from research import *
s=begin(1061,'Two apparent branch checks are equivalent','Do inverse convergence and integral E completion add independent constraints here?',{'derived_branches':[10620,11610],'original_tail':1400},['C940','C952','C1059'])
tail=inv(s['inputs']['original_tail']);rows=[{'inverse_radius':u,'completed':u+tail,'residue23':(u+tail)%23,'E_image':E*(u+tail),'converges':u==10620,'integral':(E*(u+tail)).denominator==1} for u in s['inputs']['derived_branches']]
finish(s,{'branches':rows,'branch_displacement_mod23':990%23,'scope':'equivalence only in the fixed two-branch register domain'},'With the same original tail retained, convergence and integral E completion select the same cumulative branch. They are equivalent checks within this domain, not independent confirmations.','Transfer calendar calibration while retaining the source’s licensed E route.',{'same_selector':all(r['converges']==r['integral'] for r in rows),'tail_provenance':tail==4100,'residues':[r['residue23'] for r in rows]==[0,1]})