s1216.py

from research import *
s=begin(1216,'Reconstruct the hidden interior effect of head cancellation','Which cumulative boundaries move even though the head error is zero?',{},['C1215'])
rows=json.loads((ROOT/'model/whole_genealogy_rounded_changes.json').read_text())['rows'];eps=[x['rounded_dL']-x['exact_dL'] for x in rows];field=[sum(eps[i:]) for i in range(len(eps)+1)];labels=[x['name'] for x in rows]+['terminal'];nz=[{'boundary':n,'difference_error':v} for n,v in zip(labels,field) if v]
a=artifact('model/whole_genealogy_rounding_interior_field.json',json.dumps({'boundaries':labels,'field':field,'nonzero':nz,'recurrence':'field[i]-field[i+1]=local difference_error[i]','scope':'same terminal, matched19-row domain; native insertion has zero extra rounding error'},indent=2)+'\n')
finish(s,{'interior_field':a,'nonzero_boundaries':nz},'The head cancellation hides a−4 comparison shift at Noah, Shem and Arphaxad, followed by−2 at Shelah. Adjacent differences recover the three local rounding changes exactly.','Check compatibility with separately rounded remaining years and identify the carry change.',{'head_terminal_zero':field[0]==field[-1]==0,'recurrence':all(field[i]-field[i+1]==eps[i] for i in range(len(eps))),'nonzero4':len(nz)==4})