"""Authored single-feature reference distance versus a fixed sigmoid confidence; not an OOD guarantee."""
from fractions import Fraction as F
import math,json
REFERENCE=[F(-2),F(-1),F(0),F(1),F(2)]
def fit_reference(values):
    mean=sum(values,F(0))/len(values);variance=sum(((x-mean)**2 for x in values),F(0))/len(values)
    if variance<=0:raise ValueError('positive reference variance')
    return mean,variance
def sigmoid(x):return 1/(1+math.exp(-x)) if x>=0 else math.exp(x)/(1+math.exp(x))
def demo():
    mean,variance=fit_reference(REFERENCE);assert mean==0 and variance==2;rows=[]
    for x in [F(-10),F(-2),F(0),F(2),F(10)]:
        distance2=(x-mean)**2/variance;p=sigmoid(3*float(x));confidence=max(p,1-p)
        rows.append({'x':str(x),'reference_standardized_distance_squared':str(distance2),'outside_authored_boundary':distance2>4,'fixed_classifier_positive_probability':p,'fixed_classifier_max_probability':confidence,'classifier_label':int(p>=.5),'semantic_domain_membership_verified':False})
    assert [r['outside_authored_boundary'] for r in rows]==[True,False,False,False,True]
    assert rows[0]['fixed_classifier_max_probability']>.999 and rows[-1]['fixed_classifier_max_probability']>.999
    try:fit_reference([F(1),F(1)])
    except ValueError:zero_variance_rejected=True
    else:raise AssertionError('zero variance accepted')
    return {'reference_values':[str(x) for x in REFERENCE],'mean':str(mean),'population_variance_divide_by_n':str(variance),'distance_boundary':4,'threshold_selected_by_author_not_fitted_for_error_rate':True,'classifier':'fixed sigmoid(3*x), not trained here and not claimed calibrated','rows':rows,'zero_reference_variance_rejected':zero_variance_rejected,'real_text_OOD_or_accuracy_measured':False,'sklearn_detector_executed':False}
if __name__=='__main__':print(json.dumps(demo(),ensure_ascii=False,indent=2))