s690.py

from research import *
s=begin(690,'Reconstruct the three cumulative completion paths','Can one retained2940 component generate the12600/12740/13440 family?',{'source_head':14006,'hinge':4346,'tail':1406,'upper':9660,'retained_lower':2940},['Supplement A §10.2; inherited source family'])
ks=[F(1),P,E]; rows=[{'upper':k*9660,'lower':2940,'total':k*9660+2940,'head':4346+k*9660} for k in ks]
finish(s,{'paths':rows,'calendar_bodies':[35*360,35*364,40*336],'upper_gain':[r['upper']-9660 for r in rows]},'Holding4346→1406 fixed while converting only the9660 upper arm generates all three source totals12600/12740/13440. The generated heads14006/14146/14846 retain their existing status. This realizes the micro register family through retained macro components, not one whole-span conversion.','Consolidate the micro-to-Rounded bridge and decide which anchored routes best explain its placement.',{'source_paths':[r['total'] for r in rows]==[12600,12740,13440],'heads':[r['head'] for r in rows]==[14006,14146,14846],'gains':[r['upper']-9660 for r in rows]==[0,140,840]})