s1221.py

from research import *
s=begin(1221,'Characterize source shifts that descend to rounded cells','When can the Rounded value alone determine the Rounded shifted value for every input?',{},['C1213','C1220'])
def Qz(x):return 5*((x+2)//5)
witnesses=[]
for d in [1,2,3,4]:
 values=[Qz(x+d) for x in range(98,103)];witnesses.append({'shift_residue':d,'same_cell_inputs':list(range(98,103)),'shifted_rounds':values})
a=artifact('model/rounded_cell_shift_criterion.json',json.dumps({'criterion':'A translation descends to all nearest-five cells iff its integer shift is divisible by5.','proof':'Multiples of5 translate entire cells. For a nonzero residue1..4, a five-point cell straddles a new cell boundary after translation; adding multiples of5 changes neither fact.','witnesses':witnesses,'scope':'Restricted finite source domains can avoid a split accidentally; universal necessity does not forbid that.'},indent=2)+'\n')
finish(s,{'criterion':a},'Only multiples of five act on all Rounded cells without residual information. The off-grid27 and−24 changes therefore need source residues; their successful finite examples do not define a universal rounded-only rule.','Conclude the second block’s local-to-Rounded bridge and begin the Strategy’s equal-gain source provenance.',{'each_splits':all(len(set(x['shifted_rounds']))==2 for x in witnesses),'same_initial_cell':all(Qz(x)==100 for x in range(98,103))})