s748.py

from research import *
s=begin(748,'Identify the ordered reconstruction operator','Does the complete boundary profile determine itslocalcontributionsuniquely once theterminal is fixed?',{'local_vector':[27,100,100,100,100,60,60],'terminal':0,'operator':'uppertriangularsuffixsum'},['C742,C747; Research Strategy §5F'])
d=[27,100,100,100,100,60,60]; n=len(d); S=[[int(j>=i) for j in range(n)] for i in range(n)]; profile=[sum(S[i][j]*d[j] for j in range(n)) for i in range(n)]+[0]; recovered=[profile[i]-profile[i+1] for i in range(n)]
finish(s,{'suffix_matrix':S,'profile':profile,'recovered_rows':recovered,'determinant':1,'rank':n},'The suffix-sum matrix is triangular with unit diagonal. With terminal fixed, every ordered boundary determines exactly one local row vector, recovered by adjacent differences. This gives theStrategy a small linear mechanism for whole-family explanation, while total-only evaluation loses theordering.','Test thewhole rounded-row family for compatibility between lifespan projection androunding.',{'recovered':recovered==d,'unit_diagonal':all(S[i][i]==1 for i in range(n)),'triangular':all(S[i][j]==0 for i in range(n) for j in range(i))})