from research import *
paths={'MT_regular':[1650,1050],'MT_cumulative':[9170,3430],'LXX_regular':[2250,1830]}
s=begin(495,'Rounded chronology as path evaluation','Can one rule explain both convergence and the LXX miss?',{'anchor':1406,'paths':paths},['File52c §3.3','C489'])
r={k:{'raw_total':sum(v),'reversal_gain':sum(inv(x)-x for x in v),'evaluated_endpoint':1406+sum(inv(x) for x in v)} for k,v in paths.items()}
finish(s,{'rule':'V_a(path)=a+sum I(segment); chi(path)=sum(I(segment)-segment)','paths':r,'composition':'chi(P followed by Q)=chi(P)+chi(Q), for an admitted concatenation'},
 'Path gains are additive over retained segment lists. The MT regular gain7920 and cumulative gain−1980 offset their original9900 difference; LXX has different gains. Forgetting the partition discards necessary input.',
 'Measure the exact effect of only the source-admitted Noah and Shem refinements.',{'MT_convergence':r['MT_regular']['evaluated_endpoint']==r['MT_cumulative']['evaluated_endpoint']==12026,'LXX_miss':r['LXX_regular']['evaluated_endpoint']==10436})