s1174.py

from research import *
s=begin(1174,'Test order against the biography domain','Can commuting formulas fail to define both source-compatible intermediate paths?',{'row':[1,1,2],'d':2,'e':1},['C1173'])
b,r,L=1,1,2;d,e=2,1;Rfirst=[b+d,r-d,L];Afirst=[b,r+e,L+e];endpoint=[b+d,r-d+e,L+e]
a=artifact('model/row_order_domain_counterexample.json',json.dumps({'row':[b,r,L],'R_first':Rfirst,'A_first':Afirst,'common_endpoint':endpoint,'status':'pure algebraic diagnostic; not a chronological row','interpretation':'A_first remains nonnegative through both steps; R_first leaves the domain despite the same valid endpoint'},indent=2)+'\n')
finish(s,{'order_counterexample':a},'The formulas commute on unrestricted coordinates, yet R-first produces a negative remainder in this diagnostic while A-first remains valid. A common endpoint therefore does not authorize every intermediate route.','Check how the complete source packet uses the domain-qualified operations.',{'same_endpoint':Rfirst[0]==Afirst[0]+d and Rfirst[1]+e==Afirst[1]-d,'R_invalid':Rfirst[1]<0,'A_path_valid':min(Afirst)>=0 and min(endpoint)>=0})