from research import *
s=begin(1029,'NT equal-block coarsening preserves reflection','Does the complete77-edge NT field carry reflection through seven-edge blocks?',{'edges':77,'block_size':7},['File43','File54','C1028'])
blocks=[set(range(7*b,7*b+7)) for b in range(11)];images=[{76-i for i in B} for B in blocks];mapping=[blocks.index(B) for B in images];boundaries=list(range(0,78,7));mapped_boundaries=[77-i for i in boundaries]
finish(s,{'block_map':mapping,'selected_boundaries':boundaries,'reflected_boundaries':mapped_boundaries},'Reflection permutes all eleven equal seven-edge blocks, so the NT490 coarsening passes the criterion. This explains why one contraction preserves the reflection that the Toledot section quotient loses.','Compare the three kinds of retained information now exposed.',{'all_blocks':mapping==list(reversed(range(11))),'boundary_invariance':set(mapped_boundaries)==set(boundaries),'eleven_blocks':len(blocks)==11})