from research import *
s=begin(1260,'Separate a shared scaling coefficient from the value five','What condition permits any common nonzero coefficientκ?',{},['C1259'])
u,T,C=F(100),F(60),F(130);k=13*u/(2*C)
a=artifact('model/regular_kernel_common_coefficient.json',json.dumps(clean({'assumptions':'u andC nonzero; declared positive source scales','equations':['25u/2=kappa(C+2T)','13u/2=kappa C'],'compatibility':'6C=13T','coefficient':'kappa=13u/(2C)','source_kappa':k,'proof':'Eliminatekappa usingthesecondequation:25C=13C+26T, hence6C=13T; substitute back.','five_requirement':'kappa5 additionallyrequiresC=13u/10','scope':'Logicalparameteranalysis, notsearch for newsourcevalues.'}),indent=2)+'\n')
finish(s,{'common_coefficient':a,'source_kappa':k},'A common coefficient requires the ratio6C=13T. The specific valuefive additionally calibratesC to the centuryu. This distinguishes a shared structural ratio from its observed numerical scale.','Relate thepair’s midpoint andhalfwidth to itsNoah950 comparison without adding independentconstraints.',{'compatibility':6*C==13*T,'kappa5':k==5,'both_heads':k*C==650 and k*(C+2*T)==1250})