from research import *
s=begin(814,'Integrate the shared12600 completion without identifying paths','Which invariant joins the two established Actual/Rounded completion routes?',{'head':14004,'components':[12075,483]},['C731 retained-core integration; File52c downstream connection'])
a,b=12075,483;partial=a+E*b;uniform=J*(a+b)
out={'partial_span':partial,'whole_J_span':uniform,'partial_junction':14004-a,'uniform_J_junction':14004-J*a,'common_endpoint':14004-partial,'paired_plus2':[14006,14004-partial+2]}
finish(s,out,'The two routes share12600 and endpoint1404 but have different internal junctions. The+2 paired translation reaches Rounded14006/1406. This is equality of outer measurement, not equality of complete transformed paths.','State the distinct calendar and shape invariants in the integrated map.',{'same_total':partial==uniform==12600,'junctions_differ':out['partial_junction']!=out['uniform_J_junction'],'rounded_pair':out['paired_plus2']==[14006,1406]})