"z":"0.6*exp(i*0.049087)"}},{"canonical_key":"laguerre_polynomial","closed_form":null,"disk_radius":0.3,"engine_version":"boundary_v3.1","family":"laguerre","param_values":{"n":8},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.31303877474063263,"theta":6.03774838,"z":"0.6*exp(i*6.037748)"}},{"canonical_key":"laguerre_polynomial","closed_form":null,"disk_radius":0.3,"engine_version":"boundary_v3.1","family":"laguerre","param_values":{"n":9},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.5253357741499645,"theta":6.03774838,"z":"0.6*exp(i*6.037748)"}},{"canonical_key":"laguerre_polynomial","closed_form":null,"disk_radius":0.3,"engine_version":"boundary_v3.1","family":"laguerre","param_values":{"n":10},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.6442518684447618,"theta":0.3436117,"z":"0.6*exp(i*0.343612)"}},{"canonical_key":"laguerre_polynomial","closed_form":null,"disk_radius":0.3,"engine_version":"gft-0.1.0-reaudit-20260610","family":"laguerre","param_values":{"n":7},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-1.4179938507271894,"truncation_caveat":true,"z":[0.99,0.0]}},{"canonical_key":"laguerre_polynomial","closed_form":null,"disk_radius":0.3,"engine_version":"gft-0.1.0-reaudit-20260610","family":"laguerre","param_values":{"n":8},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-1.8011445150920862,"truncation_caveat":true,"z":[0.99,0.0]}},{"canonical_key":"laguerre_polynomial","closed_form":null,"disk_radius":0.3,"engine_version":"gft-0.1.0-reaudit-20260610","family":"laguerre","param_values":{"n":9},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-2.2394959632219926,"truncation_caveat":true,"z":[0.9605927690132365,-0.2395026766436712]}},{"canonical_key":"laguerre_polynomial","closed_form":null,"disk_radius":0.3,"engine_version":"gft-0.1.0-reaudit-20260610","family":"laguerre","param_values":{"n":10},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-3.1406321206082684,"truncation_caveat":true,"z":[0.941545951132202,0.3059268244311979]}},{"canonical_key":"mittag_leffler_2p","closed_form":null,"disk_radius":0.3,"engine_version":"boundary_v3.0","family":"mittag_leffler_2p","param_values":{"alpha":0.75,"beta":0.5},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.41994235233317806,"theta":3.16613635,"z":"0.6*exp(i*3.166136)"}},{"canonical_key":"mittag_leffler_2p","closed_form":null,"disk_radius":0.3,"engine_version":"gft-0.1.0-reaudit-20260610","family":"mittag_leffler_2p","param_values":{"alpha":0.75,"beta":0.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-2.53025161443816,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"mittag_leffler_2p","closed_form":null,"disk_radius":0.3,"engine_version":"boundary_v3.1","family":"mittag_leffler_2p","param_values":{"alpha":0.75,"beta":0.5},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.38032890075640285,"theta":2.9943305,"z":"0.6*exp(i*2.99433)"}},{"canonical_key":"poly_z_z2_z3","closed_form":null,"disk_radius":0.3,"engine_version":"boundary_v3.0","family":"poly_z_z2_z3","param_values":{},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.1634951144947788,"theta":4.18469959,"z":"0.6*exp(i*4.1847)"}},{"canonical_key":"poly_z_z2_z3","closed_form":null,"disk_radius":0.3,"engine_version":"boundary_v3.1","family":"poly_z_z2_z3","param_values":{},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.16205994548792932,"theta":2.08621387,"z":"0.6*exp(i*2.086214)"}},{"canonical_key":"poly_z_z2_z3","closed_form":null,"disk_radius":0.3,"engine_version":"gft-0.1.0-reaudit-20260610","family":"poly_z_z2_z3","param_values":{},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-97.50335005555235,"truncation_caveat":true,"z":[-0.49500000000000044,-0.857365149746594]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.3,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":1.25,"beta":0.5},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.1148063400305325,"theta":3.19068004,"z":"0.6*exp(i*3.19068)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.3,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":1.25,"beta":0.75},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.000441275198426607,"theta":3.14466062,"z":"0.6*exp(i*3.144661)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.3,"engine_version":"boundary_v3.0","family":"wright","param_values":{"alpha":1.5,"beta":0.5},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.08876310980727652,"theta":3.19068004,"z":"0.6*exp(i*3.19068)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.3,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":1.25,"beta":0.5},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.11973818511612892,"theta":3.16613635,"z":"0.6*exp(i*3.166136)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.3,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":1.25,"beta":0.75},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.0004621722726954966,"theta":3.1417844,"z":"0.6*exp(i*3.141784)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.3,"engine_version":"boundary_v3.1","family":"wright","param_values":{"alpha":1.5,"beta":0.5},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.09412303095138212,"theta":3.16613635,"z":"0.6*exp(i*3.166136)"}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.3,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":1.25,"beta":0.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-3.311557202144671,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.3,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":1.25,"beta":0.75},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-2.417241700690444,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"wright_normalized","closed_form":null,"disk_radius":0.3,"engine_version":"gft-0.1.0-reaudit-20260610","family":"wright","param_values":{"alpha":1.5,"beta":0.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-3.73798635063485,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"-z*(z+1)/(z-1)","closed_form":"z*(1 + z)/(1 - z)","disk_radius":0.3,"engine_version":"boundary_v3.0","family":"z_1_plus_z_over_1mz","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form","witness":{"Re_g_upper_bound":-0.6219469615739868,"theta":2.94524311,"z":"0.6*exp(i*2.945243)"}},{"canonical_key":"-z*(z+1)/(z-1)","closed_form":"z*(1 + z)/(1 - z)","disk_radius":0.3,"engine_version":"gft-0.1.0-reaudit-20260610","family":"z_1_plus_z_over_1mz","param_values":{},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-100.65371075324877,"truncation_caveat":true,"z":[0.03427482503883466,-0.9815025710396783]}},{"canonical_key":"-z*(z+1)/(z-1)","closed_form":"z*(1 + z)/(1 - z)","disk_radius":0.3,"engine_version":"boundary_v3.1","family":"z_1_plus_z_over_1mz","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form_v31","witness":{"Re_g_upper_bound":-0.6219469615739868,"theta":2.94524311,"z":"0.6*exp(i*2.945243)"}},{"canonical_key":"z*exp(2*z)","closed_form":"z*exp(2*z)","disk_radius":0.3,"engine_version":"boundary_v3.0","family":"z_exp_2z","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form","witness":{"Re_g_upper_bound":-0.17694233648387625,"theta":2.94524311,"z":"0.6*exp(i*2.945243)"}},{"canonical_key":"z*exp(2*z)","closed_form":"z*exp(2*z)","disk_radius":0.3,"engine_version":"boundary_v3.1","family":"z_exp_2z","param_values":{},"property":"starlike","verifier":"boundary_scan_centered_v31","witness":{"Re_g_upper_bound":-0.17084255604623103,"theta":3.36248589,"z":"0.6*exp(i*3.362486)"}},{"canonical_key":"z*exp(2*z)","closed_form":"z*exp(2*z)","disk_radius":0.3,"engine_version":"boundary_v3.1","family":"z_exp_2z","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form_v31","witness":{"Re_g_upper_bound":-0.17694233648387625,"theta":2.94524311,"z":"0.6*exp(i*2.945243)"}},{"canonical_key":"z*exp(2*z)","closed_form":"z*exp(2*z)","disk_radius":0.3,"engine_version":"gft-0.1.0-reaudit-20260610","family":"z_exp_2z","param_values":{},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-0.9799999999949284,"truncation_caveat":true,"z":[-0.99,1.2124003311558797e-16]}},{"canonical_key":"z/(z-1)**4","closed_form":"z/(1-z)**4","disk_radius":0.3,"engine_version":"boundary_v3.0","family":"z_over_1_minus_z_4th","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form","witness":{"Re_g_upper_bound":-0.4814991271072325,"theta":2.74889357,"z":"0.6*exp(i*2.748894)"}},{"canonical_key":"z/(z-1)**4","closed_form":"z/(1-z)**4","disk_radius":0.3,"engine_version":"gft-0.1.0-reaudit-20260610","family":"z_over_1_minus_z_4th","param_values":{},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-244.52572238949082,"truncation_caveat":true,"z":[0.19014344990770973,0.6631090136098873]}},{"canonical_key":"z/(z-1)**4","closed_form":"z/(1-z)**4","disk_radius":0.3,"engine_version":"boundary_v3.1","family":"z_over_1_minus_z_4th","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form_v31","witness":{"Re_g_upper_bound":-0.4814991271072325,"theta":2.74889357,"z":"0.6*exp(i*2.748894)"}},{"canonical_key":"-z/(z-1)**3","closed_form":"z/(1-z)**3","disk_radius":0.3,"engine_version":"boundary_v3.0","family":"z_over_1_minus_z_cubed","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form","witness":{"Re_g_upper_bound":-0.12159171448471678,"theta":2.94524311,"z":"0.6*exp(i*2.945243)"}},{"canonical_key":"-z/(z-1)**3","closed_form":"z/(1-z)**3","disk_radius":0.3,"engine_version":"gft-0.1.0-reaudit-20260610","family":"z_over_1_minus_z_cubed","param_values":{},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-158.18489142168693,"truncation_caveat":true,"z":[0.4343378156958079,-0.6439322926996849]}},{"canonical_key":"-z/(z-1)**3","closed_form":"z/(1-z)**3","disk_radius":0.3,"engine_version":"boundary_v3.1","family":"z_over_1_minus_z_cubed","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form_v31","witness":{"Re_g_upper_bound":-0.12159171448471678,"theta":2.94524311,"z":"0.6*exp(i*2.945243)"}},{"canonical_key":"z/(z+1)**3","closed_form":"z/(1+z)**3","disk_radius":0.3,"engine_version":"boundary_v3.0","family":"z_over_1_plus_z_cubed","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form","witness":{"Re_g_upper_bound":-0.1215917144847168,"theta":6.08683577,"z":"0.6*exp(i*6.086836)"}},{"canonical_key":"z/(z+1)**3","closed_form":"z/(1+z)**3","disk_radius":0.3,"engine_version":"gft-0.1.0-reaudit-20260610","family":"z_over_1_plus_z_cubed","param_values":{},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-158.18489142149406,"truncation_caveat":true,"z":[-0.4343378156958077,0.6439322926996849]}},{"canonical_key":"z/(z+1)**3","closed_form":"z/(1+z)**3","disk_radius":0.3,"engine_version":"boundary_v3.1","family":"z_over_1_plus_z_cubed","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form_v31","witness":{"Re_g_upper_bound":-0.1215917144847168,"theta":6.08683577,"z":"0.6*exp(i*6.086836)"}},{"canonical_key":"bessel_i_normalized","closed_form":null,"disk_radius":0.0,"engine_version":"boundary_v3.0","family":"bessel_i","param_values":{"nu":-0.9},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-1.3073437109561545,"theta":3.04341788,"z":"0.3*exp(i*3.043418)"}},{"canonical_key":"bessel_i_normalized","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"bessel_i","param_values":{"nu":-0.9},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-64.41825244858035,"truncation_caveat":true,"z":[-0.4133613445378151,5.062216474794815e-17]}},{"canonical_key":"bessel_j_normalized","closed_form":null,"disk_radius":0.0,"engine_version":"boundary_v3.0","family":"bessel_j","param_values":{"nu":-0.9},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-1.307343710956155,"theta":6.18501054,"z":"0.3*exp(i*6.185011)"}},{"canonical_key":"bessel_j_normalized","closed_form":null,"disk_radius":0.0,"engine_version":"boundary_v3.0","family":"bessel_j","param_values":{"nu":-0.8},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-1.0643739733514506,"theta":6.18501054,"z":"0.6*exp(i*6.185011)"}},{"canonical_key":"bessel_j_normalized","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"bessel_j","param_values":{"nu":-0.9},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-64.41825244858035,"truncation_caveat":true,"z":[0.4133613445378151,0.0]}},{"canonical_key":"bessel_j_normalized","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"bessel_j","param_values":{"nu":-0.8},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-142.1080156746521,"truncation_caveat":true,"z":[0.8715126050420168,0.0]}},{"canonical_key":"bi_sqrt2_bound","closed_form":null,"disk_radius":0.0,"engine_version":"boundary_v3.0","family":"bi_sqrt2_bound","param_values":{},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-2.9993631036621,"theta":3.04341788,"z":"0.6*exp(i*3.043418)"}},{"canonical_key":"bi_sqrt2_bound","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"bi_sqrt2_bound","param_values":{},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-476.89796959050415,"truncation_caveat":true,"z":[-0.7056302521008403,8.641478296168339e-17]}},{"canonical_key":"convex_order_extremal","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"convex_order","param_values":{"alpha":0.1},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-18.979666923146084,"truncation_caveat":true,"z":[0.8207471968294914,-0.5536009744360391]}},{"canonical_key":"convex_order_extremal","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"convex_order","param_values":{"alpha":0.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-88.86488833885248,"truncation_caveat":true,"z":[-0.49500000000000044,-0.857365149746594]}},{"canonical_key":"convex_order_extremal","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"convex_order","param_values":{"alpha":0.0521},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-33.5871068087679,"truncation_caveat":true,"z":[0.8207471968294912,0.5536009744360394]}},{"canonical_key":"convex_order_extremal","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"convex_order","param_values":{"alpha":0.1042},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-18.14190867349692,"truncation_caveat":true,"z":[0.8207471968294914,-0.5536009744360391]}},{"canonical_key":"convex_order_extremal","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"convex_order","param_values":{"alpha":0.1563},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-12.968573562839294,"truncation_caveat":true,"z":[0.9516490789789357,0.2728809822588292]}},{"canonical_key":"convex_order_extremal","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"convex_order","param_values":{"alpha":0.2084},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-8.875653285642626,"truncation_caveat":true,"z":[0.9516490789789357,0.2728809822588292]}},{"canonical_key":"z+2*z**2","closed_form":"z + 2z^2","disk_radius":0.0,"engine_version":"boundary_v3.0","family":"ctc_z_plus_2z2","param_values":{},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.43028849954868525,"theta":3.23976742,"z":"0.3*exp(i*3.239767)"}},{"canonical_key":"z+2*z**2","closed_form":"z + 2z^2","disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ctc_z_plus_2z2","param_values":{},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-63.38461538461455,"truncation_caveat":true,"z":[-0.4923529411764705,6.029584534625496e-17]}},{"canonical_key":"de_branges_a2_2","closed_form":null,"disk_radius":0.0,"engine_version":"boundary_v3.0","family":"de_branges_boundary_a2","param_values":{},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.43028849954868525,"theta":3.23976742,"z":"0.3*exp(i*3.239767)"}},{"canonical_key":"de_branges_a2_2","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"de_branges_boundary_a2","param_values":{},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-63.38461538461455,"truncation_caveat":true,"z":[-0.4923529411764705,6.029584534625496e-17]}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.0,"engine_version":"boundary_v3.0","family":"janowski","param_values":{"A":1.0,"B":-1.0},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.8652027890292434,"theta":2.01258279,"z":"0.6*exp(i*2.012583)"}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.0,"engine_version":"boundary_v3.0","family":"janowski","param_values":{"A":0.75,"B":-1.0},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.5347864064716007,"theta":2.01258279,"z":"0.6*exp(i*2.012583)"}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"janowski","param_values":{"A":1.0,"B":-1.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-64.95437862829394,"truncation_caveat":true,"z":[-0.3751204527523677,0.7691109053331442]}},{"canonical_key":"janowski_starlike_extremal","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"janowski","param_values":{"A":0.75,"B":-1.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-55.864305415515695,"truncation_caveat":true,"z":[-0.36732762211223724,-0.8250313473348766]}},{"canonical_key":"z/(1-z)**(2*alpha)","closed_form":"z/(1-z)^(2*alpha)","disk_radius":0.0,"engine_version":"boundary_v3.0","family":"koebe_alpha","param_values":{"alpha":1.5},"property":"starlike","verifier":"boundary_scan_closed_form","witness":{"Re_g_upper_bound":-0.11727499521264018,"theta":2.84706834,"z":"0.6*exp(i*2.847068)"}},{"canonical_key":"z/(1-z)**(2*alpha)","closed_form":"z/(1-z)^(2*alpha)","disk_radius":0.0,"engine_version":"boundary_v3.0","family":"koebe_alpha","param_values":{"alpha":2.5},"property":"starlike","verifier":"boundary_scan_closed_form","witness":{"Re_g_upper_bound":-0.14459989361456937,"theta":2.94524311,"z":"0.3*exp(i*2.945243)"}},{"canonical_key":"z/(1-z)**(2*alpha)","closed_form":"z/(1-z)^(2*alpha)","disk_radius":0.0,"engine_version":"boundary_v3.0","family":"koebe_alpha","param_values":{"alpha":2.25},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.037630541644581836,"theta":3.20371888,"z":"0.3*exp(i*3.203719)"}},{"canonical_key":"z/(1-z)**(2*alpha)","closed_form":"z/(1-z)^(2*alpha)","disk_radius":0.0,"engine_version":"boundary_v3.0","family":"koebe_alpha","param_values":{"alpha":3.0},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-0.3793740366662568,"theta":3.00583535,"z":"0.3*exp(i*3.005835)"}},{"canonical_key":"z/(1-z)**(2*alpha)","closed_form":"z/(1-z)^(2*alpha)","disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"koebe_alpha","param_values":{"alpha":1.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-107.04468443509516,"truncation_caveat":true,"z":[0.31428489640892354,-0.8634906561591519]}},{"canonical_key":"z/(1-z)**(2*alpha)","closed_form":"z/(1-z)^(2*alpha)","disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"koebe_alpha","param_values":{"alpha":2.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-244.59715464172172,"truncation_caveat":true,"z":[0.6618628136385869,0.5171039030151222]}},{"canonical_key":"z/(1-z)**(2*alpha)","closed_form":"z/(1-z)^(2*alpha)","disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"koebe_alpha","param_values":{"alpha":0.4},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-17.837747083761897,"truncation_caveat":true,"z":[0.9516490789789357,0.2728809822588292]}},{"canonical_key":"z/(1-z)**(2*alpha)","closed_form":"z/(1-z)^(2*alpha)","disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"koebe_alpha","param_values":{"alpha":0.6},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-383.74914887530707,"truncation_caveat":true,"z":[0.5949152356949368,-0.761456777791907]}},{"canonical_key":"z/(1-z)**(2*alpha)","closed_form":"z/(1-z)^(2*alpha)","disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"koebe_alpha","param_values":{"alpha":0.75},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-107.04468443509516,"truncation_caveat":true,"z":[0.31428489640892354,-0.8634906561591519]}},{"canonical_key":"z/(1-z)**(2*alpha)","closed_form":"z/(1-z)^(2*alpha)","disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"koebe_alpha","param_values":{"alpha":0.9},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-182.25404465670474,"truncation_caveat":true,"z":[-0.2108379814507693,0.8456249560679293]}},{"canonical_key":"z/(1-z)**(2*alpha)","closed_form":"z/(1-z)^(2*alpha)","disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"koebe_alpha","param_values":{"alpha":1.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-388.81663778530583,"truncation_caveat":true,"z":[-0.624179204256013,-0.5620134798787216]}},{"canonical_key":"z/(1-z)**(2*alpha)","closed_form":"z/(1-z)^(2*alpha)","disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"koebe_alpha","param_values":{"alpha":1.1},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-117.03055806989269,"truncation_caveat":true,"z":[-0.6065685453665486,0.5461567713918984]}},{"canonical_key":"z/(1-z)**(2*alpha)","closed_form":"z/(1-z)^(2*alpha)","disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"koebe_alpha","param_values":{"alpha":1.25},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-244.59715464172172,"truncation_caveat":true,"z":[0.6618628136385869,0.5171039030151222]}},{"canonical_key":"z/(1-z)**(2*alpha)","closed_form":"z/(1-z)^(2*alpha)","disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"koebe_alpha","param_values":{"alpha":1.75},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-261.5591507791479,"truncation_caveat":true,"z":[0.5889529924450025,0.4941902387413569]}},{"canonical_key":"z/(1-z)**(2*alpha)","closed_form":"z/(1-z)^(2*alpha)","disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"koebe_alpha","param_values":{"alpha":2.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-244.52572238949082,"truncation_caveat":true,"z":[0.19014344990770973,0.6631090136098873]}},{"canonical_key":"z/(1-z)**(2*alpha)","closed_form":"z/(1-z)^(2*alpha)","disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"koebe_alpha","param_values":{"alpha":2.25},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-1176.654151058957,"truncation_caveat":true,"z":[0.6951390015927522,-0.3094958237858294]}},{"canonical_key":"z/(1-z)**(2*alpha)","closed_form":"z/(1-z)^(2*alpha)","disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"koebe_alpha","param_values":{"alpha":3.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-168.89884647157,"truncation_caveat":true,"z":[-0.5266728241231426,-0.07401903831733232]}},{"canonical_key":"kummer_1f1","closed_form":null,"disk_radius":0.0,"engine_version":"boundary_v3.0","family":"kummer_1f1","param_values":{"a":5.0,"c":2.0},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-1.4923501065913949,"theta":3.27658296,"z":"0.6*exp(i*3.276583)"}},{"canonical_key":"kummer_1f1","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"kummer_1f1","param_values":{"a":5.0,"c":2.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-837.757057271894,"truncation_caveat":true,"z":[-0.934705882352941,1.1446845669677317e-16]}},{"canonical_key":"large_a3","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"large_a3","param_values":{},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-69.74037231207133,"truncation_caveat":true,"z":[-0.01993963681347081,-0.5709964901599018]}},{"canonical_key":"lommel_s_normalized","closed_form":null,"disk_radius":0.0,"engine_version":"boundary_v3.0","family":"lommel_s","param_values":{"mu":4,"nu":0.5},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-12.833109759753006,"theta":2.30461439,"z":"0.3*exp(i*2.304614)"}},{"canonical_key":"lommel_s_normalized","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"lommel_s","param_values":{"mu":1,"nu":0.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-121.44646403732709,"truncation_caveat":true,"z":[0.2274372739042572,0.42774730023795904]}},{"canonical_key":"lommel_s_normalized","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"lommel_s","param_values":{"mu":2,"nu":0.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-61.24079651868381,"truncation_caveat":true,"z":[-0.3915231495378786,0.06903609483548294]}},{"canonical_key":"lommel_s_normalized","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"lommel_s","param_values":{"mu":3,"nu":0.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-312.7241731724779,"truncation_caveat":true,"z":[-0.344848227462342,-0.06080604675110077]}},{"canonical_key":"lommel_s_normalized","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"lommel_s","param_values":{"mu":4,"nu":0.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-93.36840619640708,"truncation_caveat":true,"z":[-0.20788032367299988,0.230874489057977]}},{"canonical_key":"lommel_s_normalized","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"lommel_s","param_values":{"mu":5,"nu":0.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-951.1694566941075,"truncation_caveat":true,"z":[0.2508315149377759,0.12233870407449797]}},{"canonical_key":"lommel_s_normalized","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"lommel_s","param_values":{"mu":6,"nu":0.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-76.40593950966118,"truncation_caveat":true,"z":[0.22243264423118037,0.10848764935242292]}},{"canonical_key":"lommel_s_normalized","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"lommel_s","param_values":{"mu":7,"nu":0.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-74.1619345376595,"truncation_caveat":true,"z":[0.20113349120123372,0.09809935831086664]}},{"canonical_key":"lommel_s_normalized","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"lommel_s","param_values":{"mu":8,"nu":0.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-139.31028669591396,"truncation_caveat":true,"z":[-0.07791187552137667,0.19283865882796628]}},{"canonical_key":"ma_minda_1_z_z2_2","closed_form":null,"disk_radius":0.0,"engine_version":"boundary_v3.0","family":"maminda_1_z_z2_2","param_values":{},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-2.3794338711823158,"theta":3.04341788,"z":"0.6*exp(i*3.043418)"}},{"canonical_key":"ma_minda_1_z_z2_2","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"maminda_1_z_z2_2","param_values":{},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-266.621557150003,"truncation_caveat":true,"z":[-0.729327731092437,8.931688714117545e-17]}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"mittag_leffler","param_values":{"alpha":0.1},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-13.31701231162759,"truncation_caveat":true,"z":[-0.49500000000000044,-0.857365149746594]}},{"canonical_key":"mittag_leffler_normalized","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"mittag_leffler","param_values":{"alpha":0.05},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-90.08911132111392,"truncation_caveat":true,"z":[-0.49500000000000044,-0.857365149746594]}},{"canonical_key":"mittag_leffler_2p","closed_form":null,"disk_radius":0.0,"engine_version":"boundary_v3.0","family":"mittag_leffler_2p","param_values":{"alpha":1.0,"beta":0.5},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-1.2958698603736993,"theta":3.3133985,"z":"0.6*exp(i*3.313399)"}},{"canonical_key":"mittag_leffler_2p","closed_form":null,"disk_radius":0.0,"engine_version":"boundary_v3.0","family":"mittag_leffler_2p","param_values":{"alpha":1.5,"beta":0.5},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-4.744293208708326,"theta":3.19068004,"z":"0.6*exp(i*3.19068)"}},{"canonical_key":"mittag_leffler_2p","closed_form":null,"disk_radius":0.0,"engine_version":"boundary_v3.0","family":"mittag_leffler_2p","param_values":{"alpha":2.0,"beta":0.5},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-1.465960048750093,"theta":3.04341788,"z":"0.6*exp(i*3.043418)"}},{"canonical_key":"mittag_leffler_2p","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"mittag_leffler_2p","param_values":{"alpha":1.0,"beta":0.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-136.03115817475043,"truncation_caveat":true,"z":[-0.8478151260504201,1.0382740803863567e-16]}},{"canonical_key":"mittag_leffler_2p","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"mittag_leffler_2p","param_values":{"alpha":1.5,"beta":0.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-94.44701084299344,"truncation_caveat":true,"z":[-0.6898319327731092,8.448004684202203e-17]}},{"canonical_key":"mittag_leffler_2p","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"mittag_leffler_2p","param_values":{"alpha":2.0,"beta":0.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-703.2996205489062,"truncation_caveat":true,"z":[-0.8241176470588235,1.0092530385914363e-16]}},{"canonical_key":"z*(3*z+1)","closed_form":"z + 3*z**2","disk_radius":0.0,"engine_version":"boundary_v3.0","family":"poly_z_3z2","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form","witness":{"Re_g_upper_bound":-3.5890607078153876,"theta":3.04341788,"z":"0.3*exp(i*3.043418)"}},{"canonical_key":"z*(3*z+1)","closed_form":"z + 3*z**2","disk_radius":0.0,"engine_version":"boundary_v3.1","family":"poly_z_3z2","param_values":{},"property":"starlike","verifier":"boundary_scan_closed_form_v31","witness":{"Re_g_upper_bound":-3.5890607078153876,"theta":3.04341788,"z":"0.3*exp(i*3.043418)"}},{"canonical_key":"z*(3*z+1)","closed_form":"z + 3*z**2","disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"poly_z_3z2","param_values":{},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-46.57142857142821,"truncation_caveat":true,"z":[-0.32647058823529407,3.9981116089810645e-17]}},{"canonical_key":"q_exp","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"q_exp","param_values":{"q":0.05},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-8.527013246193762,"truncation_caveat":true,"z":[-0.8898061058361754,0.4339874353211865]}},{"canonical_key":"q_exp","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"q_exp","param_values":{"q":0.025},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-20.026527421500063,"truncation_caveat":true,"z":[-0.49500000000000044,-0.857365149746594]}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.0,"engine_version":"boundary_v3.0","family":"ruscheweyh","param_values":{"lambda":2.5},"property":"starlike","verifier":"boundary_scan_polynomial","witness":{"Re_g_upper_bound":-15.30900672189227,"theta":4.17688587,"z":"0.8*exp(i*4.176886)"}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ruscheweyh","param_values":{"lambda":1.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-88.86488833885248,"truncation_caveat":true,"z":[-0.49500000000000044,-0.857365149746594]}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ruscheweyh","param_values":{"lambda":1.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-176.91682060828225,"truncation_caveat":true,"z":[0.06520178634083233,-0.9324289858016828]}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ruscheweyh","param_values":{"lambda":2.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-528.2005142787034,"truncation_caveat":true,"z":[0.7242401715190179,-0.5261912850984637]}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ruscheweyh","param_values":{"lambda":0.6},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-9.452578092556704,"truncation_caveat":true,"z":[0.9516490789789357,0.2728809822588292]}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ruscheweyh","param_values":{"lambda":0.75},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-15.948495568861174,"truncation_caveat":true,"z":[0.9516490789789357,0.2728809822588292]}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ruscheweyh","param_values":{"lambda":0.8},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-18.979666923146006,"truncation_caveat":true,"z":[0.8207471968294914,-0.5536009744360391]}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ruscheweyh","param_values":{"lambda":0.9},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-34.537551176791546,"truncation_caveat":true,"z":[0.8207471968294912,0.5536009744360394]}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ruscheweyh","param_values":{"lambda":1.1},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-215.30953860944584,"truncation_caveat":true,"z":[-0.49105042016806766,-0.8505242768091371]}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ruscheweyh","param_values":{"lambda":1.25},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-471.64406975347157,"truncation_caveat":true,"z":[0.06740585643560469,-0.9639486566334218]}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ruscheweyh","param_values":{"lambda":1.4},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-790.228024750828,"truncation_caveat":true,"z":[0.5851888191099597,0.7490075322727422]}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ruscheweyh","param_values":{"lambda":1.6},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-94.31743317278209,"truncation_caveat":true,"z":[0.06409975129344615,-0.9166691503858133]}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ruscheweyh","param_values":{"lambda":1.75},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-70.92354898340409,"truncation_caveat":true,"z":[0.06299771624605997,-0.9009093149699438]}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ruscheweyh","param_values":{"lambda":1.9},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-178.19495240487362,"truncation_caveat":true,"z":[0.7306307259283663,0.5308342946543873]}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ruscheweyh","param_values":{"lambda":2.25},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-128.69625994507413,"truncation_caveat":true,"z":[0.29267152264582247,-0.8041083997867986]}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ruscheweyh","param_values":{"lambda":2.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-113.70677328372678,"truncation_caveat":true,"z":[0.2845665074846594,0.7818400536471662]}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ruscheweyh","param_values":{"lambda":2.75},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-147.06761148164392,"truncation_caveat":true,"z":[-0.19555014401455498,0.7843087891637655]}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ruscheweyh","param_values":{"lambda":3.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-229.2259867849846,"truncation_caveat":true,"z":[0.4704751704273787,0.6475535186068382]}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ruscheweyh","param_values":{"lambda":3.5},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-170.8296961162982,"truncation_caveat":true,"z":[-0.18217328625786747,0.7306571431226222]}},{"canonical_key":"ruscheweyh","closed_form":null,"disk_radius":0.0,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ruscheweyh","param_values":{"lambda":4.0},"property":"starlike","verifier":"pointwise_starlike_iv","witness":{"Re_upper_bound":-105.49444717918377,"truncation_caveat":true,"z":[-0.53025569017887,0.47744436794899714]}},{"canonical_key":"atanh(z)","closed_form":"atanh(z)","disk_radius":null,"engine_version":"gft-0.1.0-reaudit-20260610","family":"arctanh_z","param_values":{},"property":"nehari_univalent","verifier":"pointwise_nehari_univalent_iv","witness":{"criterion_lower_bound":5.115046032760909,"threshold":2.0,"truncation_caveat":true,"z":[0.13668201940506597,0.9725431024691372]}},{"canonical_key":"atanh(z)","closed_form":"atanh(z)","disk_radius":null,"engine_version":"gft-0.1.0-reaudit-20260610","family":"arctanh_z","param_values":{},"property":"becker_univalent","verifier":"pointwise_becker_univalent_iv","witness":{"criterion_lower_bound":1.7223017673780425,"threshold":1.0,"truncation_caveat":true,"z":[0.1377813699504648,0.9803653880541546]}},{"canonical_key":"z+z**2","closed_form":"z + z^2","disk_radius":null,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ctc_z_plus_z2","param_values":{},"property":"becker_univalent","verifier":"pointwise_becker_univalent_iv","witness":{"criterion_lower_bound":2973.999747899431,"threshold":1.0,"truncation_caveat":true,"z":[-0.5002521008403361,6.126321340608566e-17]}},{"canonical_key":"z+z**2+z**3/2","closed_form":"z + z^2 + z^3/2","disk_radius":null,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ctc_z_plus_z2_plus_z3_2","param_values":{},"property":"nehari_univalent","verifier":"pointwise_nehari_univalent_iv","witness":{"criterion_lower_bound":1529.2850484318442,"threshold":2.0,"truncation_caveat":true,"z":[-0.660334627425535,-0.4797611895392261]}},{"canonical_key":"z+z**2+z**3/2","closed_form":"z + z^2 + z^3/2","disk_radius":null,"engine_version":"gft-0.1.0-reaudit-20260610","family":"ctc_z_plus_z2_plus_z3_2","param_values":{},"property":"becker_univalent","verifier":"pointwise_becker_univalent_iv","witness":{"criterion_lower_bound":32.11749175944935,"threshold":1.0,"truncation_caveat":true,"z":[-0.660334627425535,-0.4797611895392261]}},{"canonical_key":"z/(1-z)**2","closed_form":"z/(1-z)^2","disk_radius":null,"engine_version":"gft-0.1.0-reaudit-20260610","family":"koebe","param_values":{},"property":"nehari_univalent","verifier":"pointwise_nehari_univalent_iv","witness":{"criterion_lower_bound":281712.35684408894,"threshold":2.0,"truncation_caveat":true,"z":[0.20756187777110346,-0.7238542905296869]}},{"canonical_key":"z/(1-z)**2","closed_form":"z/(1-z)^2","disk_radius":null,"engine_version":"gft-0.1.0-reaudit-20260610","family":"koebe","param_values":{},"property":"becker_univalent","verifier":"pointwise_becker_univalent_iv","witness":{"criterion_lower_bound":432.00245046086224,"threshold":1.0,"truncation_caveat":true,"z":[0.20756187777110346,-0.7238542905296869]}},{"canonical_key":"-log(1-z)","closed_form":"-log(1-z)","disk_radius":null,"engine_version":"gft-0.1.0-reaudit-20260610","family":"log_1_minus_z_neg","param_values":{},"property":"becker_univalent","verifier":"pointwise_becker_univalent_iv","witness":{"criterion_lower_bound":1.8063843475894743,"threshold":1.0,"truncation_caveat":true,"z":[-0.49500000000000044,-0.857365149746594]}},{"canonical_key":"z*(3*z+1)","closed_form":"z + 3*z**2","disk_radius":null,"engine_version":"gft-0.1.0-reaudit-20260610","family":"poly_z_3z2","param_values":{},"property":"nehari_univalent","verifier":"pointwise_nehari_univalent_iv","witness":{"criterion_lower_bound":427156.20152982825,"threshold":2.0,"truncation_caveat":true,"z":[-0.16848739495798318,2.0633754893197e-17]}},{"canonical_key":"z*(3*z+1)","closed_form":"z + 3*z**2","disk_radius":null,"engine_version":"gft-0.1.0-reaudit-20260610","family":"poly_z_3z2","param_values":{},"property":"becker_univalent","verifier":"pointwise_becker_univalent_iv","witness":{"criterion_lower_bound":533.6392049127251,"threshold":1.0,"truncation_caveat":true,"z":[-0.16848739495798318,2.0633754893197e-17]}},{"canonical_key":"3*z**3+z","closed_form":"z + 3*z**3","disk_radius":null,"engine_version":"gft-0.1.0-reaudit-20260610","family":"poly_z_3z3","param_values":{},"property":"nehari_univalent","verifier":"pointwise_nehari_univalent_iv","witness":{"criterion_lower_bound":1102790.3190638646,"threshold":2.0,"truncation_caveat":true,"z":[2.0474242074820665e-17,0.33436974789915963]}},{"canonical_key":"3*z**3+z","closed_form":"z + 3*z**3","disk_radius":null,"engine_version":"gft-0.1.0-reaudit-20260610","family":"poly_z_3z3","param_values":{},"property":"becker_univalent","verifier":"pointwise_becker_univalent_iv","witness":{"criterion_lower_bound":858.3201818835206,"threshold":1.0,"truncation_caveat":true,"z":[2.0474242074820665e-17,0.33436974789915963]}},{"canonical_key":"z*cos(z)","closed_form":"z*cos(z)","disk_radius":null,"engine_version":"gft-0.1.0-reaudit-20260610","family":"z_cos_z","param_values":{},"property":"nehari_univalent","verifier":"pointwise_nehari_univalent_iv","witness":{"criterion_lower_bound":9014.353735958946,"threshold":2.0,"truncation_caveat":true,"z":[0.8636134453781512,0.0]}},{"canonical_key":"z*cos(z)","closed_form":"z*cos(z)","disk_radius":null,"engine_version":"gft-0.1.0-reaudit-20260610","family":"z_cos_z","param_values":{},"property":"becker_univalent","verifier":"pointwise_becker_univalent_iv","witness":{"criterion_lower_bound":77.57404129539401,"threshold":1.0,"truncation_caveat":true,"z":[0.8636134453781512,0.0]}},{"canonical_key":"z*exp(2*z)","closed_form":"z*exp(2*z)","disk_radius":null,"engine_version":"gft-0.1.0-reaudit-20260610","family":"z_exp_2z","param_values":{},"property":"nehari_univalent","verifier":"pointwise_nehari_univalent_iv","witness":{"criterion_lower_bound":13262553.375103379,"threshold":2.0,"truncation_caveat":true,"z":[-0.5002521008403361,6.126321340608566e-17]}},{"canonical_key":"z*exp(2*z)","closed_form":"z*exp(2*z)","disk_radius":null,"engine_version":"gft-0.1.0-reaudit-20260610","family":"z_exp_2z","param_values":{},"property":"becker_univalent","verifier":"pointwise_becker_univalent_iv","witness":{"criterion_lower_bound":2972.500252211303,"threshold":1.0,"truncation_caveat":true,"z":[-0.5002521008403361,6.126321340608566e-17]}},{"canonical_key":"z*exp(-z)","closed_form":"z*exp(-z)","disk_radius":null,"engine_version":"gft-0.1.0-reaudit-20260610","family":"z_exp_negz","param_values":{},"property":"nehari_univalent","verifier":"pointwise_nehari_univalent_iv","witness":{"criterion_lower_bound":5.979949004996268,"threshold":2.0,"truncation_caveat":true,"z":[0.99,0.0]}},{"canonical_key":"z*exp(-z)","closed_form":"z*exp(-z)","disk_radius":null,"engine_version":"gft-0.1.0-reaudit-20260610","family":"z_exp_negz","param_values":{},"property":"becker_univalent","verifier":"pointwise_becker_univalent_iv","witness":{"criterion_lower_bound":2.2499999364451617,"threshold":1.0,"truncation_caveat":true,"z":[0.5002521008403361,0.0]}},{"canonical_key":"z*exp(z)","closed_form":"z*exp(z)","disk_radius":null,"engine_version":"gft-0.1.0-reaudit-20260610","family":"z_exp_z","param_values":{},"property":"becker_univalent","verifier":"pointwise_becker_univalent_iv","witness":{"criterion_lower_bound":2.249999936445161,"threshold":1.0,"truncation_caveat":true,"z":[-0.5002521008403361,6.126321340608566e-17]}},{"canonical_key":"z/(1-z)","closed_form":"z/(1-z)","disk_radius":null,"engine_version":"gft-0.1.0-reaudit-20260610","family":"z_over_1_minus_z","param_values":{},"property":"becker_univalent","verifier":"pointwise_becker_univalent_iv","witness":{"criterion_lower_bound":146.96512912725072,"threshold":1.0,"truncation_caveat":true,"z":[0.5122622564306923,0.7050685082909731]}},{"canonical_key":"z/(1-z/2)","closed_form":"z/(1 - z/2)","disk_radius":null,"engine_version":"gft-0.1.0-reaudit-20260610","family":"z_over_1_minus_z2","param_values":{},"property":"becker_univalent","verifier":"pointwise_becker_univalent_iv","witness":{"criterion_lower_bound":1.0717847206933115,"threshold":1.0,"truncation_caveat":true,"z":[0.27117647058823524,0.0]}},{"canonical_key":"z/(1-z/2)**2","closed_form":"z/(1 - z/2)^2","disk_radius":null,"engine_version":"gft-0.1.0-reaudit-20260610","family":"z_over_1_minus_z2_sq","param_values":{},"property":"becker_univalent","verifier":"pointwise_becker_univalent_iv","witness":{"criterion_lower_bound":2.0398258385009873,"threshold":1.0,"truncation_caveat":true,"z":[0.15268907563025208,0.0]}},{"canonical_key":"z/(1+z)","closed_form":"z/(1+z)","disk_radius":null,"engine_version":"gft-0.1.0-reaudit-20260610","family":"z_over_1_plus_z","param_values":{},"property":"becker_univalent","verifier":"pointwise_becker_univalent_iv","witness":{"criterion_lower_bound":146.96512912773352,"threshold":1.0,"truncation_caveat":true,"z":[-0.5122622564306925,-0.705068508290973]}},{"canonical_key":"z/(1+z**2)","closed_form":"z/(1+z^2)","disk_radius":null,"engine_version":"gft-0.1.0-reaudit-20260610","family":"z_over_1_plus_z2","param_values":{},"property":"nehari_univalent","verifier":"pointwise_nehari_univalent_iv","witness":{"criterion_lower_bound":56234.03265649605,"threshold":2.0,"truncation_caveat":true,"z":[0.5169052659866159,-0.7114590627003216]}},{"canonical_key":"z/(1+z**2)","closed_form":"z/(1+z^2)","disk_radius":null,"engine_version":"gft-0.1.0-reaudit-20260610","family":"z_over_1_plus_z2","param_values":{},"property":"becker_univalent","verifier":"pointwise_becker_univalent_iv","witness":{"criterion_lower_bound":191.88314795596287,"threshold":1.0,"truncation_caveat":true,"z":[0.5169052659866159,-0.7114590627003216]}}]}
