from research import *
s=begin(813,'Integrate the primary File52c component paths','How do the primary regular and cumulative inverse paths meet in the shared path model?',{'regular':[1650,1050],'cumulative':[9170,3430],'anchor':1406},['latest File52c §§3.3–3.4; inherited C731'])
out={}
for name,components in s['inputs'].items():
    if name=='anchor':continue
    transformed=[inv(x) for x in components]
    out[name]={'source_components':components,'single_pass_components':transformed,'endpoint':1406+sum(transformed),'unsplit_single_pass_endpoint':1406+inv(sum(components))}
finish(s,{'paths':out,'status':'integration check of established File52c constructions; no second inversion'},'Both admitted subdivided paths evaluate to12026. Their unsplit totals yield different endpoints, confirming why the component list belongs to the source object. This integrates an established result rather than adding another independent hit.','Compare the retained-component and whole-span Key paths at their shared completion.',{'primary_endpoint':all(x['endpoint']==12026 for x in out.values()),'subdivision_required':all(x['unsplit_single_pass_endpoint']!=12026 for x in out.values())})