s906.py

from research import *
s=begin(906,'Derive the retained-subdivision criterion','When can two constructions share an outer span but disagree at an internal biography?',{'S':144900,'l':147,'k':P},['C898','C831 complete-path criterion'])
S,l,k=F(144900),F(147),P
uniform=[k*(S-l),k*l];retained=[k*S-l,l];cut_difference=(k-1)*l
model={'uniform_partition':uniform,'retained_partition':retained,'same_outer':k*S,'cut_difference':cut_difference,'general_formula':'(k−1)*l','agreement_condition':'k=1 or l=0','source_role':'retention is an appointed subdivision after outer expansion'}
a=artifact('model/subdivision_retention_criterion.json',json.dumps(clean(model),indent=2)+'\n')
finish(s,{'criterion':a,'partitions':{'uniform':uniform,'retained':retained},'cut_difference':cut_difference},'Uniform expansion and retained biography have the same outer span but internal cuts differing by(k−1)l. They coincide only for unit scale or zero-length biography. The complete path, rather than its total, distinguishes these constructions.','Compare the distinct mechanisms behind apparent operation-order effects.',{'outer_equal':sum(uniform)==sum(retained)==147000,'cut_delta':uniform[1]-retained[1]==cut_difference==F(49,23),'nontrivial':cut_difference!=0})