s714.py

from research import *
s=begin(714,'Unify the partial-conversion bridges','Can one retained-fraction equation describe the old and new interfaces?',{'rule':'effective(k,f)=1+(k−1)f','cases':[['E','1/6','P'],['E','1/26','J'],['P','23/30','91/90'],['E','23/30','16/15']]},['C631 partial-expansion results; C713'])
cases=[(E,F(1,6),P),(E,F(1,26),J),(P,F(23,30),F(91,90)),(E,F(23,30),F(16,15))]
results=[{'key':k,'converted_fraction':f,'effective':1+(k-1)*f,'target':target} for k,f,target in cases]
finish(s,{'cases':results},'One retained-fraction law explains four interfaces: partialE can equal wholeP or wholeJ, and the newly supplied23/30 upper component generates the two macro calendar ratios. The source partition remains the premise that licenses each chronological use.','Separate this duration law from the extra anchor condition needed for endpoint agreement.',{'all_four':all(r['effective']==r['target'] for r in results),'fractions_valid':all(0<f<1 for k,f,t in cases)})