from research import *
s=begin(538,'The14 gain links reconciliation and clutch scales','What common arithmetic underlies147/161/175 and the full/half clutch values?',{'source_values':[147,161,175],'calendar_factor':E},['File60 §§2.6,3.3; File62 dependency note'])
finish(s,{'coefficients_over7':[F(x,7) for x in [147,161,175]],'E_gain':E*161-161,'half_relation':{'input':F(161,2),'output':E*F(161,2),'gain':(E-1)*F(161,2)},'center_identity':147+175},
 'The progression is7×(21,23,25). E raises161 to175 by14; halving gives80.5→87.5 by7. This provides a value-level bridge to T14/H7, while their chronology domains still require the File61/62 source rules.',
 'Reconstruct the ordered147 rails, testing translation of both endpoints rather than isolated widths.',{'progression':161-147==175-161==14,'half':E*F(161,2)==F(175,2),'center':147+175==2*161})