from research import *
s=begin(706,'Recover the fixed-set overlap inventory','Which of the source-listed cycle totals closes the whole declared field?',{'cycle_totals':[5840,5842,5844,5846],'fixed_field_center':-2921},['Supplement A §13.3; C704–C705'])
X=set(-2921+15*r+2*g+F(p,4) for r in [-1,1] for g in [-1,0,1] for p in [-1,1]); M={-x for x in X}; rows=[]
for L in [5840,5842,5844,5846]:
    overlap=len({x+L for x in X}&M); rows.append([L,overlap,12-overlap])
finish(s,{'columns':['total','overlap','outside'],'rows':rows,'fixed_source_set':True},'The complete fixed-set inventory is8/12/8/4 overlaps for5840/5842/5844/5846. Only5842 covers every node. Selected-route matches at other totals remain valid local comparisons but do not establish whole-field closure.','Derive the conditional placement theorem from centers rather than searching more candidate dates.',{'inventory':rows==[[5840,8,4],[5842,12,0],[5844,8,4],[5846,4,8]],'unique_listed_full':sum(row[1]==12 for row in rows)==1})