s894.py

from research import *
s=begin(894,'Identify the information lost by a body-only comparison','Can the expanded span alone recover a macro head?',{},['C892–893'])
rows=json.loads((ROOT/'model/six_macro_heads.json').read_text());groups={}
for r in rows:groups.setdefault(str(r['body']),[]).append({'id':r['id'],'R':r['R'],'M':r['M']})
pairs={k:v for k,v in groups.items() if len(v)>1}
proof={'body':'B=12(C−R)','kernel':'(C,R)→(C+t,R+t) keeps B fixed','lost':'one placement coordinate and all semantic labels','recovery':'given B and R, C=R+B/12 and M=R+B'}
a=artifact('model/carrier_body_information_loss.json',json.dumps({'pairs':pairs,'proof':proof},indent=2)+'\n')
finish(s,{'equal_body_pairs':pairs,'artifact':a},'Identical144900 or143520 bodies occupy different source-appointed positions. A body-only match loses a translation coordinate; retaining the target restores the numeric pair, while source labels still need their own record.','Reconstruct the entire ordered carrier chain from endpoint changes.',{'two_pairs':len(pairs)==2,'different_positions':all(len({r['M'] for r in rs})==2 for rs in pairs.values()),'recovery':all(F(r['body'],12)+r['R']==r['C'] for r in rows)})