s857.py

from research import *
s=begin(857,'Test complete coverage and the affine obstruction','Can the two original endpoint columns be related by one global affine map?',{},['C852–856'])
f=json.loads((ROOT/'model/inverse_paired_field.json').read_text());g=json.loads((ROOT/'model/inverse_gain_field.json').read_text())
pairs=[(x,y) for x,y in zip(f,g) if y['delta']==990][:2];other=next((x,y) for x,y in zip(f,g) if y['delta']==1980)
u,v=[x['routes']['Nativity']['endpoint'] for x,y in pairs];U,V=[x['routes']['Conquest']['endpoint'] for x,y in pairs]
slope=F(V-U,v-u);shift=U-slope*u;x,y=other;nx=x['routes']['Nativity']['endpoint'];actual=x['routes']['Conquest']['endpoint'];pred=slope*nx+shift
partition=[z['name'] for z in json.loads((ROOT/'model/inverse_long_core_branches.json').read_text())]+[z['name'] for z in json.loads((ROOT/'model/inverse_short_core_branches.json').read_text())]+[x['name'] for x,y in zip(f,g) if y['n']%10==0]
finish(s,{'forced_affine':{'slope':slope,'shift':shift,'defining_sources':[x['name'] for x,y in pairs]},'counterexample':{'source':x['name'],'predicted':pred,'actual':actual},'coverage':len(partition)},'Two distinct990-gap rows force a translation by990, which fails on the1980 branch. The digit-register model covers the complete manifest where a single affine column map cannot.','Integrate the gain field with the source-path model without conflating it with rounding.',{'complete_once':len(partition)==len(set(partition))==32,'affine_fails':pred!=actual,'forced_translation':slope==1 and shift==990})