s525.py

from research import *
s=begin(525,'Freeze a compact construction grammar','Which operation types are actually needed for the completed family reconstructions?',{'evidence_range':'C482–C524','source_objects':'ordered biographies plus tradition, frame, phase, node role and coordinate chart'},['Strategy §§1,5B–5G','completed sequential ledger'])
ops=[{'operation':'row change','domain':'compatible biography or admitted insertion','example':'(b,r)->(b+d,r−d); Cainan130/330'}, {'operation':'chronological projection','domain':'ordered source rows and supplied terminal anchor','example':'regular sums begetting intervals; cumulative sums lifespans'}, {'operation':'round with residual','domain':'declared begetting or lifespan list','example':'nearest5 with retained exact residual'}, {'operation':'evaluate reversed path','domain':'source-admitted integer spans with retained segmentation','example':'a+sum I(s_i)'}, {'operation':'anchored dilation','domain':'declared linear coordinate chart, source nodes and held anchor','example':'a+k(x−a), with supplied E/P/J'}, {'operation':'scoped translation/state switch','domain':'source-authorized affected nodes or finite switch field','example':'native/equalized frame or OFF->ON once'}, {'operation':'reflection','domain':'declared comparison chart and source roles','example':'q->−q for Rounded Mirror away from origin'}]
finish(s,{'operations':ops,'relations':['L=b+r and cumulative repartition conservation','weighted residual4deltaC+deltaR=0 in its selected state','calendar d*K_d=8400/23','affine composition/conjugacy and pivot congruences','path concatenation retains segments; general additivity after forgetting them is rejected']},
 'Seven operation types suffice to express the reconstructed examples. Inputs still include source rows, admitted partitions, anchors and state selections. This is a useful candidate grammar; neither an unrestricted transformation group nor a proven globally smallest presentation is claimed.',
 'Map these operations onto the three family axes and their Mirrors as an explanatory topology.',{'no_free_anchor_operation':not any(x['operation']=='fit arbitrary anchor' for x in ops),'finite_insertions_preserved':True,'count':len(ops)==7})