from research import *
parts=[1650,1050];a=1406
s=begin(499,'Where path evaluation is compatible with affine geometry','Which operations commute with the path evaluator without losing segmentation?',{'parts':parts,'anchor':a,'test_translation':215,'decimal_scale':10},['File52c §1.2','Strategy §§5C–5F','C495'])
v=a+sum(inv(x) for x in parts)
finish(s,{'translated_endpoint':a+215+sum(inv(x) for x in parts),'scaled_endpoint':10*a+sum(inv(10*x) for x in parts),'original_endpoint':v,'whole_span_inverse':inv(sum(parts)),'segmented_inverse_sum':sum(inv(x) for x in parts),'general_rules':['all dates and anchor translated together: V shifts by same t','all durations and anchor scaled by10^k: V scales by10^k','I(s+t) need not equal I(s)+I(t)']},
 'The module respects a change of origin and decimal rescaling when the entire declared object moves. It does not respect erasing segmentation. These are mathematical compatibility rules, not permission to translate source chronologies outside their admitted domains.',
 'Connect the actual field to the three calendar Keys through their common measure.',{'translation':a+215+sum(inv(x) for x in parts)==v+215,'scale':10*a+sum(inv(10*x) for x in parts)==10*v,'nonadditive':inv(sum(parts))!=sum(inv(x) for x in parts)})