from research import *
s=begin(882,'Isolate the partial-action order asymmetry','Can equal scalar endpoints conceal different intermediate grids?',{'forced_input':6877},['C881 P/J domains'])
jp=[F(6877),J*6877,P*J*6877]
pj=[F(6877),P*6877,J*P*6877]
a=artifact('model/PJ_order_witness.json',json.dumps(clean({'J_then_P':jp,'P_then_J':pj,'role':'formal denominator witness, not a new chronology'}),indent=2)+'\n')
finish(s,{'J_then_P':jp,'P_then_J':pj,'artifact':a},'6877→6900→7000 stays integral under J→P;6877→20930/3→7000 under P→J has a fractional intermediate. The same final number therefore does not identify the same staged integer-grid route.','Check source-authorized File51a chains against the new theorem.',{'same_final':jp[-1]==pj[-1]==7000,'distinct_intermediate':jp[1].denominator==1 and pj[1].denominator==3,'minimal_domain':6877==13*23**2})