from research import *
s=begin(848,'Transfer the projection model to the four-household ledger','Do equal regrouped totals recover the ordered household inputs?',{'source_vector':[33,16,14,7]},['File58 §1.4 Genesis46 printed-household subtotal register'])
v=[33,16,14,7];pair=lambda x:[x[0]+x[1],x[2]+x[3]];bracket=lambda x:[x[0]+x[3],x[1]+x[2]];prefix=lambda x:[sum(x[:k]) for k in range(1,5)]
kernel=[1,-1,1,-1];diagnostic=[a+b for a,b in zip(v,kernel)]
finish(s,{'source_pair':pair(v),'source_bracket':bracket(v),'source_prefix':prefix(v),'invisible_regrouping_direction':kernel,'diagnostic_prefix':prefix(diagnostic),'scope':'printed source subtotals only; no person-count repair or chronology projection'},'The same four counts produce49/21 and40/30 through two declared partitions. Both partitions miss one direction of change that the ordered prefix register detects. Retaining order adds information beyond shared totals.','State the precise extension of the path grammar established by the list holdout.',{'pair_preserved':pair(v)==pair(diagnostic)==[49,21],'bracket_preserved':bracket(v)==bracket(diagnostic)==[40,30],'order_detects':prefix(v)!=prefix(diagnostic)})