{"dataset_id":"kreuzer-skarke","exclusions":[{"assumptions":["Heterotic E\u2088\u00d7E\u2088 (or Spin(32)/\u2124\u2082) on a CY3","Standard embedding: gauge connection = spin connection (or index equals the Euler characteristic index)","Net chiral generation count n_gen = |\u03c7|/2","Target phenomenology: exactly three net generations"],"detail":"\u03c7=-200, |\u03c7|=200, n_gen=|\u03c7|/2=100. |\u03c7|\u22606 so standard-embedding 3-generation models are ruled out (would give n_gen=100, not 3).","euler_abs":200,"euler_char":-200,"id":"heterotic_standard_embedding_3gen","kind":"exclusion","label":"Heterotic standard-embedding 3-generation index","n_generations":100,"ok":false,"rules_out":"Standard-embedding heterotic models with net chirality n_gen = |\u03c7|/2 = 3 generations"},{"assumptions":["Type IIB / O3\u2013O7 orientifold sketch on a CY3","Tadpole identity L = |\u03c7|/24 (Euler characteristic budget)","Stated minimum budget L_min=1 for the model class under study","No additional localized sources that enlarge the effective budget"],"detail":"L=|\u03c7|/24=8.33333 with |\u03c7|=200. L \u2265 L_min=1: does not rule out models needing that budget.","euler_abs":200,"id":"ks_tadpole_budget","kind":"exclusion","label":"IIB/KS D3 tadpole budget L = |\u03c7|/24","ok":true,"rules_out":"Flux + D3 constructions that require tadpole budget L \u2265 L_min=1","tadpole_L":8.333333,"tadpole_L_min":1.0}],"h11":1,"h21":101,"h31":null,"honesty":"Necessary conditions under stated assumptions only \u2014 never sufficiency from Hodge numbers alone.","status":"success"}