s937.py

from research import *
s=begin(937,'Reduce the junction to two compatibility equations','Which equations remain after placement and coefficient bookkeeping are removed?',{},['C934–936'])
q=json.loads((ROOT/'model/junction_path_coordinates.json').read_text())['coordinates']
r,c=q['regular_legs'],q['cumulative_legs'];u=sum(inv(x) for x in r);v=sum(inv(x) for x in c);R=sum(r);C=sum(c)
out={'totals':{'regular':R,'cumulative':C},'evaluations':{'regular':u,'cumulative':v},'constraints':['u=v','5u=4C+R'],'equivalent_recovery':'C=(5u−R)/4','source_warning':'u andv are evaluated from original legs, not free fitted outputs'}
a=artifact('model/junction_reduced_constraints.json',json.dumps(out,indent=2)+'\n')
finish(s,{'reduced_constraints':a,'u_v_weighted':[u,v,F(4*C+R,5)]},'The selected junction is captured by two statements: the component evaluations agree, and that common duration equals(4C+R)/5. Absolute12026 is then placement;14726 is continuation. The next task is whether the digit-register structure already forces either statement.','Derive aggregate-digit evaluation for the four original component spans.',{'two_equalities':u==v and 5*u==4*C+R,'originals_only':r==[1650,1050] and c==[9170,3430]})