s1309.py

from research import *
s=begin(1309,'Register measure-preserving grouping and symmetry descent','What additionalcondition letsreflection act onagroupedobject?',{},['C1308','inherited/model/toledot_quotient.json','C1024–C1029 inherited'])
q=json.loads((ROOT/'inherited/model/toledot_quotient.json').read_text());fibre=[9,10];images=[12-i for i in fibre];classes=[q['occurrence_to_section'][i-1] for i in images]
r={'id':'grouping_reflection_descent','class':'domain_condition','criterion':'Reflectiondescendsiff anytwoelementsinthesamegroup havereflections inthesamegroup.','proof':'Amaponthequotientiswell-defined exactlywhentherepresentativechoice doesnotchangeitsoutputclass.','measure_relation':'Pushforwardofoccurrencemeasureusesmultiplicity evenwhenreflectiondoesnotdescend.','Toledot_witness':{'collapsed_occurrences':fibre,'reflections':images,'output_sections':classes},'NT_contrast':'Theinheritedprimaryseven-edgegroupinghasreflection-compatiblefibres.','evidence':['inherited/model/toledot_quotient.json','C1024–C1029']}
a=artifact('model/relation_grouping_reflection.json',json.dumps(r,indent=2)+'\n')
finish(s,{'grouping_relation':a},'Toledot’scollapsedEsauoccurrences reflectintodifferentsections, soitsreflectiondoesnotdescend even thoughmultiplicitypreserves themeasure. TheNT groupingworks becauseitsfibres respectitsreflection.','Register theinversefamily’s dependenceontheoriginalpartition.',{'different_classes':len(set(classes))==2,'images':images==[3,2],'occurrence_count':len(q['occurrence_names'])==11})