s498.py

from research import *
s=begin(498,'Decimal gains explain the path increments','Which algebraic properties of decimal reversal generate the observed increments?',{'three_digit_core':'10*(100a+10b+c)','two_digit_core':'100*(10a+b)','source_segments':[1650,1050,9170,3430,1400]},['File52c §1.2','C481','C495–C497'])
vals=[1650,1050,9170,3430,1400];g={x:inv(x)-x for x in vals}
finish(s,{'gains':g,'three_digit_gain':'990*(c-a)','two_digit_gain':'900*(b-a)','general_invariant':'digit sum mod9; with10^k placeholders, gain divisible by9*10^k','not_23_preserving_example':{'input':230,'inverse':inv(230),'inverse_mod23':inv(230)%23}},
 'The primary990 increments and the2700 tail increment are decimal-place effects. Reversal does not by itself preserve the23-lattice; its conjunction with the Key families still requires particular source inputs.',
 'Determine the exact compatible scaling and translation rules for the rounded path module.',{'gains':list(g.values())==[3960,3960,-1980,0,2700],'negative23':230%23==0 and inv(230)%23!=0})