s1065.py

from research import *
s=begin(1065,'Symbolic branch support conditions','How do the source branch formulas constrain a common integer pivot?',{},['C1064','C850–C858'])
from math import gcd
factors=[90,990];q=[23,69,299];reduced={str(f):[d//gcd(f,d) for d in q] for f in factors}
table=[{'branch':'three-to-two core','gap':'90(14+a−b−10c)','remaining_divisors':reduced['90']},{'branch':'three-to-one core','gap':'990(1−c)','remaining_divisors':reduced['990']},{'branch':'retained-zero Jacob','gap':0,'difference_obstruction':False},{'branch':'retained-zero Adam','gap':7200,'difference_obstruction':True}]
finish(s,{'branch_conditions':table,'qualification':'difference compatibility never supplies the missing pivot residue or source authorization'},'The paired-branch law gives divisibility conditions before any pivot placement is considered. A zero gap removes only the difference obstruction; it does not appoint a pivot.','Represent the complete paired field and inherited nine-member field by their difference meshes.',{'reduced_divisors':reduced=={'90':[23,23,299],'990':[23,23,299]},'Adam_obstructed':all(7200%d for d in q)})