s707.py

from research import *
s=begin(707,'Derive the fixed-template placement condition','What does whole-field mirror closure determine once the shape is fixed?',{'translation':5842,'symmetric_template_center':0,'shape':'fixed literal twelve-node template'},['Supplement A §13.4'])
L=5842; center=-F(L,2)
offsets=sorted(15*r+2*g+F(p,4) for r in [-1,1] for g in [-1,0,1] for p in [-1,1])
finish(s,{'required_center':center,'center_equation':'c+L=−c','template_symmetric':offsets==sorted(-x for x in offsets),'scope':'unique placement conditional on fixed shape, chart and L'},'Whole-field closure forces c=−L/2=−2921, and the fixed symmetric template makes that condition sufficient. The period determines placement only after shape, phase chart and closure requirement have been supplied; it does not independently determine them.','Compare the source’s anchored calendar-body placement packet with this fixed-template result.',{'necessary':center+L==-center,'sufficient_shape':offsets==sorted(-x for x in offsets),'center':center==-2921})