s855.py

from research import *
s=begin(855,'Explain every shortened-core branch','Which positional changes produce the later nonconstant paired differences?',{},['C852–854'])
f=json.loads((ROOT/'model/inverse_gain_field.json').read_text());out=[]
for x in f:
    n=x['n'];a,b,c=n//100,(n//10)%10,n%10
    if c==0 or n>=240:continue
    if n>=150:kind='three-to-two';pred=1260+90*a-90*b-900*c
    else:kind='three-to-one';pred=990-990*c
    out.append({'name':x['name'],'n':n,'register_change':kind,'predicted':pred,'observed':x['delta']})
a=artifact('model/inverse_short_core_branches.json',json.dumps(out,indent=2)+'\n')
finish(s,{'branches':a,'formulas':{'three_to_two':'1260+90a−90b−900c','three_to_one':'990−990c'}},'The later variations follow core-length changes, which move the same digits into different place values. The nonlinear field therefore needs its digit register, not extra chronological corrections.','Resolve the two retained-zero source cases and complete the partition.',{'all_shortened':all(x['predicted']==x['observed'] for x in out),'both_changes':set(x['register_change'] for x in out)=={'three-to-two','three-to-one'}})