s1066.py

from research import *
s=begin(1066,'Complete paired-field difference mesh','How does the full source field compare with the already selected nine-member pillar field?',{},['File52c §§3.7.3,paired endpoint tables','C1065','C513'])
from math import gcd
src=json.loads((ROOT/'prep/interface_constraints/inputs.json').read_text());pairs=src['original_endpoint_pairs'];X=[p[k] for p in pairs for k in ['Nativity','Conquest']];nine=src['nine_member_endpoint_literals'];origin=1731
g=lambda vals:__import__('functools').reduce(gcd,[abs(x-origin) for x in vals])
fullmesh,ninemesh=g(X),g(nine)
a=artifact('model/paired_field_difference_mesh.json',json.dumps(clean({'source_pairs':pairs,'existing_nine_members':nine,'source_reference':origin,'inherited_E_reference':601,'full_source_mesh':fullmesh,'nine_source_mesh':ninemesh,'full_E_mesh':E*fullmesh,'nine_E_mesh':E*ninemesh,'status':'difference representation only; no target outcomes or frequency tally'}),indent=2)+'\n')
finish(s,{'mesh_field':a,'source_meshes':[fullmesh,ninemesh],'E_meshes':[E*fullmesh,E*ninemesh]},'The full paired field has difference mesh5, while the inherited nine-member field has mesh115. Uniform E gives exact meshes125/23 and125, respectively. This relates the complete rational field to the existing integer subfield without enlarging it.','Ask whether additional uniform Key measurements can recover lost component information.',{'meshes':(fullmesh,ninemesh)==(5,115),'existing_reference':14726+E*(1731-14726)==601,'subset':set(nine)<=set(X)})